From 74bc9466173078f937b62f126a5bd87265203983 Mon Sep 17 00:00:00 2001 From: Alexander Heinlein Date: Mon, 6 Jan 2025 11:21:37 +0100 Subject: [PATCH] Msc projects. 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mode 100644 teaching/msc-theses/spectral-neural-operators/index.html create mode 100644 teaching/msc-theses/stabilization-pinns/index.html create mode 100644 teaching/msc-theses/traffic-modelling-ml/index.html create mode 100644 teaching/msc-theses/turbulence-ml-part1/index.html create mode 100644 teaching/msc-theses/turbulence-ml-part2/index.html create mode 100644 teaching/seminars/2015_2016-ws/numII/index.html create mode 100644 teaching/seminars/2020_2021-ws/machine-learning/index.html diff --git a/.all-contributorsrc b/.all-contributorsrc deleted file mode 100644 index cfa9c210cd12..000000000000 --- a/.all-contributorsrc +++ /dev/null @@ -1,55 +0,0 @@ -{ - "files": [ - "README.md" - ], - "imageSize": 100, - "commit": false, - "contributorsPerLine": 7, - "projectName": "al-folio", - "projectOwner": "alshedivat", - "repoType": "github", - "repoHost": "https://github.com", - "badgeTemplate": "[core_contributors]: https://img.shields.io/badge/core_contributors-<%= contributors.length %>-orange.svg 'Number of core contributors'", - "contributorTemplate": "\">\" width=\"<%= options.imageSize %>px;\" alt=\"\"/>
<%= contributor.name %>", - "skipCi": true, - "contributors": [ - { - "login": "alshedivat", - "name": "Maruan", - "avatar_url": "https://avatars.githubusercontent.com/u/2126561?v=4", - "profile": "http://maruan.alshedivat.com", - "contributions": [ - "design", - "code" - ] - }, - { - "login": "rohandebsarkar", - "name": "Rohan Deb Sarkar", - "avatar_url": "https://avatars.githubusercontent.com/u/50144004?v=4", - "profile": "http://rohandebsarkar.github.io", - "contributions": [ - "code" - ] - }, - { - "login": "pourmand1376", - "name": "Amir Pourmand", - "avatar_url": "https://avatars.githubusercontent.com/u/32064808?v=4", - "profile": "https://amirpourmand.ir", - "contributions": [ - "code" - ] - }, - { - "login": "george-gca", - "name": "George", - "avatar_url": "https://avatars.githubusercontent.com/u/31376482?v=4", - "profile": "https://george-gca.github.io/", - "contributions": [ - "code" - ] - } - ], - "commitConvention": "angular" -} diff --git a/.github/ISSUE_TEMPLATE/bug_report.md b/.github/ISSUE_TEMPLATE/bug_report.md deleted file mode 100644 index 511f585150ba..000000000000 --- a/.github/ISSUE_TEMPLATE/bug_report.md +++ /dev/null @@ -1,38 +0,0 @@ ---- -name: Bug report -about: Create a report to help us improve -title: '' -labels: bug -assignees: '' - ---- - -**Acknowledge the following** -- [ ] I carefully read and followed the [Getting Started](https://github.com/alshedivat/al-folio#getting-started) guide. -- [ ] I read through [FAQ](https://github.com/alshedivat/al-folio#faq) and searched through the [past issues](https://github.com/alshedivat/al-folio/issues), none of which addressed my issue. -- [ ] The issue I am raising is a potential bug in al-folio and not just a usage question.
[For usage questions, please post in the [Discussions](https://github.com/alshedivat/al-folio/discussions) instead of raising an issue.] - -**Describe the bug** -A clear and concise description of what the bug is. - -**To Reproduce** -Steps to reproduce the behavior: -1. Go to '...' -2. Click on '....' -3. Scroll down to '....' -4. See error - -**Expected behavior** -A clear and concise description of what you expected to happen. - -**Screenshots** -If applicable, add screenshots to help explain your problem. - -**System (please complete the following information):** - - OS: [e.g. iOS] - - Browser (and its version) [e.g. chrome, safari] - - Jekyll version [e.g. 3.8.7] -- Ruby version [e.g. 2.6.5] - -**Additional context** -Add any other context about the problem here. diff --git a/.github/ISSUE_TEMPLATE/feature_request.md b/.github/ISSUE_TEMPLATE/feature_request.md deleted file mode 100644 index 11fc491ef1da..000000000000 --- a/.github/ISSUE_TEMPLATE/feature_request.md +++ /dev/null @@ -1,20 +0,0 @@ ---- -name: Feature request -about: Suggest an idea for this project -title: '' -labels: enhancement -assignees: '' - ---- - -**Is your feature request related to a problem? Please describe.** -A clear and concise description of what the problem is. Ex. I'm always frustrated when [...] - -**Describe the solution you'd like** -A clear and concise description of what you want to happen. - -**Describe alternatives you've considered** -A clear and concise description of any alternative solutions or features you've considered. - -**Additional context** -Add any other context or screenshots about the feature request here. diff --git a/.github/stale.yml b/.github/stale.yml deleted file mode 100644 index 8ec2004d8caa..000000000000 --- a/.github/stale.yml +++ /dev/null @@ -1,18 +0,0 @@ -# Number of days of inactivity before an issue becomes stale -daysUntilStale: 60 -# Number of days of inactivity before a stale issue is closed -daysUntilClose: 7 -# Issues with these labels will never be considered stale -exemptLabels: - - pinned - - security - - enhancement -# Label to use when marking an issue as stale -staleLabel: wontfix -# Comment to post when marking an issue as stale. Set to `false` to disable -markComment: > - This issue has been automatically marked as stale because it has not had - recent activity. It will be closed if no further activity occurs. Thank you - for your contributions. -# Comment to post when closing a stale issue. Set to `false` to disable -closeComment: false diff --git a/.github/workflows/deploy-docker-tag.yml b/.github/workflows/deploy-docker-tag.yml deleted file mode 100644 index e101aa4b4e47..000000000000 --- a/.github/workflows/deploy-docker-tag.yml +++ /dev/null @@ -1,40 +0,0 @@ -name: Docker Image CI (Upload Tag) - -on: - push: - tags: - - 'v*' - -jobs: - - build: - - runs-on: ubuntu-latest - - steps: - - name: Checkout - uses: actions/checkout@v3 - - name: Buildx - uses: docker/setup-buildx-action@v1 - - - - name: Docker meta - id: meta - uses: docker/metadata-action@v4 - with: - images: amirpourmand/al-folio - - - name: Login - uses: docker/login-action@v1 - with: - username: ${{ secrets.DOCKER_USERNAME }} - password: ${{ secrets.DOCKER_PASSWORD }} - - - name: Build and push - uses: docker/build-push-action@v3 - with: - context: . - push: ${{ github.event_name != 'pull_request' }} - tags: ${{ steps.meta.outputs.tags }} - labels: ${{ steps.meta.outputs.labels }} - diff --git a/.github/workflows/deploy-image.yml b/.github/workflows/deploy-image.yml deleted file mode 100644 index 3582c4e84cd3..000000000000 --- a/.github/workflows/deploy-image.yml +++ /dev/null @@ -1,36 +0,0 @@ -name: Docker Image CI - -on: - push: - branches: [ master ] - -jobs: - - build: - - runs-on: ubuntu-latest - if: github.repository_owner == 'alshedivat' - - steps: - - name: Checkout - uses: actions/checkout@v3 - - - name: Set up QEMU - uses: docker/setup-qemu-action@v2 - - - name: Buildx - uses: docker/setup-buildx-action@v2 - - - name: Login - uses: docker/login-action@v2 - with: - username: ${{ secrets.DOCKER_USERNAME }} - password: ${{ secrets.DOCKER_PASSWORD }} - - - name: Build and push - uses: docker/build-push-action@v4 - with: - context: . - push: true - platforms: linux/amd64,linux/arm64/v8 - tags: amirpourmand/al-folio diff --git a/.github/workflows/deploy.yml b/.github/workflows/deploy.yml deleted file mode 100644 index 7174c87a9332..000000000000 --- a/.github/workflows/deploy.yml +++ /dev/null @@ -1,38 +0,0 @@ -name: deploy - -on: - push: - branches: - - master - - main - pull_request: - branches: - - master - - main - workflow_dispatch: - -permissions: - contents: write - -jobs: - deploy: - runs-on: ubuntu-latest - steps: - - name: Checkout 🛎️ - uses: actions/checkout@v3 - - name: Setup Ruby - uses: ruby/setup-ruby@v1 - with: - ruby-version: '3.2.2' - bundler-cache: true - - name: Install and Build 🔧 - run: | - npm install -g mermaid.cli - export JEKYLL_ENV=production - bundle exec jekyll build - - name: Deploy 🚀 - if: github.event_name != 'pull_request' - uses: JamesIves/github-pages-deploy-action@v4 - with: - folder: _site - diff --git a/.nojekyll b/.nojekyll new file mode 100644 index 000000000000..e69de29bb2d1 diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml deleted file mode 100644 index ca7e46543084..000000000000 --- a/.pre-commit-config.yaml +++ /dev/null @@ -1,10 +0,0 @@ -# See https://pre-commit.com for more information -# See https://pre-commit.com/hooks.html for more hooks -repos: -- repo: https://github.com/pre-commit/pre-commit-hooks - rev: v4.3.0 - hooks: - - id: trailing-whitespace - - id: end-of-file-fixer - - id: check-yaml - - id: check-added-large-files diff --git a/404.html b/404.html index 2b454cad7248..2858775bdfb4 100644 --- a/404.html +++ b/404.html @@ -1,9 +1 @@ ---- -layout: page -permalink: /404.html -title: "Page not found" -description: "Looks like there has been a mistake. Nothing exists here." -redirect: true ---- - -

You will be redirected to the main page within 3 seconds. If not redirected, please go back to the home page.

+ Page not found | Alexander Heinlein

Page not found

Looks like there has been a mistake. Nothing exists here.

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\ No newline at end of file diff --git a/Gemfile b/Gemfile deleted file mode 100644 index 7e6ccbe33dec..000000000000 --- a/Gemfile +++ /dev/null @@ -1,26 +0,0 @@ -source 'https://rubygems.org' -group :jekyll_plugins do - gem 'classifier-reborn' - gem 'jekyll' - gem 'jekyll-archives' - gem 'jekyll-diagrams' - gem 'jekyll-email-protect' - gem 'jekyll-feed' - gem 'jekyll-imagemagick' - gem 'jekyll-link-attributes' - gem 'jekyll-minifier' - gem 'jekyll-paginate-v2' - gem 'jekyll-scholar' - gem 'jekyll-sitemap' - gem 'jekyll-toc' - gem 'jekyll-twitter-plugin' - gem 'jemoji' - gem 'mini_racer' - gem 'unicode_utils' - gem 'webrick' - gem 'faraday-retry' -end -group :other_plugins do - gem 'feedjira' - gem 'httparty' -end diff --git a/_bibliography/papers.bib b/_bibliography/papers.bib deleted file mode 100644 index f23539927cc3..000000000000 --- a/_bibliography/papers.bib +++ /dev/null @@ -1,1231 +0,0 @@ ---- ---- -References -========== - -# published - -@techreport{Giammatteo:2024:EAC, - author = {Elena Giammatteo and Alexander Heinlein and Matthias Schlottbom}, - title = {An extension of the approximate component mode synthesis method to the heterogeneous Helmholtz equation}, - journal = {IMA Journal of Numerical Analysis}, - pages = {drae076}, - year = {2024}, - doi = {10.1093/imanum/drae076}, - abbr = {IMAJNA}, - abstract = {In this work, we propose and analyze an extension of the approximate component mode synthesis (ACMS) method to the two-dimensional heterogeneous Helmholtz equation. The ACMS method has originally been introduced by Hetmaniuk and Lehoucq as a multiscale method to solve elliptic partial differential equations. The ACMS method uses a domain decomposition to separate the numerical approximation by splitting the variational problem into two independent parts: local Helmholtz problems and a global interface problem. While the former are naturally local and decoupled such that they can be easily solved in parallel, the latter requires the construction of suitable local basis functions relying on local eigenmodes and suitable extensions. We carry out a full error analysis of this approach focusing on the case where the domain decomposition is kept fixed, but the number of eigenfunctions is increased. The theoretical results in this work are supported by numerical experiments verifying algebraic convergence for the method. In certain, practically relevant cases, even super-algebraic convergence for the local Helmholtz problems can be achieved without oversampling.}, - note = {Accepted for publication in the IMA Journal of Numerical Analysis}, - url = {https://doi.org/10.1093/imanum/drae076}, - preprint = {https://arxiv.org/abs/2303.06671}, - keywords = {published, reviewed, recent}, - bibtex_show = {true} -} - -@article{Dolean:2024:MDD, - author = {Victorita Dolean and Alexander Heinlein and Siddhartha Mishra and Ben Moseley}, - title = {Multilevel domain decomposition-based architectures for physics-informed neural networks}, - journal = {Computer Methods in Applied Mechanics and Engineering}, - volume = {429}, - number = {1}, - pages = {117116}, - year = {2024}, - doi = {10.1016/j.cma.2024.117116}, - abbr = {CMAME}, - abstract = {Physics-informed neural networks (PINNs) are a powerful approach for solving problems involving differential equations, yet they often struggle to solve problems with high frequency and/or multi-scale solutions. Finite basis physics-informed neural networks (FBPINNs) improve the performance of PINNs in this regime by combining them with an overlapping domain decomposition approach. In this work, FBPINNs are extended by adding multiple levels of domain decompositions to their solution ansatz, inspired by classical multilevel Schwarz domain decomposition methods (DDMs). Analogous to typical tests for classical DDMs, we assess how the accuracy of PINNs, FBPINNs and multilevel FBPINNs scale with respect to computational effort and solution complexity by carrying out strong and weak scaling tests. Our numerical results show that the proposed multilevel FBPINNs consistently and significantly outperform PINNs across a range of problems with high frequency and multi-scale solutions. Furthermore, as expected in classical DDMs, we show that multilevel FBPINNs improve the accuracy of FBPINNs when using large numbers of subdomains by aiding global communication between subdomains.}, - url = {https://www.sciencedirect.com/science/article/pii/S0045782524003724?via%3Dihub}, - preprint = {https://arxiv.org/abs/2306.05486}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Grimm:2024:SHS, - author = {Viktor Grimm and Alexander Heinlein and Axel Klawonn}, - title = {A short note on solving partial differential equations using convolutional neural networks}, - booktitle = {Domain Decomposition Methods in Science and Engineering XXVII}, - pages = {3-14}, - publisher = {Springer International Publishing}, - year = {2024}, - doi = {10.1007/978-3-031-50769-4_1}, - abbr = {Springer LNCSE}, - abstract = {The approach of using physics-based machine learning to solve PDEs has recently become very popular. A recent approach to solve PDEs based on CNNs uses finite difference stencils to include the residual of the partial differential equation into the loss function. In this work, the relation between the network training and the solution of a respective finite difference linear system of equations using classical numerical solvers is discussed. It turns out that many beneficial properties of the linear equation system are neglected in the network training. Finally, numerical results which underline the benefits of classical numerical solvers are presented.}, - url = {https://link.springer.com/chapter/10.1007/978-3-031-50769-4_1}, - preprint = {http://kups.ub.uni-koeln.de/id/eprint/64227}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Dolean:2024:FBP, - author = {Victorita Dolean and Alexander Heinlein and Siddhartha Mishra and Ben Moseley}, - title = {Finite basis physics-informed neural networks as a Schwarz domain decomposition method}, - booktitle = {Domain Decomposition Methods in Science and Engineering XXVII}, - pages = {165-172}, - publisher = {Springer International Publishing}, - year = {2024}, - doi = {10.1007/978-3-031-50769-4_19}, - abbr = {Springer LNCSE}, - abstract = {Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to incorporate the residual of the PDE as well as boundary conditions into its loss function when training it. This provides a simple and mesh-free approach for solving problems relating to PDEs. However, a key limitation of PINNs is their lack of accuracy and efficiency when solving problems with larger domains and more complex, multi-scale solutions. In a more recent approach, finite basis physics-informed neural networks (FBPINNs) [8] use ideas from domain decomposition to accelerate the learning process of PINNs and improve their accuracy. In this work, we show how Schwarz-like additive, multiplicative, and hybrid iteration methods for training FBPINNs can be developed. We present numerical experiments on the influence of these different training strategies on convergence and accuracy. Furthermore, we propose and evaluate a preliminary implementation of coarse space correction for FBPINNs.}, - url = {https://link.springer.com/chapter/10.1007/978-3-031-50769-4_19}, - preprint = {https://arxiv.org/abs/2211.05560}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@article{Balzani:2024:CFP, - author = {Daniel Balzani and Alexander Heinlein and Axel Klawonn and Jascha Knepper and Sharan Nurani Ramesh and Oliver Rheinbach and Lea Sa{\ss}mannshausen and Klemens Uhlmann}, - title = {A computational framework for pharmaco-mechanical interactions in arterial walls using parallel monolithic domain decomposition methods}, - journal = {GAMM-Mitteilungen}, - volume = {47}, - number = {1}, - pages = {e202370002}, - year = {2024}, - doi = {10.1002/gamm.202370002}, - abbr = {GAMM-Mitteilungen}, - abstract = {A computational framework is presented to numerically simulate the effects of antihypertensive drugs, in particular calcium channel blockers, on the mechanical response of arterial walls. A stretch-dependent smooth muscle model by Uhlmann and Balzani is modified to describe the interaction of pharmacological drugs and the inhibition of smooth muscle activation. The coupled deformation-diffusion problem is then solved using the finite element software FEDDLib and overlapping Schwarz preconditioners from the Trilinos package FROSch. These preconditioners include highly scalable parallel GDSW (generalized Dryja–Smith–Widlund) and RGDSW (reduced GDSW) preconditioners. Simulation results show the expected increase in the lumen diameter of an idealized artery due to the drug-induced reduction of smooth muscle contraction, as well as a decrease in the rate of arterial contraction in the presence of calcium channel blockers. Strong and weak parallel scalability of the resulting computational implementation are also analyzed.}, - url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/gamm.202370002}, - preprint = {https://arxiv.org/abs/2307.02972}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2023:CDS, - author = {Alexander Heinlein and Bj{\"o}rn Kiefer and Stefan Pr{\"u}ger and Oliver Rheinbach and Friederike R{\"o}ver}, - title = {A Comparison Of Direct Solvers In FROSch Applied To Chemo-Mechanics}, - booktitle = {10th edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering}, - year = {2023}, - doi = {10.23967/c.coupled.2023.008}, - abbr = {Coupled2023}, - abstract = {Sparse direct linear solvers are at the computational core of domain decomposition preconditioners and therefore have a strong impact on their performance. In this paper, we consider the Fast and Robust Overlapping Schwarz (FROSch) solver framework of the Trilinos software library, which contains a parallel implementations of the GDSW domain decomposition preconditioner. We compare three different sparse direct solvers used to solve the subdomain problems in FROSch. The preconditioner is applied to different model problems; linear elasticity and more complex fully-coupled deformation diffusion-boundary value problems from chemo-mechanics. We employ FROSch in fully algebraic mode, and therefore, we do not expect numerical scalability. Strong scalability is studied from 64 to 4096 cores, where good scaling results are obtained up to 1728 cores. The increasing size of the coarse problem increases the solution time for all sparse direct solvers.}, - url = {https://www.scipedia.com/public/_2023i}, - preprint = {https://arxiv.org/abs/2310.12659}, - keywords = {published}, - bibtex_show = {true} -} - -@article{Ehlers:2023:MLP, - author = {Svenja Ehlers and Marco Klein and Alexander Heinlein and Mathies Wedler and Nicolas Desmars and Norbert Hoffmann and Merten Stender}, - title = {Machine learning for phase-resolved reconstruction of nonlinear ocean wave surface elevations from sparse remote sensing data}, - journal = {Ocean Engineering}, - volume = {288}, - number = {}, - pages = {116059}, - year = {2023}, - issn = {0029-8018}, - doi = {10.1016/j.oceaneng.2023.116059}, - abbr = {Ocean Engineering}, - abstract = {Accurate short-term prediction of phase-resolved water wave conditions is crucial for decision-making in ocean engineering. However, the initialization of remote-sensing-based wave prediction models first requires a reconstruction of wave surfaces from sparse measurements like radar. Existing reconstruction methods either rely on computationally intensive optimization procedures or simplistic modeling assumptions that compromise real-time capability or accuracy of the entire prediction process. We therefore address these issues by proposing a novel approach for phase-resolved wave surface reconstruction using neural networks based on the U-Net and Fourier neural operator (FNO) architectures. Our approach utilizes synthetic yet highly realistic training data on uniform one-dimensional grids, that is generated by the high-order spectral method for wave simulation and a geometric radar modeling approach. The investigation reveals that both models deliver accurate wave reconstruction results and show good generalization for different sea states when trained with spatio-temporal radar data containing multiple historic radar snapshots in each input. Notably, the FNO-based network performs better in handling the data structure imposed by wave physics due to its global approach to learn the mapping between input and desired output in Fourier space.}, - url = {https://www.sciencedirect.com/science/article/pii/S0029801823024435}, - preprint = {https://arxiv.org/abs/2305.11913}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Yamazaki:2023:EST, - author = {Ichitaro Yamazaki and Alexander Heinlein and Sivasankaran Rajamanickam}, - title = {An Experimental Study of Two-level Schwarz Domain-Decomposition Preconditioners on GPUs}, - booktitle={2023 IEEE International Parallel and Distributed Processing Symposium (IPDPS)}, - pages = {680-689}, - year = {2023}, - doi = {10.1109/IPDPS54959.2023.00073}, - abbr = {IPDPS}, - abstract = {The generalized Dryja–Smith–Widlund (GDSW) preconditioner is a two-level overlapping Schwarz domain decomposition (DD) preconditioner that couples a classical one-level overlapping Schwarz preconditioner with an energy-minimizing coarse space. When used to accelerate the convergence rate of Krylov subspace iterative methods, the GDSW preconditioner provides robustness and scalability for the solution of sparse linear systems arising from the discretization of a wide range of partial different equations. In this paper, we present FROSch (Fast and Robust Schwarz), a domain decomposition solver package which implements GDSW-type preconditioners for both CPU and GPU clusters. To improve the solver performance on GPUs, we use a novel decomposition to run multiple MPI processes on each GPU, reducing both solver’s computational and storage costs and potentially improving the convergence rate. This allowed us to obtain competitive or faster performance using GPUs compared to using CPUs alone. We demonstrate the performance of FROSch on the Summit supercomputer with NVIDIA V100 GPUs, where we used NVIDIA Multi-Process Service (MPS) to implement our decomposition strategy.The solver has a wide variety of algorithmic and implementation choices, which poses both opportunities and challenges for its GPU implementation. We conduct a thorough experimental study with different solver options including the exact or inexact solution of the local overlapping subdomain problems on a GPU. We also discuss the effect of using the iterative variant of the incomplete LU factorization and sparse-triangular solve as the approximate local solver, and using lower precision for computing the whole FROSch preconditioner. Overall, the solve time was reduced by factors of about 2× using GPUs, while the GPU acceleration of the numerical setup time depend on the solver options and the local matrix sizes.}, - url = {https://ieeexplore.ieee.org/document/10177474}, - preprint = {https://arxiv.org/abs/2304.04876}, - altmetric = {}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@article{Frei:2023:TPT, - author = {Stefan Frei and Alexander Heinlein}, - title = {Towards parallel time-stepping for the numerical simulation of atherosclerotic plaque growth}, - journal = {Journal of Computational Physics}, - volume = {}, - number = {}, - pages = {112347}, - year = {2023}, - issn = {0021-9991}, - doi = {10.1016/j.jcp.2023.112347}, - abbr = {JCOMP}, - abstract = {The numerical simulation of atherosclerotic plaque growth is computationally prohibitive, since it involves a complex cardiovascular fluid-structure interaction (FSI) problem with a characteristic time scale of milliseconds to seconds, as well as a plaque growth process governed by reaction-diffusion equations, which takes place over several months. In this work we combine a temporal homogenization approach, which separates the problem in computationally expensive FSI problems on a micro scale and a reaction-diffusion problem on the macro scale, with parallel time-stepping algorithms. It has been found in the literature that parallel time-stepping algorithms do not perform well when applied directly to the FSI problem. To circumvent this problem, a parareal algorithm is applied on the macro-scale reaction-diffusion problem instead of the micro-scale FSI problem. We investigate modifications in the coarse propagator of the parareal algorithm, in order to further reduce the number of costly micro problems to be solved. The approaches are tested in detailed numerical investigations based on serial simulations.}, - url = {https://www.sciencedirect.com/science/article/pii/S0021999123004424}, - altmetric = {}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@article{Heinlein:2023:MLE, - author = {Alexander Heinlein and Oliver Rheinbach and Friederike R\"over}, - title = {A Multi-Level Extension of the {GDSW} Overlapping {Schwarz} Preconditioner in Two Dimensions}, - journal = {Computational Methods in Applied Mathematics}, - volume = {}, - number = {}, - pages = {}, - year = {2023}, - issn = {}, - doi = {10.1515/cmam-2022-0168}, - abbr = {CMAM}, - abstract = {Multilevel extensions of overlapping Schwarz domain decomposition preconditioners of Generalized Dryja–Smith–Widlund (GDSW) type are considered in this paper. The original GDSW preconditioner is a two-level overlapping Schwarz domain decomposition preconditioner, which can be constructed algebraically from the fully assembled stiffness matrix. The FROSch software, which belongs to the ShyLU package of the Trilinos software library, provides parallel implementations of different variants of GDSW preconditioners. The coarse problem can limit the parallel scalability of two-level GDSW preconditioners. As a remedy, in the past, three-level GDSW approaches have been proposed, which can significantly extend the range of scalability. Here, a multilevel extension of the GDSW preconditioner is introduced and analyzed. Finally, parallel results for the implementation in FROSch for up to 40 000 cores of the SuperMUC-NG supercomputer at Leibniz Supercomputing Centre (LRZ) and to 48 000 cores of the JUWELS supercomputer at Jülich Supercomputing Centre (JSC) are presented.}, - url = {https://doi.org/10.1515/cmam-2022-0168}, - altmetric = {}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Frei:2022:ECC, - author = {Stefan Frei and Alexander Heinlein}, - title = {Efficient coarse correction for parallel time-stepping in plaque growth simulations}, - booktitle = {ECCOMAS2022}, - year = {2022}, - doi = {10.23967/eccomas.2022.015}, - abbr = {WCCM-ECCOMAS}, - abstract = {In order to make the numerical simulation of atherosclerotic plaque growth feasible, a temporal homogenization approach is employed. The resulting macro-scale problem for the plaque growth can be further accelerated by using parallel time integration schemes, such as the parareal algorithm. However, the parallel scalability is dominated by the computational cost of the coarse propagator. Therefore, in this paper, an interpolation-based coarse propagator, which uses growth values from previously computed micro-scale problems, is introduced. For a simple model problem, it is shown that this approach reduces both the computational work for a single parareal iteration as well as the required number of parareal iterations.}, - url = {https://www.scipedia.com/public/Frei_et_al_2022a}, - preprint = {https://arxiv.org/abs/2207.02081}, - dimensions = {true}, - keywords = {published}, - bibtex_show = {true} -} - -@inproceedings{Kemna:2023:FST, - author = {Mirko Kemna and Alexander Heinlein and Cornelis Vuik}, - title = {Reduced order fluid modeling with generative adversarial networks}, - booktitle = {Proc. Appl. Math. Mech.}, - volume = {23}, - number = {1}, - pages = {e202200241}, - year = {2023}, - doi = {10.1002/pamm.202200241}, - abbr = {PAMM}, - abstract = {Surrogate models based on convolutional neural networks (CNNs) for computational fluid dynamics (CFD) simulations are investigated. In particular, the flow field inside two-dimensional channels with a sudden expansion and an obstacle is predicted using an image representation of the geometry as the input. Generative adversarial neural networks (GANs) have been shown to excel at such image-to-image translation tasks. This motivates the focus of this work on investigating the specific effect of adversarial training on model performance. Numerical results show that the overall accuracy of the GANs is generally lower compared to an identical generator model trained directly on the ground truth using an L1 data loss. On the other hand, GAN predictions are often visually more convincing and exhibit a lower continuity residual.}, - url = {https://onlinelibrary.wiley.com/doi/10.1002/pamm.202200241}, - dimensions = {true}, - keywords = {published}, - bibtex_show = {true} -} - -@article{Balzani:2023:CAW, - author = {Daniel Balzani and Alexander Heinlein and Axel Klawonn and Oliver Rheinbach and J{\"o}rg Schr{\"o}der}, - title = {Comparison of Arterial Wall Models in Fluid-Structure Interaction Simulations}, - journal = {Computational Mechanics}, - volume = {72}, - number = {5}, - pages = {949-965}, - year = {2023}, - doi = {10.1007/s00466-023-02321-y}, - abbr = {CM}, - abstract = {Monolithic fluid-structure interaction (FSI) of blood flow with arterial walls is considered, making use of sophisticated nonlinear wall models. These incorporate the effects of almost incompressibility as well as of the anisotropy caused by embedded collagen fibers. In the literature, relatively simple structural models such as Neo-Hooke are often considered for FSI with arterial walls. Such models lack, both, anisotropy and incompressibility. In this paper, numerical simulations of idealized heart beats in a curved benchmark geometry, using simple and sophisticated arterial wall models, are compared: we consider three different almost incompressible, anisotropic arterial wall models as a reference and, for comparison, a simple, isotropic Neo-Hooke model using four different parameter sets. The simulations show significant quantitative and qualitative differences in the stresses and displacements as well as the lumen cross sections. For the Neo-Hooke models, a significantly larger amplitude in the in- and outflow areas during the heart beat is observed, presumably due to the lack of fiber stiffening. For completeness, we also consider a linear elastic wall using 16 different parameter sets. However, using our benchmark setup, we were not successful in achieving good agreement with our nonlinear reference calculation.}, - url = {https://link.springer.com/article/10.1007/s00466-023-02321-y}, - preprint = {http://kups.ub.uni-koeln.de/id/eprint/55586}, - altmetric={148711121}, - dimensions={true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Ramesh:2023:FST, - author = {Sharan Nurani Ramesh and Klemens Uhlmann and Lea Sa{\ss}mannshausen and Oliver Rheinbach and Axel Klawonn and Alexander Heinlein and Daniel Balzani}, - title = {First steps towards modeling the interaction of cardiovascular agents and smooth muscle activation in arterial walls}, - booktitle = {Proc. Appl. Math. Mech.}, - volume = {22}, - number = {1}, - pages = {e202200133}, - year = {2023}, - doi = {10.1002/pamm.202200133}, - abbr = {PAMM}, - abstract = {A temporal homogenization approach for the numerical simulation of atherosclerotic plaque growth is extended to fully coupled fluid-structure interaction (FSI) simulations. The numerical results indicate that the two-scale approach yields significantly different results compared to a simple heuristic averaging, where only stationary long-scale FSI problems are solved, confirming the importance of incorporating stress variations on small time-scales. In the homogenization approach, a periodic fine-scale problem, which is periodic with respect to the heart beat, has to be solved for each long-scale time step. Even if no exact initial conditions are available, periodicity can be achieved within only 2--3 heart beats by simple time-stepping.}, - url = {https://onlinelibrary.wiley.com/doi/10.1002/pamm.202200133}, - dimensions = {true}, - keywords = {published}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2023:TLE, - author = {Alexander Heinlein and Axel Klawonn and Oliver Rheinbach and Friederike R\"over}, - title = {A Three-Level Extension for Fast and Robust Overlapping Schwarz (FROSch) Preconditioners with Reduced Dimensional Coarse Space}, - booktitle = {Domain Decomposition Methods in Science and Engineering XXVI}, - pages = {505-513}, - publisher = {Springer International Publishing}, - year = {2023}, - doi = {10.1007/978-3-030-95025-5_54}, - abbr = {Springer LNCSE}, - abstract = {The Fast and Robust Overlapping Schwarz (FROSch) preconditioner framework is part of the Trilinos software library and contains parallel implementations of the Generalized-Dryja-Smith-Widlund (GDSW) type overlapping Schwarz domain decomposition preconditioners. It provides implementations of the classical GDSW coarse space as well as of reduced dimensional GDSW coarse spaces, where the coarse problem is smaller compared to the classical approach. To extend the parallel scalability of these approaches, a three-level extension has recently been introduced into the framework. In this paper, we present results, obtained on the SuperMUC-NG supercomputer using up to 85K MPI ranks. The results indicate superior weak parallel scalability of the three-level method compared to the two-level method.}, - url = {https://link.springer.com/chapter/10.1007/978-3-030-95025-5_54}, - preprint = {https://tu-freiberg.de/sites/default/files/media/fakultaet-fuer-mathematik-und-informatik-fakultaet-1-9277/prep/2021-02.pdf}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2023:PGL, - author = {Alexander Heinlein and Axel Klawonn and Martin Lanser and Janine Weber}, - title = {Predicting the geometric location of critical edges in adaptive GDSW overlapping domain decomposition methods using deep learning}, - booktitle = {Domain Decomposition Methods in Science and Engineering XXVI}, - pages = {307-315}, - publisher = {Springer International Publishing}, - year = {2023}, - doi = {10.1007/978-3-030-95025-5_32}, - abbr = {Springer LNCSE}, - abstract = {Overlapping GDSW domain decomposition methods are considered for diffusion problems in two dimensions discretized by finite elements. For a diffusion coefficient with high contrast, the condition number is usually dependent on it. A remedy is given by adaptive domain decomposition methods, where the coarse space is enhanced by additional coarse basis functions. These are chosen problem-dependently by solving small local eigenvalue problems. Here, the eigenvalue problems (EVPs) are associated with the edges of the domain decomposition interface; edges, where these EVPs have to be solved are denoted as critical edges. For many applications, not all edges are critical and the solution of the EVPs is not necessary. In an earlier work, a strategy to predict the location of critical edges, based on deep learning, has been proposed for adaptive FETI-DP, a class of nonoverlapping methods. In the present work, this strategy is successfully applied to adaptive GDSW; differences in the classification process for this overlapping method are described. Choosing the classification threshold has been a challenge in all these approaches. Here, for the first time, a heuristic based on the receiver operating characteristic (ROC) curve and the precision-recall graph is discussed. Results for a challenging realistic coefficient function are presented.}, - url = {https://link.springer.com/chapter/10.1007/978-3-030-95025-5_32}, - preprint = {https://kups.ub.uni-koeln.de/36257}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@article{Heinlein:2022:PST, - author = {Alexander Heinlein and Oliver Rheinbach and Friederike R{\"o}ver}, - title = {Parallel Scalability of Three-Level FROSch Preconditioners to 220 000 Cores using the Theta Supercomputer}, - journal = {SIAM Journal on Scientific Computing}, - volume = {0}, - number = {0}, - pages = {S173-S198}, - year = {2022}, - doi = {10.1137/21M1431205}, - abbr = {SISC}, - abstract = {The parallel performance of the three-level fast and robust overlapping Schwarz (FROSch) preconditioners is investigated for linear elasticity. The FROSch framework is part of the Trilinos software library and contains a parallel implementation of different preconditioners with energy minimizing coarse spaces of generalized Dryja--Smith--Widlund type. The three-level extension is constructed by a recursive application of the FROSch preconditioner to the coarse problem. In this paper, the additional steps in the implementation in order to apply the FROSch preconditioner recursively are described in detail. Furthermore, it is shown that no explicit geometric information is needed in the recursive application of the preconditioner. In particular, the rigid body modes, including the rotations, can be interpolated on the coarse level without additional geometric information. Parallel results for a three-dimensional linear elasticity problem obtained on the Theta supercomputer (Argonne Leadership Computing Facility, Argonne, IL) using up to 220 000 cores are discussed and compared to results obtained on the SuperMUC-NG supercomputer (Leibniz Supercomputing Centre, Garching, Germany). Notably, it can be observed that a hierarchical communication operation in FROSch related to the coarse operator starts to dominate the computing time on Theta, which has a dragonfly interconnect, for 100 000 message passing interface (MPI) ranks or more. The same operation, however, scales well and stays within the order of a second in all experiments performed on SuperMUC-NG, which uses a fat tree network. Using hybrid MPI/OpenMP parallelization, the onset of the MPI communication problem on Theta can be delayed. Further analysis of the performance of FROSch on large supercomputers with dragonfly interconnects will be necessary.}, - url = {https://epubs.siam.org/doi/pdf/10.1137/21M1431205}, - preprint = {https://tu-freiberg.de/sites/default/files/media/fakultaet-fuer-mathematik-und-informatik-fakultaet-1-9277/prep/2021-03.pdf}, - altmetric = {134914157}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@article{Heinlein:2022:AND, - author = {Alexander Heinlein and Axel Klawonn and Martin Lanser}, - title = {Adaptive nonlinear domain decomposition methods with an application to the $p$-Laplacian}, - journal = {SIAM Journal on Scientific Computing}, - volume = {}, - number = {}, - pages = {152-S172}, - year = {2022}, - doi = {10.1137/21M1433605}, - abbr = {SISC}, - abstract = {In this article, different nonlinear domain decomposition methods are applied to nonlinear problems with highly-heterogeneous coefficient functions with jumps. In order to obtain a robust solver with respect to nonlinear as well as linear convergence, adaptive coarse spaces are employed. First, as an example for a nonlinearly left-preconditioned domain decomposition method, the two-level restricted nonlinear Schwarz method H1-RASPEN (Hybrid Restricted Additive Schwarz Preconditioned Exact Newton) is combined with an adaptive generalized Dryja–Smith–Widlund (GDSW) coarse space. Second, as an example for a nonlinearly right-preconditioned domain decomposition method, a nonlinear FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) method is equipped with an edge-based adaptive coarse space. Both approaches are compared with the respective nonlinear domain decomposition methods with classical coarse spaces as well as with the respective Newton-Krylov methods with adaptive coarse spaces. For some two-dimensional pLaplace model problems with different spatial coefficient distributions, it can be observed that the best linear and nonlinear convergence can only be obtained when combining the nonlinear domain decomposition methods with adaptive coarse spaces.}, - url = {https://epubs.siam.org/doi/pdf/10.1137/21M1433605}, - preprint = {https://kups.ub.uni-koeln.de/id/eprint/52537}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@article{Zinsser:2022:IDT, - author = {Mario Zin{\ss}er and Benedikt Braun and Tim Helder and Theresa Magorian Friedlmeier and Bart Pieters and Alexander Heinlein and Martin Denk and Dominik G\"oddeke and Michael Powalla}, - title = {Irradiation-dependent Topology Optimization of Metallization Grid Patterns and Variation of Contact Layer Thickness used for Latitude-based Yield Gain of Thin-film Solar Modules}, - journal = {MRS Advances}, - volume = {}, - number = {}, - pages = {}, - year = {2022}, - doi = {10.1557/s43580-022-00321-3}, - abbr = {MRS Advances}, - abstract = {We show that the concept of topology optimization for metallization grid patterns of thin-film solar devices can be applied to monolithically integrated solar cells. Different irradiation intensities favour different topological grid designs as well as a different thickness of the transparent conductive oxide (TCO) layer. For standard laboratory efficiency determination, an irradiation power of 1000 W/m2 is generally applied. However, this power rarely occurs for real world solar modules operating at mid-latitude locations. Therefore, contact layer thicknesses but also lateral grid patterns should be optimized for lower irradiation intensities. This results in material production savings for the grid and TCO layer of up to 50 % and simultaneously a significant gain in yield of over 1 % for regions with a low annual mean irradiation.}, - url = {https://doi.org/10.1557/s43580-022-00321-3}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@article{Heinlein:2022:AGD, - author = {Alexander Heinlein and Axel Klawonn and Jascha Knepper and Oliver Rheinbach and Olof B. Widlund}, - title = {Adaptive GDSW Coarse Spaces of Reduced Dimension for Overlapping Schwarz Methods}, - journal = {SIAM Journal on Scientific Computing}, - volume = {44}, - number = {3}, - pages = {A1176-A1204}, - year = {2022}, - doi = {10.1137/20M1364540}, - abbr = {SISC}, - abstract = {A new reduced-dimension adaptive generalized Dryja--Smith--Widlund (GDSW) overlapping Schwarz method for linear second-order elliptic problems in three dimensions is introduced. It is robust with respect to large contrasts of the coefficients of the partial differential equations. The condition number bound of the new method is shown to be independent of the coefficient contrast and only dependent on a user-prescribed tolerance. The interface of the nonoverlapping domain decomposition is partitioned into nonoverlapping patches. The new coarse space is obtained by selecting a few eigenvectors of certain local eigenproblems which are defined on these patches. These eigenmodes are energy-minimally extended to the interior of the nonoverlapping subdomains and added to the coarse space. By using a new interface decomposition, the reduced-dimension adaptive GDSW overlapping Schwarz method usually has a smaller coarse space than existing GDSW and adaptive GDSW domain decomposition methods. A robust condition number estimate is proven for the new reduced-dimension adaptive GDSW method which is also valid for existing adaptive GDSW methods. Numerical results for the equations of isotropic linear elasticity in three dimensions confirming the theoretical findings are presented.}, - url = {https://doi.org/10.1137/20M1364540}, - preprint = {https://kups.ub.uni-koeln.de/id/eprint/12113}, - pdf = {publications/2022/2022-heinlein-agd.pdf}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@article{Heinlein:2022:FRO, - author = {Alexander Heinlein and Mauro Perego and Sivasankaran Rajamanickam}, - title = {FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica}, - journal = {SIAM Journal on Scientific Computing}, - volume = {44}, - number = {2}, - pages = {B339-B367}, - year = {2022}, - doi = {10.1137/21M1395260}, - abbr = {SISC}, - abstract = {Numerical simulations of Greenland and Antarctic ice sheets involve the solution of large-scale highly nonlinear systems of equations on complex shallow geometries. This work is concerned with the construction of Schwarz preconditioners for the solution of the associated tangent problems, which are challenging for solvers mainly because of the strong anisotropy of the meshes and wildly changing boundary conditions that can lead to poorly constrained problems on large portions of the domain. Here, two-level generalized Dryja--Smith--Widlund (GDSW)--type Schwarz preconditioners are applied to different land ice problems, i.e., a velocity problem, a temperature problem, as well as the coupling of the former two problems. We employ the message passing interface (MPI)--parallel implementation of multilevel Schwarz preconditioners provided by the package FROSch (fast and robust Schwarz) from the Trilinos library. The strength of the proposed preconditioner is that it yields out-of-the-box scalable and robust preconditioners for the single physics problems. To the best of our knowledge, this is the first time two-level Schwarz preconditioners have been applied to the ice sheet problem and a scalable preconditioner has been used for the coupled problem. The preconditioner for the coupled problem differs from previous monolithic GDSW preconditioners in the sense that decoupled extension operators are used to compute the values in the interior of the subdomains. Several approaches for improving the performance, such as reuse strategies and shared memory OpenMP parallelization, are explored as well. In our numerical study we target both uniform meshes of varying resolution for the Antarctic ice sheet as well as nonuniform meshes for the Greenland ice sheet. We present several weak and strong scaling studies confirming the robustness of the approach and the parallel scalability of the FROSch implementation. Among the highlights of the numerical results are a weak scaling study for up to 32K processor cores (8K MPI ranks and 4 OpenMP threads) and 566M degrees of freedom for the velocity problem as well as a strong scaling study for up to 4K processor cores (and MPI ranks) and 68M degrees of freedom for the coupled problem.}, - url = {https://doi.org/10.1137/21M1395260}, - preprint = {https://kups.ub.uni-koeln.de/id/eprint/30668}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@article{Eichinger:2022:SCN, - author = {Matthias Eichinger and Alexander Heinlein and Axel Klawonn}, - title = {Surrogate convolutional neural network models for steady computational fluid dynamics simulations}, - journal = {Electronic Transactions on Numerical Analysis (ETNA)}, - volume = {56}, - pages = {235--255}, - year = {2022}, - doi = {10.1553/etna_vol56s235}, - abbr = {ETNA}, - abstract = {A convolution neural network (CNN)-based approach for the construction of reduced order surrogate models for computational fluid dynamics (CFD) simulations is introduced; it is inspired by the approach of Guo, Li, and Iori [X. Guo, W. Li, and F. Iorio, Convolutional neural networks for steady flow approximation, in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD'16, New York, USA, 2016, ACM, pp. 481--490]. In particular, the neural networks are trained in order to predict images of the flow field in a channel with varying obstacle based on an image of the geometry of the channel. A classical CNN with bottleneck structure and a U-Net are compared while varying the input format, the number of decoder paths, as well as the loss function used to train the networks. This approach yields very low prediction errors, in particular, when using the U-Net architecture. Furthermore, the models are also able to generalize to unseen geometries of the same type. A transfer learning approach enables the model to be trained to a new type of geometries with very low training cost. Finally, based on this transfer learning approach, a sequential learning strategy is introduced, which significantly reduces the amount of necessary training data.}, - url = {https://epub.oeaw.ac.at/?arp=0x003d4c21}, - preprint = {https://kups.ub.uni-koeln.de/29760/}, - dimensions = {true}, - keywords = {published, reviewed, highlighted4}, - bibtex_show = {true} -} - -@inproceedings{Frei:2021:THN, - author = {Stefan Frei and Alexander Heinlein and Thomas Richter}, - title = {On temporal homogenization in the numerical simulation of atherosclerotic plaque growth}, - booktitle = {Proc. Appl. Math. Mech.}, - volume = {21}, - number = {1}, - pages = {e202100055}, - year = {2021}, - doi = {10.1002/pamm.202100055}, - abbr = {PAMM}, - abstract = {A temporal homogenization approach for the numerical simulation of atherosclerotic plaque growth is extended to fully coupled fluid-structure interaction (FSI) simulations. The numerical results indicate that the two-scale approach yields significantly different results compared to a simple heuristic averaging, where only stationary long-scale FSI problems are solved, confirming the importance of incorporating stress variations on small time-scales. In the homogenization approach, a periodic fine-scale problem, which is periodic with respect to the heart beat, has to be solved for each long-scale time step. Even if no exact initial conditions are available, periodicity can be achieved within only 2--3 heart beats by simple time-stepping.}, - url = {https://onlinelibrary.wiley.com/doi/10.1002/pamm.202100055}, - preprint = {https://arxiv.org/abs/2106.09394}, - dimensions = {true}, - keywords = {published}, - bibtex_show = {true} -} - -@article{Grimm:2022:ETD, - author = {Viktor Grimm and Alexander Heinlein and Axel Klawonn and Martin Lanser and Janine Weber}, - title = {Estimating the time-dependent contact rate of SIR and SEIR models in mathematical epidemiology using physics-informed neural networks}, - journal = {Electronic Transactions on Numerical Analysis (ETNA)}, - volume = {56}, - pages = {1–27}, - year = {2022}, - doi = {10.1553/etna_vol56s1}, - abbr = {ETNA}, - abstract = {The course of an epidemic can be often successfully described mathematically using compartment models. These models result in a system of ordinary differential equations. Two well-known examples are the SIR and the SEIR models. The transition rates between the different compartments are defined by certain parameters which are specific for the respective virus. Often, these parameters can be taken from the literature or can be determined from statistics. However, the contact rate or the related effective reproduction number are in general not constant and thus cannot easily be determined. Here, a new machine learning approach based on physics-informed neural networks is presented that can learn the contact rate from given data for the dynamical systems given by the SIR and SEIR models. The new method generalizes an already known approach for the identification of constant parameters to the variable or time-dependent case. After introducing the new method, it is tested for synthetic data generated by the numerical solution of SIR and SEIR models. Here, the case of exact and perturbed data is considered. In all cases, the contact rate can be learned very satisfactorily. Finally, the SEIR model in combination with physics-informed neural networks is used to learn the contact rate for COVID-19 data given by the course of the epidemic in Germany. The simulation of the number of infected individuals over the course of the epidemic, using the learned contact rate, is very promising.}, - url = {https://epub.oeaw.ac.at/?arp=0x003cfd4a}, - preprint = {https://kups.ub.uni-koeln.de/id/eprint/12159}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@article{Heinlein:2021:CML1, - author = {Alexander Heinlein and Axel Klawonn and Martin Lanser and Janine Weber}, - title = {Combining Machine Learning and Adaptive Coarse Spaces - A Hybrid Approach for Robust FETI-DP Methods in Three Dimensions}, - journal = {SIAM Journal on Scientific Computing}, - volume = {43}, - number = {5}, - pages = {S816-S838}, - year = {2021}, - doi = {10.1137/20M1344913}, - abbr = {SISC}, - abstract = {The hybrid ML-FETI-DP algorithm combines the advantages of adaptive coarse spaces in domain decomposition methods and certain supervised machine learning techniques. Adaptive coarse spaces ensure robustness of highly scalable domain decomposition solvers, even for highly heterogeneous coefficient distributions with arbitrary coefficient jumps. However, their construction requires the setup and solution of local generalized eigenvalue problems, which is typically computationally expensive. The idea of ML-FETI-DP is to interpret the coefficient distribution as image data and predict whether an eigenvalue problem has to be solved or can be neglected while still maintaining robustness of the adaptive FETI-DP method. For this purpose, neural networks are used as image classifiers. In the present work, the ML-FETI-DP algorithm is extended to three dimensions, which requires both a complex data preprocessing procedure to construct consistent input data for the neural network as well as a representative training and validation data set to ensure generalization properties of the machine learning model. Numerical experiments for stationary diffusion and linear elasticity problems with realistic coefficient distributions show that a large number of eigenvalue problems can be saved; in the best case of the numerical results presented here, 97% of the eigenvalue problems can be avoided to be set up and solved.}, - url = {https://doi.org/10.1137/20M1344913}, - preprint = {https://kups.ub.uni-koeln.de/id/eprint/9845}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Eichinger:2021:SFP, - author = {Matthias Eichinger and Alexander Heinlein and Axel Klawonn}, - title = {Stationary flow predictions using convolutional neural networks}, - booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2019}, - pages = {541--549}, - publisher = {Springer International Publishing}, - year = {2021}, - doi = {10.1007/978-3-030-55874-1_53}, - abbr = {Springer LNCSE}, - abstract = {Computational Fluid Dynamics (CFD) simulations are a numerical tool to model and analyze the behavior of fluid flow. However, accurate simulations are generally very costly because they require high grid resolutions. In this paper, an alternative approach for computing flow predictions using Convolutional Neural Networks (CNNs) is described; in particular, a classical CNN as well as the U-Net architecture are used. First, the networks are trained in an expensive offline phase using flow fields computed by CFD simulations. Afterwards, the evaluation of the trained neural networks is very cheap. Here, the focus is on the dependence of the stationary flow in a channel on variations of the shape and the location of an obstacle. CNNs perform very well on validation data, where the averaged error for the best networks is below 3%. In addition to that, they also generalize very well to new data, with an averaged error below 10%.}, - preprint = {https://kups.ub.uni-koeln.de/id/eprint/10440}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2021:FAT, - author = {Alexander Heinlein and Christian Hochmuth and Axel Klawonn}, - title = {Fully algebraic two-level overlapping {S}chwarz preconditioners for elasticity problems}, - booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2019}, - pages = {531--539}, - publisher = {Springer International Publishing}, - year = {2021}, - doi = {10.1007/978-3-030-55874-1_52}, - abbr = {Springer LNCSE}, - abstract = {Different parallel two-level overlapping Schwarz preconditioners with Generalized Dryja-Smith-Widlund (GDSW) and Reduced dimension GDSW (RGDSW) coarse spaces for elasticity problems are considered. GDSW type coarse spaces can be constructed from the fully assembled system matrix, but they additionally need the index set of the interface of the corresponding nonoverlapping domain decomposition and the null space of the elasticity operator, i.e., the rigid body motions. In this paper, fully algebraic variants, which are constructed solely from the uniquely distributed system matrix, are compared to the classical variants which make use of this additional information; the fully algebraic variants use an approximation of the interface and an incomplete algebraic null space. Nevertheless, the parallel performance of the fully algebraic variants is competitive compared to the classical variants for a stationary homogeneous model problem and a dynamic heterogeneous model problem with coefficient jumps in the shear modulus; the largest parallel computations were performed on 4,096 MPI (Message Passing Interface) ranks. The parallel implementations are based on the Trilinos package FROSch.}, - preprint = {https://kups.ub.uni-koeln.de/id/eprint/10441}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2021:MLA, - author = {Alexander Heinlein and Axel Klawonn and Martin Lanser and Janine Weber}, - title = {Machine Learning in Adaptive Domain Decomposition Methods - Reducing the Effort in Sampling}, - booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2019}, - pages = {593--603}, - publisher = {Springer International Publishing}, - year = {2021}, - doi = {10.1007/978-3-030-55874-1_58}, - abbr = {Springer LNCSE}, - abstract = {The convergence rate of classic domain decomposition methods in general deteriorates severely for large discontinuities in the coefficient functions of the considered partial differential equation. To retain the robustness for such highly heterogeneous problems, the coarse space can be enriched by additional coarse basis functions. These can be obtained by solving local generalized eigenvalue problems on subdomain edges. In order to reduce the number of eigenvalue problems and thus the computational cost, we use a neural network to predict the geometric location of critical edges, i.e., edges where the eigenvalue problem is indispensable. As input data for the neural network, we use function evaluations of the coefficient function within the two subdomains adjacent to an edge. In the present article, we examine the effect of computing the input data only in a neighborhood of the edge, i.e., on slabs next to the edge. We show numerical results for both the training data as well as for a concrete test problem in form of a microsection subsection for linear elasticity problems. We observe that computing the sampling points only in one half or one quarter of each subdomain still provides robust algorithms.}, - preprint = {https://kups.ub.uni-koeln.de/id/eprint/10439}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2021:CST, - author = {Alexander Heinlein and Oliver Rheinbach and Friederike R\"over}, - title = {Choosing the Subregions in Three-Level FROSch Preconditioners}, - booktitle = {WCCM-ECCOMAS2020}, - year = {2021}, - abbr = {WCCM-ECCOMAS}, - abstract = {Different graph partitioning methods, i.e., linear partioning, parallel hypergraph (PHG) partioning, and two approaches using ParMETIS, are considered to generate an unstructured decomposition of the second-level coarse operator of three-level FROSch (Fast and Robust Overlapping Schwarz) preconditioners in the Trilinos software library. In our context, the parallel hypergraph method shows the most consistent results.}, - url = {https://www.scipedia.com/public/Hainlein_et_al_2021}, - preprint = {https://tu-freiberg.de/sites/default/files/media/fakultaet-fuer-mathematik-und-informatik-fakultaet-1-9277/prep/2021-01.pdf}, - dimensions = {true}, - keywords = {published}, - bibtex_show = {true} -} - -@article{Heinlein:2021:CML2, - author = {Alexander Heinlein and Axel Klawonn and Martin Lanser and Janine Weber}, - title = {Combining Machine Learning and Domain Decomposition Methods for the Solution of Partial Differential Equations – A Review}, - journal = {GAMM-Mitteilungen}, - volume = {44}, - number = {1}, - pages = {e202100001}, - year = {2021}, - doi = {10.1002/gamm.202100001}, - abbr = {GAMM-Mitteilungen}, - abstract = {Scientific machine learning, an area of research where techniques from machine learning and scientific computing are combined, has become of increasing importance and receives growing attention. Here, our focus is on a very specific area within scientific machine learning given by the combination of domain decomposition methods with machine learning techniques. The aim of the present work is to make an attempt of providing a review of existing and also new approaches within this field as well as to present some known results in a unified framework; no claim of completeness is made. As a concrete example of machine learning enhanced domain decomposition methods, an approach is presented which uses neural networks to reduce the computational effort in adaptive domain decomposition methods while retaining their robustness. More precisely, deep neural networks are used to predict the geometric location of constraints which are needed to define a robust coarse space. Additionally, two recently published deep domain decomposition approaches are presented in a unified framework. Both approaches use physics-constrained neural networks to replace the discretization and solution of the subdomain problems of a given decomposition of the computational domain. Finally, a brief overview is given of several further approaches which combine machine learning with ideas from domain decomposition methods to either increase the performance of already existing algorithms or to create completely new methods.}, - url = {https://onlinelibrary.wiley.com/doi/10.1002/gamm.202100001}, - preprint = {http://kups.ub.uni-koeln.de/id/eprint/20708}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@article{Heinlein:2020:FFE, - author = {Alexander Heinlein and Axel Klawonn and Martin Lanser and Janine Weber}, - title = {A Frugal {FETI-DP} and {BDDC} Coarse Space for Heterogeneous Problems}, - journal = {Electronic Transactions on Numerical Analysis (ETNA)}, - volume = {53}, - pages = {562-591}, - year = {2020}, - doi = {10.1553/etna_vol53s562}, - abbr = {ETNA}, - abstract = {The convergence rate of domain decomposition methods is generally determined by the eigenvalues of the preconditioned system. For second-order elliptic partial differential equations, coefficient discontinuities with a large contrast can lead to a deterioration of the convergence rate. Only by implementing an appropriate coarse space or second level, a robust domain decomposition method can be obtained. In this article, a new frugal coarse space for FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) and BDDC (Balancing Domain Decomposition by Constraints) methods is presented, which has a lower set-up cost than competing adaptive coarse spaces. In particular, in contrast to adaptive coarse spaces, it does not require the solution of any local generalized eigenvalue problems. The approach considered here aims at a low-dimensional approximation of the adaptive coarse space by using appropriate weighted averages and is robust for a broad range of coefficient distributions for diffusion and elasticity problems. In this article, the robustness is heuristically justified as well as numerically shown for several coefficient distributions. The new coarse space is compared to adaptive coarse spaces, and parallel scalability up to 262,144 parallel cores for a parallel BDDC implementation with the new coarse space is shown. The superiority of the new coarse space over classic coarse spaces with respect to parallel weak scalability and time to solution is confirmed by numerical experiments.}, - url = {https://epub.oeaw.ac.at/?arp=0x003c1ad0}, - preprint = {https://kups.ub.uni-koeln.de/id/eprint/10363}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2020:CSN, - author = {Alexander Heinlein and Martin Lanser}, - title = {Coarse Spaces for Nonlinear {S}chwarz Methods on Unstructured Grids}, - booktitle = {Domain Decomposition Methods in Science and Engineering XXV}, - pages = {268--276}, - publisher = {Springer International Publishing}, - year = {2020}, - doi = {10.1007/978-3-030-56750-7_30}, - abbr = {Springer LNCSE}, - abstract = {In recent years, nonlinear domain decomposition (DD) methods for the solution of nonlinear partial differential equations as, e.g., ASPIN (Additive Schwarz Preconditioned Inexact Newton) or Nonlinear-FETI-DP (Nonlinear - Finite Element Tearing and Interconnecting - Dual-Primal), became popular. For several model problems, these approaches outperform classical inexact Newton methods, where a corresponding linear DD method is used to solve the linearized problems, in terms of linear and nonlinear iteration counts and time to solution. As in the linear case, in nonlinear DD methods, an appropriate coarse space is often necessary for robustness and numerical scalability. In this paper, a new multiplicative implementation of a coarse space for ASPIN as well as the related RASPEN (Restricted Additive Schwarz Preconditioned Exact Newton) method is suggested. Additionally, several coarse spaces, which are also applicable for unstructured meshes and domain decompositions, are suggested. Robustness and numerical scalability is shown for different homogeneous and heterogeneous p-Laplace problems in two spatial dimensions.}, - url = {https://link.springer.com/chapter/10.1007/978-3-030-56750-7_30}, - preprint = {https://kups.ub.uni-koeln.de/9015/}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2020:MLA, - author = {Alexander Heinlein and Axel Klawonn and Martin Lanser and Janine Weber}, - title = {Machine Learning in Adaptive FETI-DP - A Comparison of Smart and Random Training Data}, - booktitle = {Domain Decomposition Methods in Science and Engineering XXV}, - pages = {218--226}, - publisher = {Springer International Publishing}, - year = {2020}, - doi = {10.1007/978-3-030-56750-7_24}, - abbr = {Springer LNCSE}, - abstract = {Adaptive FETI-DP (Finite Element Tearing and Interconnecting - Dual-Primal) methods are considered for the solution of two-dimensional scalar elliptic model problems with complex coefficient distributions where large coefficient jumps can occur along or across the domain decomposition interface. The adaptive coarse space is obtained by solving certain generalized eigenvalue problems on subdomain edges. In order to reduce the number of eigenvalue problems, a machine learning based strategy using a neural network to predict the geometric location of critical edges can be applied in a preprocessing step. Here, the effect of different types of training data sets on the robustness of the machine learning adaptive FETI-DP algorithm is investigated. Therefore, the neural network is first trained on different data sets and then the machine learning model is evaluated for a coefficient distribution obtained from a realistic dual-phase steel microstructure. It can be observed that the best results are obtained using a priori knowledge (smart data), whereas purely random data yields bad results. However, by imposing some structure on the random data and increasing the size of the data set, the performance is comparable to the smart data.}, - url = {https://link.springer.com/chapter/10.1007/978-3-030-56750-7_24}, - preprint = {https://kups.ub.uni-koeln.de/9016/}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2020:LSA, - author = {Alexander Heinlein and Axel Klawonn and Martin K\"uhn}, - title = {Local spectra of adaptive domain decomposition methods}, - booktitle = {Domain Decomposition Methods in Science and Engineering XXV}, - pages = {167--175}, - publisher = {Springer International Publishing}, - year = {2020}, - doi = {10.1007/978-3-030-56750-7_18}, - abbr = {Springer LNCSE}, - abstract = {We compare the spectra of local generalized eigenvalue problems in different adaptive coarse spaces for overlapping and nonoverlapping domain decomposition methods. In particular, we compare the AGDSW (Adaptive Generalized Dryja-Smith-Widlund), the OS-ACMS (Overlapping Schwarz-Approximate Component Mode Synthesis), and the SHEM (Spectral Harmonically Enriched Multiscale) coarse spaces for overlapping Schwarz methods, the GenEO (Generalized Eigenproblems in the Overlaps) coarse space for FETI-1 and BDD methods, and two approaches based on estimates for the $P_D$ operator for FETI-DP and BDDC methods. Therefore, we consider eight different two-dimensional coefficient functions with jumps ranging from simple channels to a realistic microstructure of a dual-phase steel. We observe significant differences in the width of the gap between good and bad eigenvalues depending on the coefficient distribution. In addition to that, eigenvalue problems involving sophisticated but more expensive harmonic extensions or deluxe-scaling can reduce the number of bad eigenvalues.}, - url = {https://link.springer.com/chapter/10.1007/978-3-030-56750-7_18}, - preprint = {https://kups.ub.uni-koeln.de/9019/}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2020:FRO, - author = {Alexander Heinlein and Axel Klawonn and Sivasankaran Rajamanickam and Oliver Rheinbach}, - title = {{FROSch}: A Fast And Robust Overlapping {S}chwarz Domain Decomposition Preconditioner Based on {X}petra in {T}rilinos}, - booktitle = {Domain Decomposition Methods in Science and Engineering XXV}, - pages = {176--184}, - publisher = {Springer International Publishing}, - year = {2020}, - doi = {10.1007/978-3-030-56750-7_19}, - abbr = {Springer LNCSE}, - abstract = {A parallel two-level overlapping Schwarz domain decomposition preconditioner has been integrated into the Trilinos ShyLU-package. The preconditioner uses an energy-minimizing coarse space and can be constructed from an assembled sparse matrix. The software implements variants of the two-level overlapping Schwarz method from [Dohrmann, Klawonn, Widlund, SINUM 2008], where it was denoted Generalized Dryja, Smith, Widlund (GDSW). The implementation is based on [Heinlein, Klawonn, Rheinbach, SISC 2016] but has been improved significantly with respect to efficiency, generality, e.g., for the use of Tpetra instead of Epetra matrices, and its interface.}, - url = {https://link.springer.com/chapter/10.1007/978-3-030-56750-7_19}, - preprint = {https://kups.ub.uni-koeln.de/9018/}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2020:TLE, - author = {Alexander Heinlein and Axel Klawonn and Oliver Rheinbach and Friederike R\"over}, - title = {A Three-Level Extension of the {GDSW} Overlapping {S}chwarz Preconditioner in Three Dimensions}, - booktitle = {Domain Decomposition Methods in Science and Engineering XXV}, - pages = {185--192}, - publisher = {Springer International Publishing}, - year = {2020}, - doi = {10.1007/978-3-030-56750-7_20}, - abbr = {Springer LNCSE}, - abstract = {A three-level extension of the GDSW overlapping Schwarz preconditioner in three dimensions is presented, constructed by recursively applying the GDSW preconditioner to the coarse problem using a standard and a reduced dimension coarse space. Numerical results, obtained for a parallel implementation using the Trilinos software library, are presented for up to 64,000 cores of the JUQUEEN supercomputer. The superior weak parallel scalability of the three-level method is verified. For large problems and a large number of cores, the three-level method is faster by more than a factor of two, compared to the standard two-level method. The three-level method shows to scale when the classical method is already be out-of-memory.}, - url = {https://link.springer.com/chapter/10.1007/978-3-030-56750-7_20}, - preprint = {https://kups.ub.uni-koeln.de/9017/}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@article{Heinlein:2020:AHN, - author = {Alexander Heinlein and Lanser, Martin}, - title = {Additive and Hybrid Nonlinear Two-Level Schwarz Methods and Energy Minimizing Coarse Spaces for Unstructured Grids}, - journal = {SIAM Journal on Scientific Computing}, - volume = {42}, - number = {4}, - pages = {A2461-A2488}, - year = {2020}, - doi = {10.1137/19M1276972}, - abbr = {SISC}, - abstract = {Nonlinear domain decomposition (DD) methods, such as ASPIN (additive Schwarz preconditioned inexact Newton), RASPEN (restricted additive Schwarz preconditioned inexact Newton), nonlinear FETI-DP (finite element tearing and interconnecting-dual primal), and nonlinear BDDC (balancing DD by constraints), can be reasonable alternatives to classical Newton--Krylov-DD methods for the solution of sparse nonlinear systems of equations, e.g., arising from a discretization of a nonlinear partial differential equation (PDE). These nonlinear DD approaches are often able to effectively tackle unevenly distributed nonlinearities and outperform Newton's method with respect to convergence speed as well as global convergence behavior. Furthermore, they often improve parallel scalability due to a superior ratio of local to global work. Nonetheless, as for linear DD methods, it is often necessary to incorporate an appropriate coarse space in a second level to obtain numerical scalability for increasing numbers of subdomains. In addition, an appropriate coarse space can also improve the nonlinear convergence of nonlinear DD methods. In this paper, we introduce four variants for integrating coarse spaces in nonlinear Schwarz methods in an additive or multiplicative way using Galerkin projections. These new variants can be interpreted as natural nonlinear equivalents to well-known linear additive and hybrid two-level Schwarz preconditioners. Furthermore, they facilitate the use of various coarse spaces, e.g., coarse spaces based on energy-minimizing extensions, which can easily be used for irregular DDs, such as, e.g., those obtained by graph partitioners. In particular, multiscale finite element method (MsFEM)-type coarse spaces are considered, and it is shown that they outperform classical approaches for certain heterogeneous nonlinear problems. The new approaches are then compared with classical Newton--Krylov-DD and nonlinear one-level Schwarz approaches for different homogeneous and heterogeneous model problems based on the $p$-Laplace operator.}, - url = {https://epubs.siam.org/doi/abs/10.1137/19M1276972}, - preprint = {https://kups.ub.uni-koeln.de/id/eprint/9845}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@article{Heinlein:2020:RDG, - author = {Alexander Heinlein and Christian Hochmuth and Axel Klawonn}, - title = {Reduced Dimension {GDSW} Coarse Spaces for Monolithic {S}chwarz Domain Decomposition Methods for Incompressible Fluid Flow Problems}, - journal = {International Journal for Numerical Methods in Engineering}, - volume = {121}, - number = {6}, - pages = {1101-1119}, - year = {2020}, - doi = {10.1002/nme.6258}, - abbr = {IJNME}, - abstract = {Summary Monolithic preconditioners for incompressible fluid flow problems can significantly improve the convergence speed compared with preconditioners based on incomplete block factorizations. However, the computational costs for the setup and the application of monolithic preconditioners are typically higher. In this article, several techniques are applied to monolithic two-level generalized Dryja-Smith-Widlund (GDSW) preconditioners to further improve the convergence speed and the computing time. In particular, reduced dimension GDSW coarse spaces, restricted and scaled versions of the first level, hybrid, and parallel coupling of the levels, and recycling strategies are investigated. Using a combination of all these improvements, for a small time-dependent Navier-Stokes problem on 240 message passing interface (MPI) ranks, a reduction of 86\% of the time-to-solution can be obtained. Even without applying recycling strategies, the time-to-solution can be reduced by more than 50\% for a larger steady Stokes problem on 4608 MPI ranks. For the largest problems with 11 979 MPI ranks, the scalability deteriorates drastically for the monolithic GDSW coarse space. On the other hand, using the reduced dimension coarse spaces, good scalability up to 11 979 MPI ranks, which corresponds to the largest problem configuration fitting on the employed supercomputer, could be achieved.}, - keywords = {algebraic preconditioner, overlapping domain decomposition, GDSW, Navier-Stokes, parallel computing, Stokes}, - url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6258}, - preprint = {https://kups.ub.uni-koeln.de/9675/}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@article{Heinlein:2019:MLA, - author = {Alexander Heinlein and Klawonn, Axel and Lanser, Martin and Weber, Janine}, - title = {Machine Learning in Adaptive Domain Decomposition Methods - Predicting the Geometric Location of Constraints}, - journal = {SIAM Journal on Scientific Computing}, - volume = {41}, - number = {6}, - pages = {A3887-A3912}, - year = {2019}, - doi = {10.1137/18M1205364}, - abbr = {SISC}, - abstract = {Domain decomposition methods are robust and parallel scalable, preconditioned iterative algorithms for the solution of the large linear systems arising in the discretization of elliptic partial differential equations by finite elements. The convergence rate of these methods is generally determined by the eigenvalues of the preconditioned system. For second-order elliptic partial differential equations, coefficient discontinuities with a large contrast can lead to a deterioration of the convergence rate. A remedy can be obtained by enhancing the coarse space with elements, which are often called constraints, that are computed by solving small eigenvalue problems on portions of the interface of the domain decomposition, i.e., edges in two dimensions or faces and edges in three dimensions. In the present work, without restriction of generality, the focus is on two dimensions. In general, it is difficult to predict where these constraints have to be added, and therefore the corresponding local eigenvalue problems have to be computed, i.e., on which edges. Here, a machine learning based strategy using neural networks is suggested to predict the geometric location of these edges in a preprocessing step. This reduces the number of eigenvalue problems that have to be solved before the iteration. Numerical experiments for model problems and realistic microsections using regular decompositions as well as decompositions from graph partitioners are provided, showing very promising results.}, - url = {https://epubs.siam.org/doi/abs/10.1137/18M1205364?journalCode=sjoce3}, - preprint = {https://kups.ub.uni-koeln.de/8645/}, - dimensions = {true}, - keywords = {published, reviewed, highlighted5}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2019:TLE, - author = {Alexander Heinlein and Klawonn, Axel and Rheinbach, Oliver and R{\"o}ver, Friederike}, - title = {A Three-Level Extension of the {GDSW} Overlapping {S}chwarz Preconditioner in Two Dimensions}, - booktitle = {Advanced Finite Element Methods with Applications: Selected Papers from the 30th Chemnitz Finite Element Symposium 2017}, - pages = {187--204}, - publisher = {Springer International Publishing}, - year = {2019}, - doi = {10.1007/978-3-030-14244-5_10}, - abbr = {Springer LNCSE}, - abstract = {A three-level extension of the GDSW overlapping Schwarz preconditioner in two dimensions is presented, constructed by recursively applying the GDSW preconditioner to the coarse problem. Numerical results, obtained for a parallel implementation using the Trilinos software library, are presented for up to 90,000 cores of the JUQUEEN supercomputer. The superior weak parallel scalability of the three-level method is verified. For large problems and a large number of cores, the three-level method is faster by more than a factor of two, compared to the standard two-level method . The three-level method can also be expected to scale when the classical method will already be out-of-memory.}, - url = {https://link.springer.com/chapter/10.1007%2F978-3-030-14244-5_10}, - preprint = {https://tu-freiberg.de/sites/default/files/media/fakultaet-fuer-mathematik-und-informatik-fakultaet-1-9277/prep/preprint_2018_04_heinlein_klawonn_rheinbach_roever.pdf}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@article{Heinlein:2019:AGD1, - author = {Alexander Heinlein and Axel Klawonn and Jascha Knepper and Oliver Rheinbach}, - title = {Adaptive {GDSW} Coarse Spaces for Overlapping {S}chwarz Methods in Three Dimensions}, - journal = {SIAM Journal on Scientific Computing}, - number = {5}, - pages = {A3045-A3072}, - volume = {41}, - year = {2019}, - doi = {10.1137/18M1220613}, - abbr = {SISC}, - abstract = {A robust two-level overlapping Schwarz method for scalar elliptic model problems with highly varying coefficient functions is introduced. While the convergence of standard coarse spaces may depend strongly on the contrast of the coefficient function, the condition number bound of the new method is independent of the coefficient function. Indeed, the condition number only depends on a user-prescribed tolerance. The coarse space is based on discrete harmonic extensions of vertex, edge, and face interface functions, which are computed from the solutions of corresponding local generalized edge and face eigenvalue problems. The local eigenvalue problems are of the size of the edges and faces of the decomposition, and the eigenvalue problems can be constructed solely from the local subdomain stiffness matrices and the fully assembled global stiffness matrix. The new AGDSW (adaptive generalized Dryja--Smith--Widlund) coarse space always contains the classical GDSW coarse space by construction of the generalized eigenvalue problems. Numerical results supporting the theory are presented for several model problems in three dimensions using structured as well as unstructured meshes and unstructured decompositions.}, - url = {https://epubs.siam.org/doi/abs/10.1137/18M1220613}, - preprint = {https://kups.ub.uni-koeln.de/8756/}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@article{Heinlein:2019:MOS, - author = {Alexander Heinlein and Christian Hochmuth and Axel Klawonn}, - title = {Monolithic Overlapping {S}chwarz Domain Decomposition Methods with {GDSW} Coarse Spaces for Incompressible Fluid Flow Problems}, - journal = {SIAM Journal on Scientific Computing}, - number = {4}, - pages = {C291--C316}, - volume = {41}, - year = {2019}, - doi = {10.1137/18M1184047}, - abbr = {SISC}, - abstract = {Monolithic overlapping Schwarz preconditioners for saddle point problems of Stokes and Navier--Stokes type are presented. In order to obtain numerically scalable algorithms, coarse spaces obtained from the generalized Dryja--Smith--Widlund (GDSW) approach are used. Numerical results of our parallel implementation are presented for various incompressible fluid flow problems. In particular, cases are considered where the problem cannot or should not be reduced using local static condensation, e.g., Stokes or Navier--Stokes problems with continuous pressure spaces. In the new monolithic preconditioners, the local overlapping problems and the coarse problem are saddle point problems with the same structure as the original problem. Our parallel implementation of these preconditioners is based on the fast and robust overlapping Schwarz (FROSch) library, which is part of the Trilinos package ShyLU. The implementation is essentially algebraic in the sense that, for the class of problems presented here, the preconditioners can be constructed from the fully assembled stiffness matrix and information about the block structure of the problem. Further information about the geometry or the null space of the underlying problem can improve the performance compared to the default settings. Parallel scalability results for several thousand cores for Stokes and Navier--Stokes model problems are reported. Each of the local problems is solved using a direct solver in serial mode, whereas the coarse problem is solved using a direct solver in serial or message passing interface (MPI)-parallel mode or using an MPI-parallel iterative Krylov solver.}, - url = {https://epubs.siam.org/doi/abs/10.1137/18M1184047}, - preprint = {https://kups.ub.uni-koeln.de/8355/}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2019:IPP, - author = {Alexander Heinlein and Axel Klawonn and Oliver Rheinbach and Olof Widlund}, - title = {Improving the Parallel Performance of Overlapping {S}chwarz Methods by Using a Smaller Energy Minimizing Coarse Space}, - booktitle = {Domain Decomposition Methods in Science and Engineering XXIV}, - pages = {383--392}, - publisher = {Springer International Publishing}, - year = {2019}, - doi = {10.1007/978-3-319-93873-8_36}, - abbr = {Springer LNCSE}, - abstract = {We consider a recent overlapping Schwarz method with an energy-minimizing coarse space of reduced size. In numerical experiments for up to 64,000 cores, we show that the parallel efficiency and the total time to solution is improved significantly, compared to our previous overlapping Schwarz method using an alternative energy-minimizing coarse space.}, - url = {https://link.springer.com/chapter/10.1007%2F978-3-319-93873-8_36}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2019:AGD2, - author = {Alexander Heinlein and Axel Klawonn and Jascha Knepper and Oliver Rheinbach}, - title = {An Adaptive {GDSW} Coarse Space for Two-Level Overlapping {S}chwarz Methods in Two Dimensions}, - booktitle = {Domain Decomposition Methods in Science and Engineering XXIV}, - pages = {373--382}, - publisher = {Springer International Publishing}, - year = {2019}, - doi = {10.1007/978-3-319-93873-8_35}, - abbr = {Springer LNCSE}, - abstract = {We propose robust coarse spaces for two-level overlapping Schwarz preconditioners, which are extensions of the energy minimizing coarse space known as GDSW (Generalized Dryja, Smith, Widlund). The resulting two-level methods with adaptive coarse spaces are robust for second order elliptic problems in two dimensions, even in presence of a highly heterogeneous coefficient function, and reduce to the standard GDSW algorithm if no additional coarse basis functions are used.}, - url = {https://link.springer.com/chapter/10.1007/978-3-319-93873-8_35}, - preprint = {https://kups.ub.uni-koeln.de/8756/}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2019:AFR, - author = {Alexander Heinlein and Oliver Rheinbach and Friederike R\"over and Stefan Sandfeld and Dominik Steinberger}, - title = {Applying the FROSch Overlapping Schwarz Preconditioner to Dislocation Mechanics in Deal.II}, - booktitle = {Proc. Appl. Math. Mech.}, - volume = {19}, - number = {1}, - pages = {e201900337}, - year = {2019}, - doi = {10.1002/pamm.201900337}, - abbr = {PAMM}, - abstract = {In this contribution, results regarding fluid-structure interaction (FSI) simulations for three-dimensional arterial walls are presented. In detail, a benchmark problem for FSI simulations in arteries of sufficient complexity, which combines sophisticated nonlinear models for the fluid and the structure, cf. [1], as well as a short segment from a patient-specific arterial geometry are considered. For the patient-specific arterial geometry a specific inflow profile suited for realistic geometries and simplified boundary conditions for the outflow are taken into account.}, - url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.201900337}, - preprint = {https://kups.ub.uni-koeln.de/9692/}, - dimensions = {true}, - keywords = {published}, - bibtex_show = {true} -} - -@inproceedings{Giese:2019:CMRa, - author = {Giese, Daniel and Heinlein, Alexander and Klawonn, Axel and Knepper, Jascha and Sonnabend, Kristina}, - title = {Comparison of MRI measurements and CFD simulations of hemodynamics in intracranial aneurysms using a 3D printed model - A benchmark problem}, - booktitle = {Proc. Appl. Math. Mech.}, - volume = {19}, - number = {1}, - pages = {e201900398}, - year = {2019}, - doi = {10.1002/pamm.201900398}, - abbr = {PAMM}, - abstract = {A benchmark for the comparison of MRI (Magnetic Resonance Imaging) measurements and CFD (Computational Fluid Dynamics) simulations for blood flow in intracranial aneurysms is presented. The benchmark setting is designed to allow for CFD simulations that are completely independent of the MRI measurements. This facilitates a fair comparison of both methods. Furthermore, results showing the good agreement of MRI and CFD are presented.}, - url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.201900398}, - preprint = {https://kups.ub.uni-koeln.de/id/eprint/9670}, - dimensions = {true}, - keywords = {published}, - bibtex_show = {true} -} - -@inproceedings{Giese:2019:CMRb, - author = {Giese, Daniel and Heinlein, Alexander and Klawonn, Axel and Knepper, Jascha and Sonnabend, Kristina}, - title = {Comparison of MRI measurements and CFD simulations of hemodynamics in intracranial aneurysms using a 3D printed model - Influence of noisy MRI measurements}, - booktitle = {Proc. Appl. Math. Mech.}, - volume = {19}, - number = {1}, - pages = {e201900401}, - year = {2019}, - doi = {10.1002/pamm.201900401}, - abbr = {PAMM}, - abstract = {MRI (Magnetic Resonance Imaging) measurements and CFD (Computational Fluid Dynamics) simulations for blood flow in intracranial aneurysms are compared for a benchmark problem. In particular, it is shown that noise and other artifacts in the MRI measurements have an influence on certain properties of the flow field, e.g., on the boundary flow and mass conservation.}, - url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.201900401}, - preprint = {https://kups.ub.uni-koeln.de/id/eprint/9671}, - dimensions = {true}, - keywords = {published}, - bibtex_show = {true} -} - -@article{Heinlein:2018:MCS, - author = {Alexander Heinlein and Klawonn, Axel and Knepper, Jascha and Rheinbach, Oliver}, - title = {Multiscale coarse spaces for overlapping Schwarz methods based on the ACMS space in 2D}, - journal = {Electronic Transactions on Numerical Analysis (ETNA)}, - pages = {156--182}, - volume = {48}, - year = {2018}, - doi = {10.1553/etna_vol48s156}, - abbr = {ETNA}, - abstract = {Two-level overlapping Schwarz domain decomposition methods for second-order elliptic problems in two dimensions are proposed using coarse spaces constructed from the Approximate Component Mode Synthesis (ACMS) multiscale discretization approach. These coarse spaces are based on eigenvalue problems using Schur complements on subdomain edges. It is then shown that the convergence of the resulting preconditioned Krylov method can be controlled by a user-specified tolerance and thus can be made independent of heterogeneities in the coefficient of the partial differential equation. The relations of this new approach to other known adaptive coarse space approaches for overlapping Schwarz methods are also discussed. Compared to one of the competing adaptive approaches, the new coarse space can be significantly smaller. Compared to other competing approaches, the eigenvalue problems are significantly cheaper to solve, i.e., the dimension of the eigenvalue problems is minimal among the competing adaptive approaches under consideration. Our local eigenvalue problems can be solved using one iteration of LobPCG for essentially the same cost as a Cholesky-decomposition of a Schur complement on a subdomain edge.}, - url = {https://epub.oeaw.ac.at/?arp=0x0038c0cb}, - preprint = {http://tu-freiberg.de/sites/default/files/media/fakultaet-fuer-mathematik-und-informatik-fakultaet-1-9277/prep/2016-09_fertig.pdf}, - altmetric = {130986919}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Fausten:2018:RFS, - author = {Simon Fausten and Daniel Balzani and Alexander Heinlein and Axel Klawonn and Oliver Rheinbach and J\"org Schr\"oder}, - title = {Remarks on Fluid-Structure Interaction Simulations in Realistic Arterial Geometries with regard to the Transmural Stress Distribution}, - booktitle = {Proc. Appl. Math. Mech.}, - volume = {18}, - number = {1}, - pages = {e201800312}, - year = {2018}, - doi = {10.1002/pamm.201800312}, - abbr = {PAMM}, - abstract = {In this contribution, Fluid-Structure-Interaction (FSI) in blood vessels, in detail the simulation of realistic arterial geometries, where the interaction of the blood flow and the vessel wall is of special interest, is considered. Based on pervious research, cf. [1], our existing framework for FSI-simulations is extended towards realistic arterial geometries. The inflow and outflow boundary conditions for the fluid, as well as the boundary conditions for the structure are enhanced and adjusted to the chosen patient-specific geometry. In detail, an inflow profile for arbitrary shaped inflow cross-sections and a zero pressure boundary condition at the outflow are applied. Furthermore, the vessel wall is discretized using realistic material parameters of the media layer. The geometry and material parameters are adopted from [2]. In order to deal with the increasing complexity of the boundary value problem parallel computing and a two-level overlapping Schwarz method with energy-minimizing coarse space are applied; cf. [3]. The numerical simulations are performed using the Open-Source software LifeV, in particular a code which has been developed in cooperation with the group of Prof. Quarteroni from the EPF Lausanne.}, - url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.201800312}, - dimensions = {true}, - keywords = {published}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2017:POS, - author = {Alexander Heinlein and Klawonn, Axel and Rheinbach, Oliver}, - title = {Parallel Overlapping Schwarz with an Energy-Minimizing Coarse Space}, - booktitle = {Domain Decomposition Methods in Science and Engineering XXIII}, - pages = {353--360}, - publisher = {Springer International Publishing}, - year = {2017}, - doi = {10.1007/978-3-319-52389-7_36}, - abbr = {Springer LNCSE}, - abstract = {Parallel results obtained with a new implementation of an overlapping Schwarz method using an energy minimizing coarse space are presented. We consider structured and unstructured domain decompositions for scalar elliptic and linear elasticity model problems in two dimensions. In particular, strong and weak parallel scalability studies for up to 1024 processor cores are presented for both types of problems. Additionally, weak scalability results for a three-dimensional linear elasticity model problem using up to 4096 processor cores are discussed. Finally, an application from fully-coupled fluid-structure interaction using a nonlinear hyperelastic material model for the structure is shown.}, - url = {https://link.springer.com/chapter/10.1007%2F978-3-319-52389-7_36}, - preprint = {http://tu-freiberg.de/sites/default/files/media/fakultaet-fuer-mathematik-und-informatik-fakultaet-1-9277/prep/2016-03_fertig.pdf}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Fausten:2017:STM, - author = {Simon Fausten and Daniel Balzani and Alexander Heinlein and Axel Klawonn and Oliver Rheinbach and J\"org Schr\"oder}, - title = {Steps Towards More Realistic FSI Simulations of Coronary Arteries}, - booktitle = {Proc. Appl. Math. Mech.}, - volume = {17}, - number = {1}, - pages = {187-188}, - year = {2017}, - doi = {10.1002/pamm.201710063}, - abbr = {PAMM}, - abstract = {In this contribution, results regarding fluid-structure interaction (FSI) simulations for three-dimensional arterial walls are presented. In detail, a benchmark problem for FSI simulations in arteries of sufficient complexity, which combines sophisticated nonlinear models for the fluid and the structure, cf. [1], as well as a short segment from a patient-specific arterial geometry are considered. For the patient-specific arterial geometry a specific inflow profile suited for realistic geometries and simplified boundary conditions for the outflow are taken into account.}, - url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.201710063}, - dimensions = {true}, - keywords = {published}, - bibtex_show = {true} -} - -@article{Heinlein:2016:PIT, - author = {Alexander Heinlein and Klawonn, Axel and Rheinbach, Oliver}, - title = {A parallel implementation of a two-level overlapping {S}chwarz method with energy-minimizing coarse space based on {T}rilinos}, - journal = {SIAM Journal on Scientific Computing}, - number = {6}, - pages = {C713--C747}, - volume = {38}, - year = {2016}, - doi = {10.1137/16M1062843}, - abbr = {SISC}, - abstract = {We describe a new implementation of a two-level overlapping Schwarz preconditioner with energy-minimizing coarse space (GDSW: generalized Dryja--Smith--Widlund) and show numerical results for an additive and a hybrid additive-multiplicative version. Our parallel implementation makes use of the Trilinos software library and provides a framework for parallel two-level Schwarz methods. We show parallel scalability for two- and three-dimensional scalar second-order elliptic and linear elasticity problems for several thousands of cores. We also discuss techniques for the parallel construction of coarse spaces which are also of interest for other parallel preconditioners and discretization methods using energy minimizing coarse functions. We finally show an application in monolithic fluid-structure interaction, where significant improvements are achieved compared to a standard algebraic, one-level overlapping Schwarz method.}, - url = {https://epubs.siam.org/doi/10.1137/16M1062843}, - preprint = {http://tu-freiberg.de/sites/default/files/media/fakultaet-fuer-mathematik-und-informatik-fakultaet-1-9277/prep/2016-04_fertig.pdf}, - altmetric = {130986917}, - dimensions = {true}, - keywords = {published, reviewed, highlighted2}, - bibtex_show = {true} -} - -@inproceedings{Heinlein:2016:PTO, - author = {Alexander Heinlein and Klawonn, Axel and Rheinbach, Oliver}, - title = {Parallel Two-Level Overlapping Schwarz Methods in Fluid-Structure Interaction}, - booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2015}, - pages = {521--530}, - publisher = {Springer International Publishing}, - year = {2016}, - doi = {10.1007/978-3-319-39929-4_50}, - abbr = {Springer LNCSE}, - abstract = {Parallel overlapping Schwarz preconditioners are considered and applied to the structural block in monolithic fluid-structure interaction (FSI). The two-level overlapping Schwarz method uses a coarse level based on energy minimizing functions. Linear elastic as well as nonlinear, anisotropic hyperelastic structural models are considered in an FSI problem of a pressure wave in a tube. Using our recent parallel implementation of a two-level overlapping Schwarz preconditioner based on the Trilinos library, the total computation time of our FSI benchmark problem was reduced by more than a factor of two compared to the algebraic one-level overlapping Schwarz method used previously. Finally, also strong scalability for our FSI problem is shown for up to 512 processor cores.}, - url = {https://link.springer.com/chapter/10.1007/978-3-319-39929-4_50}, - preprint = {http://tu-freiberg.de/sites/default/files/media/fakultaet-fuer-mathematik-und-informatik-fakultaet-1-9277/prep/2015-15_fertig_0.pdf}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@phdthesis{Heinlein:2016:POS, - author = {Alexander Heinlein}, - title = {Parallel Overlapping Schwarz Preconditioners and Multiscale Discretizations with Applications to Fluid-Structure Interaction and Highly Heterogeneous Problems}, - school = {Universit{\"a}t zu K{\"o}ln}, - year = {2016}, - url = {https://kups.ub.uni-koeln.de/6841}, - abbr = {PhD Thesis}, - abstract = {Accurate simulations of transmural wall stresses in artherosclerotic coronary arteries may help to predict plaque rupture. Therefore, a robust and efficient numerical framework for Fluid-Structure Interaction (FSI) of the blood flow and the arterial wall has to be set up, and suitable material laws for the modeling of the fluid and the structural response have to be incorporated. In this thesis, monolithic coupling algorithms and corresponding monolithic preconditioners are used to simulate FSI using highly nonlinear anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models for the arterial wall. An MPI-parallel FSI software from the LifeV library is coupled to the software FEAP in order to enable access to the structural material models implemented in FEAP. To define a benchmark test for highly nonlinear material models in FSI, a simple geometry corresponding to a section of an idealized coronary artery, suitable boundary conditions, and material parameters adapted to experimental data are used. In particular, the geometry is chosen to be nonsymmetric to make effects due to the anisotropy of the structure visible. An initialization phase and several heartbeats are simulated, and systematical studies with meshes of increasing refinement and different space discretizations are carried out. The results indicate that, for the highly nonlinear material models, piecewise quadratic or F-bar element discretizations lead to significantly better results than piecewise linear shape functions. The results using piecewise linear shape functions are less accurate with respect to the displacements and, in particular, to the approximation of the stresses. To improve the performance of the FSI simulations, a more robust preconditioner for the highly nonlinear structural material models has to be used. Therefore, a parallel implementation of the GDSW (Generalized Dryja-Smith-Widlund) preconditioner, which is a geometric two-level overlapping Schwarz preconditioner with energy-minimizing coarse space, is presented. The implementation, which is based on the software library Trilinos, is held flexible to make further extensions of the preconditioner possible. Even though the dimension of its coarse space is comparably large, parallel scalability for two and three dimensional scalar elliptic and linear elastic problems for thousands of cores is demonstrated. Also for unstructured domain decompositions and for a hybrid version of the preconditioner, convincing scalability is presented. When used as a preconditioner for the structure block in FSI simulations, the GDSW preconditioner shows excellent performance as well: scalability for up to 512 cores and a significant reduction of the simulation time and of the number of iterations with respect to the previously used preconditioner, IFPACK, are observed. IFPACK is an algebraic one-level overlapping Schwarz preconditioner. Finally, highly heterogeneous (multiscale) problems are investigated. Since the GDSW coarse space is not robust for general problems of this type, spaces based on Approximate Component Mode Synthesis (ACMS) are considered. On the basis of the ACMS space, coarse spaces for overlapping Schwarz methods are constructed, and a parallel implementation of a special finite element method is presented. For the coarse spaces, preliminary results indicating numerical scalability and robustness are discussed. For the parallel implementation of the special finite element method, very good parallel weak scalability is observed with respect to the construction of the basis functions and to the solution of the resulting linear system using the FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) method.}, - url = {https://kups.ub.uni-koeln.de/6841}, - dimensions = {true}, - keywords = {phd, reviewed, published}, - bibtex_show = {true} -} - -@article{Balzani:2016:NMF, - author = {Balzani, Daniel and Deparis, Simone and Fausten, Simon and Forti, Davide and Alexander Heinlein and Klawonn, Axel and Quarteroni, Alfio and Rheinbach, Oliver and Schr\"oder, J\"org}, - title = {Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains}, - journal = {International Journal for Numerical Methods in Biomedical Engineering}, - volume = {32}, - number = {10}, - pages = {e02756}, - year = {2016}, - doi = {10.1002/cnm.2756}, - abbr = {IJNMBE}, - abstract = {The accurate prediction of transmural stresses in arterial walls requires on the one hand robust and efficient numerical schemes for the solution of boundary value problems including fluid-structure interactions and on the other hand the use of a material model for the vessel wall that is able to capture the relevant features of the material behavior. One of the main contributions of this paper is the application of a highly nonlinear, polyconvex anisotropic structural model for the solid in the context of fluid-structure interaction, together with a suitable discretization. Additionally, the influence of viscoelasticity is investigated. The fluid-structure interaction problem is solved using a monolithic approach; that is, the nonlinear system is solved (after time and space discretizations) as a whole without splitting among its components. The linearized block systems are solved iteratively using parallel domain decomposition preconditioners. A simple but nonsymmetric curved geometry is proposed that is demonstrated to be suitable as a benchmark testbed for fluid-structure interaction simulations in biomechanics where nonlinear structural models are used. Based on the curved benchmark geometry, the influence of different material models, spatial discretizations, and meshes of varying refinement is investigated. It turns out that often-used standard displacement elements with linear shape functions are not sufficient to provide good approximations of the arterial wall stresses, whereas for standard displacement elements or F-bar formulations with quadratic shape functions, suitable results are obtained. For the time discretization, a second-order backward differentiation formula scheme is used. It is shown that the curved geometry enables the analysis of non-rotationally symmetric distributions of the mechanical fields. For instance, the maximal shear stresses in the fluid–structure interface are found to be higher in the inner curve that corresponds to clinical observations indicating a high plaque nucleation probability at such locations.}, - url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cnm.2756}, - preprint = {http://tu-freiberg.de/sites/default/files/media/fakultaet-fuer-mathematik-und-informatik-fakultaet-1-9277/prep/2015-03_fertig.pdf}, - altmetric = {21014922}, - dimensions = {true}, - keywords = {published, reviewed, highlighted1}, - bibtex_show = {true} -} - -@article{Heinlein:2015:ACM, - author = {Alexander Heinlein and Hetmaniuk, Ulrich and Klawonn, Axel and Rheinbach, Oliver}, - title = {The approximate component mode synthesis special finite element method in two dimensions: Parallel implementation and numerical results}, - journal = {Journal of Computational and Applied Mathematics}, - number = {6}, - pages = {116 - 133}, - volume = {289}, - year = {2015}, - issn = {0377-0427}, - doi = {10.1016/j.cam.2015.02.053}, - abbr = {JCAM}, - abstract = {A special finite element method based on approximate component mode synthesis (ACMS) was introduced in Hetmaniuk and Lehoucq (2010). ACMS was developed for second order elliptic partial differential equations with rough or highly varying coefficients. Here, a parallel implementation of ACMS is presented and parallel scalability issues are discussed for representative examples. Additionally, a parallel domain decomposition preconditioner (FETI-DP) is applied to solve the ACMS finite element system. Weak parallel scalability results for ACMS are presented for up to 1024 cores. Our numerical results also suggest a quadratic–logarithmic condition number bound for the preconditioned FETI-DP method applied to ACMS discretizations.}, - url = {http://www.sciencedirect.com/science/article/pii/S0377042715001405}, - note = {Sixth International Conference on Advanced Computational Methods in Engineering (ACOMEN 2014)}, - altmetric = {130986916}, - dimensions = {true}, - keywords = {published, reviewed}, - bibtex_show = {true} -} - -@inproceedings{Deparis:2015:CPS, - author = {Simone Deparis and Davide Forti and Alexander Heinlein and Axel Klawonn and Alfio Quarteroni and Oliver Rheinbach}, - title = {A Comparison of Preconditioners for the Steklov--Poincar\'e Formulation of the Fluid-Structure Coupling in Hemodynamics}, - booktitle = {Proc. Appl. Math. Mech.}, - volume = {15}, - number = {1}, - pages = {93-94}, - year = {2015}, - doi = {10.1002/pamm.201510037}, - abbr = {PAMM}, - abstract = {A Fluid-Structure Interaction (FSI) problem can be reinterpreted as a heterogeneous problem with two subdomains. It is possible to describe the coupled problem at the interface between the fluid and the structure, yielding a nonlinear Steklov-Poincar\'e problem. The linear system can be linearized by Newton iterations on the interface and the resulting linear problem can be solved by the preconditioned GMRES method. In this work we investigate the behavior of preconditioners of Neumann-Neumann and Dirichlet-Neumann type. We find that, in the context of hemodynamics, the Dirichlet-Neumann, i.e., using Dirichlet boundary conditions on the fluid side and Neumann on the structure side, outperforms the Neumann-Neumann method, except when a weighting is used such that it basically reduces to the Dirichlet-Neumann method.}, - url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.201510037}, - dimensions = {true}, - keywords = {published}, - bibtex_show = {true} -} - -@inproceedings{Balzani:2014:AAW, - author = {Daniel Balzani and Simone Deparis and Simon Fausten and Davide Forti and Alexander Heinlein and Axel Klawonn and Alfio Quarteroni and Oliver Rheinbach and J\"org Schr\"oder}, - title = {Aspects of Arterial Wall Simulations: Nonlinear Anisotropic Material Models and Fluid Structure Interaction}, - booktitle = {Proceedings of the WCCM XI}, - year = {2014}, - abbr = {WCCM XI}, - dimensions = {true}, - keywords = {published}, - bibtex_show = {true} -} - -# accepted - -@techreport{Saha:2024:TMD, - author={Tirtho S. Saha and Alexander Heinlein and Cordula Reisch}, - title={Towards Model Discovery Using Domain Decomposition and PINNs}, - year = {2024}, - month = {October}, - abbr = {MATHMOD2025}, - abstract = {We enhance machine learning algorithms for learning model parameters in complex systems represented by ordinary differential equations (ODEs) with domain decomposition methods. The study evaluates the performance of two approaches, namely (vanilla) Physics-Informed Neural Networks (PINNs) and Finite Basis Physics-Informed Neural Networks (FBPINNs), in learning the dynamics of test models with a quasi-stationary longtime behavior. We test the approaches for data sets in different dynamical regions and with varying noise level. As results, we find a better performance for the FBPINN approach compared to the vanilla PINN approach, even in cases with data from only a quasi-stationary time domain with few dynamics.}, - note = {Accepted as Full Contribution for presentation at the 11th Vienna International Conference on Mathematical Modelling (MATHMOD 2025)}, - preprint = {https://arxiv.org/abs/2410.01599}, - keywords = {accepted, reviewed, recent}, - bibtex_show = {true} -} - -@techreport{Heinlein:2024:FAR, - author = {Alexander Heinlein and Kathrin Smetana}, - title = {Algebraic construction of adaptive coarse spaces for two-level Schwarz preconditioners}, - year = {2024}, - month = {November}, - abbr = {SISC}, - abstract = {Two-level domain decomposition preconditioners lead to fast convergence and scalability of iterative solvers. However, for highly heterogeneous problems, where the coefficient function is varying rapidly on several possibly non-separated scales, the condition number of the preconditioned system generally depends on the contrast of the coefficient function leading to a deterioration of convergence. Enhancing the methods by coarse spaces constructed from suitable local eigenvalue problems, also denoted as adaptive or spectral coarse spaces, restores robust, contrast-independent convergence. However, these eigenvalue problems typically rely on non-algebraic information, such that the adaptive coarse spaces cannot be constructed from the fully assembled system matrix. In this paper, a novel algebraic adaptive coarse space, which relies on the a-orthogonal decomposition of (local) finite element (FE) spaces into functions that solve the partial differential equation (PDE) with some trace and FE functions that are zero on the boundary, is proposed. In particular, the basis is constructed from eigenmodes of two types of local eigenvalue problems associated with the edges of the domain decomposition. To approximate functions that solve the PDE locally, we employ a transfer eigenvalue problem, which has originally been proposed for the construction of optimal local approximation spaces for multiscale methods. In addition, we make use of a Dirichlet eigenvalue problem that is a slight modification of the Neumann eigenvalue problem used in the adaptive generalized Dryja-Smith-Widlund (AGDSW) coarse space. Both eigenvalue problems rely solely on local Dirichlet matrices, which can be extracted from the fully assembled system matrix. By combining arguments from multiscale and domain decomposition methods we derive a contrast-independent upper bound for the condition number. The robustness of the method is confirmed numerically for a variety of heterogeneous coefficient distributions, including binary random distributions and a coefficient function constructed from the SPE10 benchmark. The results are comparable to those of the non-algebraic AGDSW coarse space, also for those cases where the convergence of the classical algebraic generalized Dryja-Smith-Widlund (GDSW) coarse space deteriorates. Moreover, the coarse space dimension is the same or comparable to the AGDSW coarse space for all numerical experiments.}, - note = {Accepted for publication in the SIAM Journal on Scientific Computing}, - preprint = {https://arxiv.org/abs/2207.05559}, - keywords = {accepted, reviewed, recent, highlighted3}, - bibtex_show = {true} -} - -@techreport{Heinlein:2024:MDD, - author = {Alexander Heinlein and Amanda A. Howard and Damien Beecroft and Panos Stinis}, - title = {Multifidelity domain decomposition-based physics-informed neural networks and operators for time-dependent problems}, - year = {2024}, - month = {January}, - abstract = {Multiscale problems are challenging for neural network-based discretizations of differential equations, such as physics-informed neural networks (PINNs). This can be (partly) attributed to the so-called spectral bias of neural networks. To improve the performance of PINNs for time-dependent problems, a combination of multifidelity stacking PINNs and domain decomposition-based finite basis PINNs is employed. In particular, to learn the high-fidelity part of the multifidelity model, a domain decomposition in time is employed. The performance is investigated for a pendulum and a two-frequency problem as well as the Allen-Cahn equation. It can be observed that the domain decomposition approach clearly improves the PINN and stacking PINN approaches. Finally, it is demonstrated that the FBPINN approach can be extended to multifidelity physics-informed deep operator networks.}, - note = {Accepted for publication}, - preprint = {https://arxiv.org/abs/2401.07888}, - keywords = {accepted, reviewed}, - bibtex_show = {true} -} - -# submitted - -@techreport{Shang:2024:DDM, - author = {Yong Shang and Alexander Heinlein and Siddhartha Mishra and Fei Wang}, - title = {Overlapping Schwarz Preconditioners for Randomized Neural Networks with Domain Decomposition}, - year = {2024}, - month = {December}, - abstract = {Randomized neural networks (RaNNs), in which hidden layers remain fixed after random initialization, provide an efficient alternative for parameter optimization compared to fully parameterized networks. In this paper, RaNNs are integrated with overlapping Schwarz domain decomposition in two (main) ways: first, to formulate the least-squares problem with localized basis functions, and second, to construct overlapping preconditioners for the resulting linear systems. In particular, neural networks are initialized randomly in each subdomain based on a uniform distribution and linked through a partition of unity, forming a global solution that approximates the solution of the partial differential equation. Boundary conditions are enforced through a constraining operator, eliminating the need for a penalty term to handle them. Principal component analysis (PCA) is employed to reduce the number of basis functions in each subdomain, yielding a linear system with a lower condition number. By constructing additive and restricted additive Schwarz preconditioners, the least-squares problem is solved efficiently using the Conjugate Gradient (CG) and Generalized Minimal Residual (GMRES) methods, respectively. Our numerical results demonstrate that the proposed approach significantly reduces computational time for multi-scale and time-dependent problems. Additionally, a three-dimensional problem is presented to demonstrate the efficiency of using the CG method with an AS preconditioner, compared to an QR decomposition, in solving the least-squares problem.}, - note = {Submitted}, - preprint = {https://arxiv.org/abs/2412.19207}, - keywords = {submitted, reviewed, recent}, - bibtex_show = {true} -} - -@techreport{Visser:2024:PAC, - author = {Coen Visser and Alexander Heinlein and Bianca Giovanardi}, - title = {PACMANN: Point Adaptive Collocation Method for Artificial Neural Networks}, - year = {2024}, - month = {November}, - abstract = {Physics-Informed Neural Networks (PINNs) are an emerging tool for approximating the solution of Partial Differential Equations (PDEs) in both forward and inverse problems. PINNs minimize a loss function which includes the PDE residual determined for a set of collocation points. Previous work has shown that the number and distribution of these collocation points have a significant influence on the accuracy of the PINN solution. Therefore, the effective placement of these collocation points is an active area of research. Specifically, adaptive collocation point sampling methods have been proposed, which have been reported to scale poorly to higher dimensions. In this work, we address this issue and present the Point Adaptive Collocation Method for Artificial Neural Networks (PACMANN). Inspired by classic optimization problems, this approach incrementally moves collocation points toward regions of higher residuals using gradient-based optimization algorithms guided by the gradient of the squared residual. We apply PACMANN for forward and inverse problems, and demonstrate that this method matches the performance of state-of-the-art methods in terms of the accuracy/efficiency tradeoff for the low-dimensional problems, while outperforming available approaches for high-dimensional problems; the best performance is observed for the Adam optimizer. Key features of the method include its low computational cost and simplicity of integration in existing physics-informed neural network pipelines.}, - preprint = {https://arxiv.org/abs/2411.19632}, - keywords = {submitted, reviewed, recent}, - bibtex_show = {true} -} - -@techreport{Husanovic:2024:DON, - author = {Selma Husanović and Ginger Egberts and Alexander Heinlein and Fred Vermolen}, - title = {Deep operator network models for predicting post-burn contraction}, - year = {2024}, - month = {November}, - abstract = {Burn injuries present a significant global health challenge. Among the most severe long-term consequences are contractures, which can lead to functional impairments and disfigurement. Understanding and predicting the evolution of post-burn wounds is essential for developing effective treatment strategies. Traditional mathematical models, while accurate, are often computationally expensive and time-consuming, limiting their practical application. Recent advancements in machine learning, particularly in deep learning, offer promising alternatives for accelerating these predictions. This study explores the use of a deep operator network (DeepONet), a type of neural operator, as a surrogate model for finite element simulations, aimed at predicting post-burn contraction across multiple wound shapes. A DeepONet was trained on three distinct initial wound shapes, with enhancement made to the architecture by incorporating initial wound shape information and applying sine augmentation to enforce boundary conditions. The performance of the trained DeepONet was evaluated on a test set including finite element simulations based on convex combinations of the three basic wound shapes. The model achieved an $R^2$ score of $0.99$, indicating strong predictive accuracy and generalization. Moreover, the model provided reliable predictions over an extended period of up to one year, with speedups of up to 128-fold on CPU and 235-fold on GPU, compared to the numerical model. These findings suggest that DeepONets can effectively serve as a surrogate for traditional finite element methods in simulating post-burn wound evolution, with potential applications in medical treatment planning.}, - note = {Submitted}, - preprint = {https://arxiv.org/abs/2411.14555}, - keywords = {submitted, reviewed, recent}, - bibtex_show = {true} -} - -@techreport{Schmidt:2024:TGNN, - author = {Agatha Schmidt and Henrik Zunker and Alexander Heinlein and Martin J. K\"uhn}, - title = {Towards Graph Neural Network Surrogates Leveraging Mechanistic Expert Knowledge for Pandemic Response}, - year = {2024}, - month = {November}, - abstract = {During the COVID-19 crisis, mechanistic models have been proven fundamental to guide evidence-based decision making. However, time-critical decisions in a dynamically changing environment restrict the time available for modelers to gather supporting evidence. As infectious disease dynamics are often heterogeneous on a spatial or demographic scale, models should be resolved accordingly. In addition, with a large number of potential interventions, all scenarios can barely be computed on time, even when using supercomputing facilities. We suggest to combine complex mechanistic models with data-driven surrogate models to allow for on-the-fly model adaptations by public health experts. We build upon a spatially and demographically resolved infectious disease model and train a graph neural network for data sets representing early phases of the pandemic. The resulting networks reached an execution time of less than a second, a significant speedup compared to the metapopulation approach. The suggested approach yields potential for on-the-fly execution and, thus, integration of disease dynamics models in low-barrier website applications. For the approach to be used with decision-making, datasets with larger variance will have to be considered.}, - preprint = {https://arxiv.org/abs/2411.06500}, - keywords = {submitted, recent}, - bibtex_show = {true} -} - -@techreport{Giammatteo:2024:DDM, - author = {Elena Giammatteo and Alexander Heinlein and Philip L. Lederer and Matthias Schlottbom}, - title = {High-order discretized ACMS method for the simulation of finite-size two-dimensional photonic crystals}, - year = {2024}, - month = {October}, - abstract = {The computational complexity and efficiency of the approximate mode component synthesis (ACMS) method is investigated for the two-dimensional heterogeneous Helmholtz equations, aiming at the simulation of large but finite-size photonic crystals. The ACMS method is a Galerkin method that relies on a non-overlapping domain decomposition and special basis functions defined based on the domain decomposition. While, in previous works, the ACMS method was realized using first-order finite elements, we use an underlying hp–finite element method. We study the accuracy of the ACMS method for different wavenumbers, domain decompositions, and discretization parameters. Moreover, the computational complexity of the method is investigated theoretically and compared with computing times for an implementation based on the open source software package NGSolve. The numerical results indicate that, for relevant wavenumber regimes, the size of the resulting linear systems for the ACMS method remains moderate, such that sparse direct solvers are a reasonable choice. Moreover, the ACMS method exhibits only a weak dependence on the selected domain decomposition, allowing for greater flexibility in its choice. Additionally, the numerical results show that the error of the ACMS method achieves the predicted convergence rate for increasing wavenumbers. Finally, to display the versatility of the implementation, the results of simulations of large but finite-size photonic crystals with defects are presented.}, - note = {Submitted}, - preprint = {https://arxiv.org/abs/2410.07723}, - keywords = {submitted, reviewed, recent}, - bibtex_show = {true} -} - -@techreport{Shang:2024:DDM, - author = {Yong Shang and Alexander Heinlein and Siddhartha Mishra and Fei Wang}, - title = {Domain decomposition method with randomized neural networks}, - year = {2024}, - month = {August}, - abstract = {An approach for integrating randomized neural networks (RaNNs) with an overlapping Schwarz domain decomposition technique is developed to address multi-scale problems. Neural networks within each subdomain are interconnected using local window functions, enabling the construction of a global solution that serves as an approximation to the solution of the partial differential equation (PDE). Via a constraining operator the boundary conditions are enforced in a straightforward manner. The optimization of the parameters in the last layer of the RaNN yields a least-squares problem, leading to accurate solutions for the PDE. The introduction of a two-level domain decomposition method allows for capturing diverse scaling information, thereby enhancing the performance of the method.}, - note = {Submitted}, - keywords = {submitted, reviewed}, - bibtex_show = {true} -} - -@techreport{Heinlein:2024:NTL, - author = {Alexander Heinlein and Kyrill Ho and Axel Klawonn and Martin Lanser}, - title = {Nonlinear Two-Level Schwarz Methods: A Parallel Implementation in FROSch}, - year = {2024}, - month = {August}, - abstract = {Owing to the ability of nonlinear domain decomposition methods to improve the nonlinear convergence behavior of Newton's method, they have experienced a rise in popularity recently in the context of problems for which Newton'’'s method converges slowly or not at all. This article introduces a novel parallel implementation of a two-level nonlinear Schwarz solver based on the FROSch (Fast and Robust Overlapping Schwarz) solver framework, part of Sandia’s Trilinos library. First, an introduction to the key concepts underlying two-level nonlinear Schwarz methods is given, including a brief overview of the coarse space used to build the second level. Next, the parallel implementation is discussed, followed by preliminary parallel results for a scalar nonlinear diffusion problem and a 2D nonlinear plane-stress Neo-Hooke elasticity problem with large deformations.}, - note = {Submitted}, - keywords = {submitted, reviewed}, - bibtex_show = {true} -} - -@techreport{Dolean:2024:TDD, - author = {Victorita Dolean and Serge Gratton and Alexander Heinlein and Valentin Mercier}, - title = {Two-level deep domain decomposition method}, - year = {2024}, - month = {August}, - abstract = {This study presents a two-level Deep Domain Decomposition Method (Deep-DDM) augmented with a coarse-level network for solving boundary value problems using physics-informed neural networks (PINNs). The addition of the coarse level network improves scalability and convergence rates compared to the single level method. Tested on a Poisson equation with Dirichlet boundary conditions, the two-level deep DDM demonstrates superior performance, maintaining efficient convergence regardless of the number of subdomains. This advance provides a more scalable and effective approach to solving complex partial differential equations with machine learning.}, - note = {Submitted}, - preprint = {https://arxiv.org/abs/2408.12198}, - keywords = {submitted, reviewed}, - bibtex_show = {true} -} - -@techreport{Kinnewig:2024:CDF, - author = {Sebastian Kinnewig and Alexander Heinlein and Thomas Wick}, - title = {Coupling deal.II and FROSch: A Sustainable and Accessible (O)RAS Preconditioner}, - year = {2024}, - month = {August}, - abstract = {In this work, restricted additive Schwarz (RAS) and optimized restricted additive Schwarz (ORAS) preconditioners from the {\trilinos} package {\frosch} (Fast and Robust Overlapping Schwarz) are employed to solve model problems implemented using {\dealii} (differential equations analysis library). Therefore, a {\tpetra}-based interface for coupling {\dealii} and {\frosch} is implemented. While RAS preconditioners have been available before, ORAS preconditioners have been newly added to {\frosch}. The {\dealii}--{\frosch} interface works for both Lagrange-based and N\'ed\'elec finite elements. Here, as model problems, nonstationary, nonlinear, variational-monolithic fluid-structure interaction and the indefinite time-harmonic Maxwell's equations are considered. Several numerical experiments in two and three spatial dimensions confirm the performance of the preconditioners as well as the {\frosch}-{\dealii} interface. In conclusion, the overall software interface is straightforward and easy to use while giving satisfactory solver performances for challenging PDE systems.}, - note = {Submitted}, - preprint = {https://arxiv.org/abs/2410.22871}, - keywords = {submitted, reviewed}, - bibtex_show = {true} -} - -@techreport{Alves:2024:CSA, - author = {Filipe A. C. S. Alves and Alexander Heinlein and Hadi Hajibeygi}, - title = {A computational study of algebraic coarse spaces for two-level overlapping additive Schwarz preconditioners}, - year = {2024}, - month = {August}, - abstract = {The two-level overlapping additive Schwarz method offers a robust and scalable preconditioner for various linear systems resulting from elliptic problems. One of the key to these properties is the construction of the coarse space used to solve a global coupling problem, which traditionally requires information about the underlying discretization. An algebraic formulation of the coarse space reduces the complexity of its assembly. Furthermore, well-chosen coarse basis functions within this space can better represent changes in the problem's properties. Here we introduce an algebraic formulation of the multiscale finite element method (MsFEM) based on the algebraic multiscale solver (AMS) in the context of the two-level Schwarz method. We show how AMS is related to other energy-minimizing coarse spaces. Furthermore, we compare the AMS with other algebraic energy-minimizing spaces: the generalized Dryja--Smith--Widlund (GDSW), and the reduced dimension GDSW (RGDSW).}, - note = {Submitted}, - preprint = {https://arxiv.org/abs/2408.08187}, - keywords = {submitted, reviewed}, - bibtex_show = {true} -} - -@techreport{Sieburgh:2024:CSB, - author = {Erik Sieburgh and Alexander Heinlein and Vandana Dwarka and Cornelis Vuik}, - title = {Coarse Spaces Based on Higher-Order Interpolation for Schwarz Preconditioners for Helmholtz Problems}, - year = {2024}, - month = {August}, - abstract = {The development of scalable and wavenumber-robust iterative solvers for Helmholtz problems is challenging but also relevant for various application fields. In this work, two-level Schwarz domain decomposition preconditioners are enhanced by coarse space constructed using higher-order B\'ezier interpolation. The numerical results indicate numerical scalability and robustness with respect the wavenumber, as long as the wavenumber times the element size of the coarse mesh is sufficiently low.}, - note = {Submitted}, - preprint = {https://arxiv.org/abs/2408.03571}, - keywords = {submitted, reviewed}, - bibtex_show = {true} -} - -@techreport{Verburg:2024:DDU, - author = {Corné Verburg and Alexander Heinlein and Eric C. Cyr}, - title = {DDU-Net: A Domain Decomposition-based CNN for High-Resolution Image Segmentation on Multiple GPUs}, - year = {2024}, - month = {July}, - abstract = {The segmentation of ultra-high resolution images poses challenges such as loss of spatial information or computational inefficiency. In this work, a novel approach that combines encoder-decoder architectures with domain decomposition strategies to address these challenges is proposed. Specifically, a domain decomposition-based U-Net (DDU-Net) architecture is introduced, which partitions input images into non-overlapping patches that can be processed independently on separate devices. A communication network is added to facilitate inter-patch information exchange to enhance the understanding of spatial context. Experimental validation is performed on a synthetic dataset that is designed to measure the effectiveness of the communication network. Then, the performance is tested on the DeepGlobe land cover classification dataset as a real-world benchmark data set. The results demonstrate that the approach, which includes inter-patch communication for images divided into 16x16 non-overlapping subimages, achieves a 2-3% higher intersection over union (IoU) score compared to the same network without inter-patch communication. The performance of the network which includes communication is equivalent to that of a baseline U-Net trained on the full image, showing that our model provides an effective solution for segmenting ultra-high-resolution images while preserving spatial context. The code is available at https://github.com/corne00/HiRes-Seg-CNN.}, - note = {Submitted}, - preprint = {https://arxiv.org/abs/2407.21266}, - keywords = {submitted, reviewed}, - bibtex_show = {true} -} - -@techreport{Yamazaki:2024:PCB, - author = {Ichitaro Yamazaki and Alexander Heinlein and Sivasankaran Rajamanickam}, - title = {Predicting Coarse Basis Functions for Two-Level Domain Decomposition Methods Using Graph Neural Networks}, - year = {2024}, - month = {July}, - abstract = {For the robustness and numerical scalability of domain decomposition-based linear solvers, the incorporation of a coarse level, which provides global transport of information, is crucial. State-of-the-art spectral, or adaptive, methods can generate the basis functions of the coarse space, which are adapted to the specific properties of the target problem, and yield provably robust convergence for certain classes of problems. However, their construction is computationally expensive and requires non-algebraic information. To improve the practicability of the solver, in this paper, we design a hierarchical math-informed local Graph Neural Network (GNN) to generate effective coarse-space basis functions. Our GNN uses only the local subdomain matrices available as the input to the algebraic linear solvers. This approach has several advantages including: 1) it is algebraic; 2) it is local and therefore as scalable as the classical domain decomposition solvers; and 3) the cost for training, inference, and generating data sets is much lower than that needed for approaches relying on the global matrix. To study the potential of our GNN architecture, we present numerical results with homogeneous and heterogeneous problems.}, - note = {Submitted}, - keywords = {submitted, reviewed}, - bibtex_show = {true} -} - -@techreport{Howard:2024:FBK, - author = {Amanda A. Howard and Bruno Jacob and Sarah H. Murphy and Alexander Heinlein and Panos Stinis}, - title = {Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems}, - year = {2024}, - month = {June}, - abstract = {Kolmogorov-Arnold networks (KANs) have attracted attention recently as an alternative to multilayer perceptrons (MLPs) for scientific machine learning. However, KANs can be expensive to train, even for relatively small networks. Inspired by finite basis physics-informed neural networks (FBPINNs), in this work, we develop a domain decomposition method for KANs that allows for several small KANs to be trained in parallel to give accurate solutions for multiscale problems. We show that finite basis KANs (FBKANs) can provide accurate results with noisy data and for physics-informed training.}, - preprint = {https://arxiv.org/abs/2406.19662}, - keywords = {submitted}, - bibtex_show = {true} -} - -@techreport{Zandbergen:2024:IPT, - author = {Anouk Zandbergen and Tycho {van Noorden} and Alexander Heinlein}, - title = {Improving Pseudo-Time Stepping Convergence for CFD Simulations With Neural Networks}, - year = {2024}, - month = {June}, - abstract = {Computational fluid dynamics (CFD) simulations of viscous fluids described by the Navier--Stokes equations are considered. Depending on the Reynolds number of the flow, the Navier--Stokes equations may exhibit a highly nonlinear behavior. The system of nonlinear equations resulting from the discretization of the Navier--Stokes equations can be solved using nonlinear iteration methods, such as Newton's method. However, fast quadratic convergence is typically only obtained in a local neighborhood of the solution, and for many configurations, the classical Newton iteration does not converge at all. In such cases, so-called globalization techniques may help to improve convergence. In this paper, pseudo-transient continuation is employed in order to improve nonlinear convergence. The classical algorithm is enhanced by a neural network model that is trained to predict a local pseudo-time step. Generalization of the novel approach is facilitated by predicting the local pseudo-time step separately on each element using only local information on a patch of adjacent elements as input. Numerical results for standard benchmark problems, including flow through a backward facing step geometry and Couette flow, show the performance of the machine learning-enhanced globalization approach; as the software for the simulations, the CFD module of COMSOL Multiphysics® is employed.}, - note = {Submitted}, - preprint = {https://arxiv.org/abs/2310.06717}, - keywords = {submitted, reviewed}, - bibtex_show = {true} -} - -@techreport{Grimm:2023:LSO, - author = {Viktor Grimm and Alexander Heinlein and Axel Klawonn}, - title = {Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks}, - year = {2023}, - month = {August}, - abstract = {In recent years, the concept of introducing physics to machine learning has become widely popular. Most physics-inclusive ML-techniques however are still limited to a single geometry or a set of parametrizable geometries. Thus, there remains the need to train a new model for a new geometry, even if it is only slightly modified. With this work we introduce a technique with which it is possible to learn approximate solutions to the steady-state Navier--Stokes equations in varying geometries without the need of parametrization. This technique is based on a combination of a U-Net-like CNN and well established discretization methods from the field of the finite difference method. The results of our physics-aware CNN are compared to a state-of-the-art data-based approach. Additionally, it is also shown how our approach performs when combined with the data-based approach.}, - note = {Submitted}, - preprint = {https://arxiv.org/abs/2308.02137}, - keywords = {submitted, reviewed}, - bibtex_show = {true} -} diff --git a/_bibliography/talks.bib b/_bibliography/talks.bib deleted file mode 100644 index 089771861624..000000000000 --- a/_bibliography/talks.bib +++ /dev/null @@ -1,1316 +0,0 @@ ---- ---- -References -========== - -# talks - -@misc{Heinlein:2024:ISCL:TBA, - title = {TBA}, - author = {Alexander Heinlein}, - year = {2025}, - abbr = {ISCL}, - note = {Invited seminar talk. ISCL Seminar Series, Pennsylvania State University, USA, March 14}, - abstract = {TBA}, - video = {https://www.youtube.com/watch?v=087Y9pLFNqI}, - keywords = {} -} - -@misc{Heinlein:2025:SIAMCSE:DDN, - title = {Domain decomposition for neural networks}, - author = {Alexander Heinlein}, - year = {2025}, - abbr = {SIAM CSE25}, - note = {SIAM Conference on Computational Science and Engineering (CSE25), Fort Worth, Texas, U.S., March 3-7}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving research field that combines techniques from scientific computing and machine learning. This talk focuses on the application of domain decomposition methods to design neural network architectures and enhance neural network training, Specifically, it explores the use of domain decomposition techniques in neural network-based discretizations for solving partial differential equations with physics-informed neural networks (PINNs) and operator learning, as well as in classical machine learning tasks like semantic image segmentation using convolutional neural networks (CNNs). Computational results show that domain decomposition methods can improve efficiency — both in terms of time and memory — as well as enhance accuracy and robustness.}, - url = {https://www.siam.org/conferences-events/siam-conferences/cse25/}, - keywords = {} -} - -@misc{Heinlein:2025:IMG:TBA, - title = {TBA}, - author = {Alexander Heinlein}, - year = {2025}, - abbr = {Seminar}, - note = {Invited plenary talk. International Multigrid Conference (IMG) 2025, King Abdullah University of Science and Technology (KAUST), Saudi Arabia, February 3-5}, - abstract = {TBA}, - keywords = {selected} -} - -@misc{Heinlein:2025:SML:DDA, - title = {Domain decomposition and adaptive sampling for physics-informed neural networks}, - author = {Alexander Heinlein}, - year = {2025}, - abbr = {Seminar}, - note = {Invited talk. Workshop "Scientific machine learning: error estimation and analysis", Besançon, France, January 15-16}, - abstract = {TBA}, - url = {https://sites.google.com/unipv.it/sciml-errorcontrolanalysis/}, - keywords = {selected} -} - -@misc{Heinlein:2024:CASML:GCM, - title = {Geometric Challenges in Machine Learning-Based Surrogate Models}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {CASML@2024}, - note = {Invited plenary talk. International Conference on Applied AI and Scientific Machine Learning (CASML 2024), Indian Institute of Science (IISc), Bangalore, India, December 14-18}, - abstract = {Surrogate models—machine learning models designed to approximate complex and computationally expensive numerical simulations—are a key topic in scientific machine learning. These models are particularly relevant for parametrized problems, predicting solutions across a range of parameter configurations. While much of the existing work focuses on low-dimensional parameterizations, such as constant material properties, higher-dimensional parameterizations—spatially or temporally varying initial or boundary conditions, material distributions, or source terms—present significant methodological and computational challenges. Moreover, these cases are particularly important, as the potential benefits of the resulting surrogate models are even greater. This talk explores geometric aspects of machine learning-based surrogate modeling, focusing on convolutional neural networks and neural operators, such as deep operator networks (DeepONets). Both data-driven and physics-informed loss terms are being considered, and some novel directions are motivated for physics-informed neural networks (PINNs). The presentation focuses on strategies for learning complex spatial solution behaviors, addressing variations in the computational domain, and improving operator performance and scalability through spatio-temporal decomposition. Applications in multiscale and wave problems, as well as computational fluid dynamics, illustrate the potential of these methods.}, - url = {https://casml.iisc.ac.in/}, - slides = {2024/2024-heinlein-casml-surrogates/2024-heinlein-surrogates.pdf}, - keywords = {selected} -} - -@misc{Heinlein:2024:IWR:WOL, - title = {When One Level Is Not Enough -- Multilevel Domain Decomposition Methods for Physics and Data-Driven Problems}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {Seminar}, - note = {Invited seminar talk. Heidelberg University, Heidelberg, Germany, December 5}, - abstract = {Domain decomposition methods (DDMs) solve boundary value problems by decomposing them into smaller subproblems defined on an overlapping or non-overlapping decomposition of the computational domain. Their divide-and-conquer approach makes DDMs well-suited for large-scale problems and parallel computing. However, achieving robust convergence for challenging problems and scalability to large numbers of subdomains generally requires (global) information transport. This can be achieved by incorporating well-designed coarse levels, transforming DDMs from one- into multi-level algorithms. This talk highlights the importance of using multiple levels in domain decomposition methods. In the first part of the talk, coarse spaces for domain decomposition-based preconditioners will be discussed. They can provide robustness and scalability to Schwarz preconditioners for a wide range of challenging problems exhibiting, for instance, strong heterogeneities, multiple coupled physics, and/or strong nonlinearities. Numerical results using the FROSch (Fast and Robust Overlapping Schwarz) package, which is part of the Trilinos library, demonstrate the effectiveness and efficiency of these Schwarz preconditioners. The second part of the talk will explore the application of DDMs to neural networks (NNs), demonstrating improvements in terms of accuracy, computation time, and/or memory efficiency. Similar to classical domain decomposition methods, coarse levels, here in the form of small global NNs, ensure global information transport, enabling scalability. This talk will cover the application of DDMs in solving partial differential equations using physics-informed NNs (PINNs) and in image segmentation using convolutional NNs (CNNs).}, - slides = {2024/2024-heinlein-iwr-multilevel_dd/2024-heinlein-multilevel_dd.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:CASA:WOL, - title = {When One Level Is Not Enough -- Multilevel Domain Decomposition Methods for Physics and Data-Driven Problems}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {CASA}, - note = {Invited seminar talk. CASA colloquium, TU Eindhoven, Eindhoven, The Netherlands, November 20}, - abstract = {Domain decomposition methods (DDMs) solve boundary value problems by decomposing them into smaller subproblems defined on an overlapping or non-overlapping decomposition of the computational domain. Their divide-and-conquer approach makes DDMs well-suited for large-scale problems and parallel computing. However, achieving robust convergence for challenging problems and scalability to large numbers of subdomains generally requires (global) information transport. This can be achieved by incorporating well-designed coarse levels, transforming DDMs from one- into multi-level algorithms. This talk highlights the importance of using multiple levels in domain decomposition methods. In the first part of the talk, coarse spaces for domain decomposition-based preconditioners will be discussed. They can provide robustness and scalability to Schwarz preconditioners for a wide range of challenging problems exhibiting, for instance, strong heterogeneities, multiple coupled physics, and/or strong nonlinearities. Numerical results using the FROSch (Fast and Robust Overlapping Schwarz) package, which is part of the Trilinos library, demonstrate the effectiveness and efficiency of these Schwarz preconditioners. The second part of the talk will explore the application of DDMs to neural networks (NNs), demonstrating improvements in terms of accuracy, computation time, and/or memory efficiency. Similar to classical domain decomposition methods, coarse levels, here in the form of small global NNs, ensure global information transport, enabling scalability. This talk will cover the application of DDMs in solving partial differential equations using physics-informed NNs (PINNs) and in image segmentation using convolutional NNs (CNNs).}, - url = {https://casa.win.tue.nl/home/event/colloquium-alexander-heinlein-tu-delft}, - slides = {2024/2024-heinlein-casa-multilevel_dd/2024-heinlein-multilevel_dd.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:MDS:DDN, - title = {Domain Decomposition for Neural Networks: Physics-Informed Neural Networks, Operator Learning, and Image Segmentation}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {Seminar}, - note = {Invited seminar talk. Mathematics of Data Science seminar, University of Twente, Enschede, The Netherlands, November 4}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving research field that combines techniques from scientific computing and machine learning. This talk focuses on the application of domain decomposition methods to design neural network architectures and enhance neural network training. In particular, it explores how domain decomposition techniques can be employed in neural network-based discretizations to address forward and inverse problems involving partial differential equations using physics-informed neural networks (PINNs) as well as in neural operators. Furthermore, the talk explores the use of domain decomposition methods for traditional machine learning tasks, such as semantic image segmentation with convolutional neural networks (CNNs). Computational results show that domain decomposition methods can improve efficiency—both in terms of time and memory—as well as enhance accuracy and robustness.}, - keywords = {} -} - -@misc{Heinlein:2024:Konstanz:DDN, - title = {Domain decomposition for neural networks}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {Seminar}, - note = {Invited seminar talk. University of Konstanz, Konstanz, Germany, October 30}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving research field that combines techniques from scientific computing and machine learning. This talk focuses on the application of domain decomposition methods to design neural network architectures and enhance neural network training, Specifically, it explores the use of domain decomposition techniques in neural network-based discretizations for solving partial differential equations with physics-informed neural networks (PINNs) and operator learning, as well as in classical machine learning tasks like semantic image segmentation using convolutional neural networks (CNNs). Computational results show that domain decomposition methods can improve efficiency - both in terms of time and memory - as well as enhance accuracy and robustness.}, - url = {https://sites.google.com/view/network-platform-cs-math/schedule-and-abstracts}, - slides = {2024/2024-heinlein-konstanz-ddn/2024-heinlein-dd_nns.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:IGHASC:DDN, - title = {Domain decomposition for neural networks}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {IGHASC}, - note = {Indo-German Workshop on Hardware-aware Scientific Computing. Heidelberg University, Heidelberg, Germany, October 28-30}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving field of research that combines techniques from scientific computing and machine learning. In this context, this talks focuses on the enhancement of machine learning using classical numerical methods, in particular, on improving neural networks using domain decomposition-inspired architectures. In the first part of this talk, the domain decomposition paradigm is applied to the approximation of the solutions of partial differential equations (PDEs) using physics-informed neural networks (PINNs). It is observed that network architectures inspired by multi-level Schwarz domain decomposition methods can improve the performance for certain challenging problems, such as multiscale problems. Moreover, a classical machine learning task is considered, that is, image segmentation using convolutional neural networks (CNNs). Domain decomposition techniques offer a way of scaling up common CNN architectures, such as the U-Net. In particular, local subdomain networks learn local features and are coupled via a coarse network which incorporates global features.}, - url = {https://conan.iwr.uni-heidelberg.de/events/hasc_workshop2024/}, - slides = {2024/2024-heinlein-ighasc-ddn/2024-heinlein-dd_nns.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:NA:DPI, - title = {Why Domain Decomposition Preconditioning for Highly Heterogeneous Problems is Challenging and How Machine Learning Can Help}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {TU Delft}, - note = {Numerical Analysis group coffee talk. Delft University of Technology, Netherlands, October 11}, - keywords = {} -} - -@misc{Heinlein:2024:MarburgKolloquium:RAS, - title = {Domain decomposition techniques for high-performance scientific computing}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {Colloquium}, - note = {Kolloquium des Fachbereichs Mathematik und Informatik, Universit\"at Marburg, Marburg, Germany, October 10}, - keywords = {} -} - -@misc{Heinlein:2024:NHR2024:DDN, - title = {Domain decomposition for neural networks}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {NHR2024}, - note = {Invited talk. NHR Conference 2024, Darmstadt, Germany, September 9-12}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving research field that combines techniques from scientific computing and machine learning. This talk focuses on the application of domain decomposition methods to design neural network architectures and enhance neural network training, Specifically, it explores the use of domain decomposition techniques in neural network-based discretizations for solving partial differential equations with physics-informed neural networks (PINNs) and operator learning, as well as in classical machine learning tasks like semantic image segmentation using convolutional neural networks (CNNs). Computational results show that domain decomposition methods can improve efficiency — both in terms of time and memory — as well as enhance accuracy and robustness.}, - url = {https://www.nhr-verein.de/NHR-Conference}, - slides = {2024/2024-heinlein-nhr-ddn/2024-heinlein-dd_nns.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:UM:FRO, - title = {Fast and Robust Overlapping Schwarz (FROSch) Domain Decomposition Preconditioners}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {Seminar}, - note = {Invited seminar talk. University of Macau, Macao, China, August 7}, - abstract = {The Schwarz domain decomposition framework is a powerful algorithmic framework for efficiently solving partial differential equations by decomposing a complex global problem into smaller, local subproblems. The FROSch (Fast and Robust Overlapping Schwarz) package, which is part of the Trilinos software library, leverages this framework. Moreover, FROSch employs extension-based coarse spaces to allow for constructing scalable and algebraic multilevel Schwarz preconditioners. In this context, "algebraic" means that the preconditioners can be constructed using only the fully assembled, parallel distributed system matrix. This talk gives an overview of the capabilities of FROSch and delves into recent developments. This includes: 1) exploring the use of inexact local solvers on both GPUs and CPUs to improve computing times; 2) the development of monolithic and adaptive coarse spaces to broaden the range of problems FROSch can tackle; 3) investigations into utilizing machine learning techniques, such as graph neural networks, to improve the construction of coarse bases. The performance of these approaches is evaluated across various problem types, encompassing simple model problems as well as complex multi-physics problems that address real-world applications.}, - slides = {2024/2024-heinlein-um-fro/2024-heinlein-frosch.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:SIAT:DDN, - title = {Domain decomposition for neural networks}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {Seminar}, - note = {Invited seminar talk. Shenzhen Institutes of Advanced Technology, China, July 31}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving research field that combines techniques from scientific computing and machine learning. This talk specifically addresses the application of domain decomposition methods to design neural network architectures and enhance neural network training. The discussion will explore the use of these techniques in neural network-based discretizations for solving partial differential equations with physics-informed neural networks (PINNs) and operator learning, as well as in classical machine learning tasks like semantic image segmentation using convolutional neural networks (CNNs). Computational results show that domain decomposition methods can improve efficiency — both in terms of time and memory — as well as enhance accuracy and robustness.}, - slides = {2024/2024-heinlein-siat-ddn/2024-heinlein-dd_nns.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:IRMA2024:DDN, - title = {Domain decomposition for neural networks}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {SU}, - note = {Invited talk. Workshop on Scientific Machine Learning, Strasbourg University, Strasbourg, France, July 8-12}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving field of research that combines techniques from scientific computing and machine learning. In this context, this talks focuses on the enhancement of machine learning using classical numerical methods, in particular, on improving neural networks using domain decomposition-inspired architectures. In the first part of this talk, the domain decomposition paradigm is applied to the approximation of the solutions of partial differential equations (PDEs) using physics-informed neural networks (PINNs). It is observed that network architectures inspired by multi-level Schwarz domain decomposition methods can improve the performance for certain challenging problems, such as multiscale problems. Moreover, a classical machine learning task is considered, that is, image segmentation using convolutional neural networks (CNNs). Domain decomposition techniques offer a way of scaling up common CNN architectures, such as the U-Net. In particular, local subdomain networks learn local features and are coupled via a coarse network which incorporates global features.}, - url = {https://irma.math.unistra.fr/~micheldansac/SciML2024/participants.html}, - slides = {2024/2024-heinlein-irma2024-ddn/2024-heinlein-dd_nns.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:DLNM:DDP, - title = {Domain decomposition for physics-informed neural networks}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {XJU}, - note = {Invited talk. International Workshop on Deep Learning and Numerical Methods for PDEs, Xi’an, China, June 21-23}, - abstract = {Physics-informed neural networks (PINNs) are a class of methods for solving differential equation-based problems using a neural network as the discretization. PINNs have been introduced by Raissi et al. and combine the pioneering collocation approach for neural network functions introduced by Lagaris et al. with the incorporation of data via an additional loss term. PINNs are very versatile as they do not require an explicit mesh, allow for the solution of parameter identification problems, and are well-suited for high-dimensional problems. However, the training of a PINN model is generally not very robust and may require careful hyper parameter tuning. In particular, due to the so-called spectral bias, the training of PINN models is notoriously difficult when scaling up to large computational domains as well as for multiscale problems. In this talk, overlapping domain decomposition-based techniques for PINNs are being discussed. One way to incorporate the domain decomposition approach is to introduce an outer Schwarz iteration and solve the local subdomain problems using a PINN model. This approach has been introduced as the deep learning-based domain decomposition (DeepDDM) method. On the other hand, in the finite basis physics-informed neural networks (FBPINNs) approach, the domain decomposition is introduced via the network architecture, and the coupling is performed implicitly without introducing additional loss terms. Inspired by the space decomposition of classical Schwarz methods, a general framework, that also allows for multilevel extensions, can be introduced. The multilevel FBPINN method outperforms classical PINNs on several types of problems, including multiscale problems, both in terms of accuracy and efficiency. Finally, the combination of the multilevel domain decomposition strategy with multifidelity stacking PINNs, introduced as stacking FBPINNs for time-dependent problems, will be discussed. It can be observed that the combination of multifidelity stacking PINNs with a domain decomposition in time clearly improves the reference results without a domain decomposition.}, - slides = {2024/2024-heinlein-dlnm-ddp/2024-heinlein-dd_pinns.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:XUT:DDP, - title = {Domain decomposition for physics-informed neural networks}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {XUT}, - note = {Invited talk. Xi'an University of Technology, Xi’an, China, June 21}, - abstract = {Physics-informed neural networks (PINNs) are a class of methods for solving differential equation-based problems using a neural network as the discretization. PINNs have been introduced by Raissi et al. and combine the pioneering collocation approach for neural network functions introduced by Lagaris et al. with the incorporation of data via an additional loss term. PINNs are very versatile as they do not require an explicit mesh, allow for the solution of parameter identification problems, and are well-suited for high-dimensional problems. However, the training of a PINN model is generally not very robust and may require careful hyper parameter tuning. In particular, due to the so-called spectral bias, the training of PINN models is notoriously difficult when scaling up to large computational domains as well as for multiscale problems. In this talk, overlapping domain decomposition-based techniques for PINNs are being discussed. One way to incorporate the domain decomposition approach is to introduce an outer Schwarz iteration and solve the local subdomain problems using a PINN model. This approach has been introduced as the deep learning-based domain decomposition (DeepDDM) method. On the other hand, in the finite basis physics-informed neural networks (FBPINNs) approach, the domain decomposition is introduced via the network architecture, and the coupling is performed implicitly without introducing additional loss terms. Inspired by the space decomposition of classical Schwarz methods, a general framework, that also allows for multilevel extensions, can be introduced. The multilevel FBPINN method outperforms classical PINNs on several types of problems, including multiscale problems, both in terms of accuracy and efficiency. Finally, the combination of the multilevel domain decomposition strategy with multifidelity stacking PINNs, introduced as stacking FBPINNs for time-dependent problems, will be discussed. It can be observed that the combination of multifidelity stacking PINNs with a domain decomposition in time clearly improves the reference results without a domain decomposition.}, - slides = {2024/2024-heinlein-xut-ddp/2024-heinlein-dd_pinns.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:P24:ICL, - title = {The importance of coarse levels for domain decomposition methods}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {Precond 24}, - note = {Invited plenary lecture. International Conference On Preconditioning Techniques For Scientific and Industrial Applications (Precond 24), Georgia Institute of Technology, Atlanta, USA , June 10-12}, - abstract = {Domain decomposition methods (DDMs) solve boundary value problems by decomposing them into smaller subproblems defined on an overlapping or non-overlapping decomposition of the computational domain. Their divide-and-conquer approach makes them well-suited for parallel computing. However, achieving robust convergence for challenging problems and scalability to large numbers of subdomains generally requires (global) information transport. This can be achieved by incorporating a well-designed coarse level, transforming DDMs from one- to multi-level algorithms. This talk highlights the importance of coarse levels in domain decomposition methods. First, the algorithmic framework of extension-based coarse spaces will be discussed. They provide robustness and scalability to Schwarz preconditioners for a wide range of challenging problems exhibiting, for instance, strong heterogeneities, multiple coupled physics, and/or strong nonlinearities. Numerical results using the FROSch (Fast and Robust Overlapping Schwarz) package, which is part of the Trilinos library, demonstrate the effectiveness and efficiency of these Schwarz preconditioners. The second part of the talk will explore the application of DDMs to neural networks (NNs), demonstrating improvements in terms of accuracy, computation time, and/or memory efficiency. Similar to classical domain decomposition methods, coarse levels, here in the form of small global NNs, ensure global information transport, enabling scalability. This talk will cover the application of DDMs in solving partial differential equations using physics-informed NNs (PINNs) and in image segmentation using convolutional NNs (CNNs).}, - url = {https://www.math.emory.edu/~yxi26/Precond24/}, - slides = {2024/2024-heinlein-p24-icl/2024-heinlein-dd-coarse_spaces.pdf}, - keywords = {selected} -} - -@misc{Heinlein:2024:ECCOMAS2024:DDN, - title = {Domain decomposition for neural networks}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {ECCOMAS2024}, - note = {9th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2024), Lisbon, Portugal, June 3-7}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving field of research that combines techniques from scientific computing and machine learning. In this context, this talks focuses on the enhancement of machine learning using classical numerical methods, in particular, on improving neural networks using domain decomposition-inspired architectures. In the first part of this talk, the domain decomposition paradigm is applied to the approximation of the solutions of partial differential equations (PDEs) using physics-informed neural networks (PINNs). It is observed that network architectures inspired by multi-level Schwarz domain decomposition methods can improve the performance for certain challenging problems, such as multiscale problems. This part of the talk is based on joint work with Victorita Dolean (University of Strathclyde, Côte d’Azur University), Siddhartha Mishra, and Ben Moseley (ETH Zürich). Moreover, a classical machine learning task is considered, that is, image segmentation using convolutional neural networks (CNNs). Domain decomposition techniques offer a way of scaling up common CNN architectures, such as the U-Net. In particular, local subdomain networks learn local features and are coupled via a coarse network which incorporates global features. The second part of this talk is based on joint work with Eric Cyr (Sandia National Laboratories) and Corné Verburg (Delft University of Technology).}, - url = {https://eccomas2024.org/}, - slides = {2024/2024-heinlein-eccomas2024-ddn/2024-heinlein-dd_nns.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:CAS:DDP, - title = {Domain decomposition for physics-informed neural networks}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {Seminar}, - note = {Invited seminar talk. Institute of Mathematics of the Czech Academy of Sciences, Prague, Czech Republic, May 24}, - abstract = {Physics-informed neural networks (PINNs) are a class of methods for solving differential equation-based problems using a neural network as the discretization. PINNs have been introduced by Raissi et al. and combine the pioneering collocation approach for neural network functions introduced by Lagaris et al. with the incorporation of data via an additional loss term. PINNs are very versatile as they do not require an explicit mesh, allow for the solution of parameter identification problems, and are well-suited for high-dimensional problems. However, the training of a PINN model is generally not very robust and may require careful hyper parameter tuning. In particular, due to the so-called spectral bias, the training of PINN models is notoriously difficult when scaling up to large computational domains as well as for multiscale problems. In this talk, overlapping domain decomposition-based techniques for PINNs are being discussed. One way to incorporate the domain decomposition approach is to introduce an outer Schwarz iteration and solve the local subdomain problems using a PINN model. This approach has been introduced as the deep learning-based domain decomposition (DeepDDM) method. On the other hand, in the finite basis physics-informed neural networks (FBPINNs) approach, the domain decomposition is introduced via the network architecture, and the coupling is performed implicitly without introducing additional loss terms. Inspired by the space decomposition of classical Schwarz methods, a general framework, that also allows for multilevel extensions, can be introduced. The multilevel FBPINN method outperforms classical PINNs on several types of problems, including multiscale problems, both in terms of accuracy and efficiency. Finally, the combination of the multilevel domain decomposition strategy with multifidelity stacking PINNs, introduced as stacking FBPINNs for time-dependent problems, will be discussed. It can be observed that the combination of multifidelity stacking PINNs with a domain decomposition in time clearly improves the reference results without a domain decomposition.}, - url = {https://www.math.cas.cz/index.php/events/seminar/12}, - slides = {2024/2024-heinlein-cas-ddp/2024-heinlein-dd_pinns.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:HPCSE2024:FRO, - title = {Fast and Robust Overlapping Schwarz (FROSch) Domain Decomposition Preconditioners}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {HPCSE 2024}, - note = {Invited plenary lecture. High Performance Computing in Science and Engineering 2024 conference (HPCSE 2024), Beskydy, Czech Republic, May 20 - 23}, - abstract = {The Schwarz domain decomposition framework is a powerful algorithmic framework for efficiently solving partial differential equations by decomposing a complex global problem into smaller, local subproblems. The FROSch (Fast and Robust Overlapping Schwarz) package, which is part of the Trilinos software library, leverages this framework. Moreover, FROSch employs extension-based coarse spaces to allow for constructing scalable and algebraic multilevel Schwarz preconditioners. In this context, "algebraic" means that the preconditioners can be constructed using only the fully assembled, parallel distributed system matrix. This talk gives an overview of the capabilities of FROSch and delves into recent developments. This includes: 1) exploring the use of inexact local solvers on both GPUs and CPUs to improve computing times; 2) the development of monolithic and adaptive coarse spaces to broaden the range of problems FROSch can tackle; 3) investigations into utilizing machine learning techniques, such as graph neural networks, to improve the construction of coarse bases. The performance of these approaches is evaluated across various problem types, encompassing simple model problems as well as complex multi-physics problems that address real-world applications.}, - url = {https://hpcse.it4i.cz/HPCSE24/}, - slides = {2024/2024-heinlein-hpcse2024-fro/2024-heinlein-frosch.pdf}, - keywords = {selected} -} - -@misc{Heinlein:2024:CRUNCH:DDP, - title = {Domain decomposition for physics-informed neural networks}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {CRUNCH}, - note = {Invited seminar talk. CRUNCH seminar, CRUNCH Group, Division of Applied Mathematics, Brown University, USA, March 22}, - abstract = {Physics-informed neural networks (PINNs) are a class of methods for solving differential equation-based problems using a neural network as the discretization. They have been introduced by Raissi et al. and combine the pioneering collocation approach for neural network functions introduced by Lagaris et al. with the incorporation of data via an additional loss term. PINNs are very versatile as they do not require an explicit mesh, allow for the solution of parameter identification problems, and are well-suited for high-dimensional problems. However, the training of a PINN model is generally not very robust and may require a lot of hyper parameter tuning. In particular, due to the so-called spectral bias, the training of PINN models is notoriously difficult when scaling up to large computational domains as well as for multiscale problems. In this talk, overlapping domain decomposition-based techniques for PINNs are being discussed. Compared with other domain decomposition techniques for PINNs, in the finite basis physics-informed neural networks (FBPINNs) approach, the coupling is done implicitly via the overlapping regions and does not require additional loss terms. Using the classical Schwarz domain decomposition framework, a very general framework, that also allows for mult-level extensions, can be introduced. The method outperforms classical PINNs on several types of problems, including multiscale problems, both in terms of accuracy and efficiency. Furthermore, the combination of the multi-level domain decomposition strategy with multifidelity stacking PINNs for time-dependent problems will be discussed. It can be observed that the combination of multifidelity stacking PINNs with a domain decomposition in time clearly improves the reference results without a domain decomposition.}, - url = {https://sites.brown.edu/crunch-group/seminars/machine-learning-x-seminars/machine-learning-x-seminars-2022-2/}, - slides = {2024/2024-heinlein-crunch-ddp/2024-heinlein-dd_pinns.pdf}, - video = {https://www.youtube.com/watch?v=087Y9pLFNqI}, - keywords = {} -} - -@misc{Heinlein:2024:Sandia:DDP, - title = {Fast and Robust Overlapping Schwarz (FROSch) Preconditioners in Trilinos}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {Sandia}, - note = {Seminar talk, Sandia National Laboratories, USA, March 19}, - abstract = {Schwarz methods are an algorithmic framework for a large class of domain decomposition methods. FROSch (Fast and Robust Overlapping Schwarz), which is part of the Trilinos package ShyLU, provides a highly scalable implementation of the Schwarz framework. FROSch mostly focuses on Schwarz operators that are algebraic in the sense that they can be constructed from a fully assembled, parallel distributed matrix. This is facilitated by the use of extension-based coarse spaces, such as generalized Dryja-Smith-Wildund (GDSW) type coarse spaces. This talk gives an overview of the FROSch software framework and summarizes current developments.}, - slides = {2024/2024-heinlein-sandia-fro/2024-heinlein-frosch.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:SIAMPP:ESP, - title = {Efficient Schwarz Preconditioning Techniques on Current Hardware Using FROSch}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {SIAMPP}, - note = {SIAM Conference on Parallel Processing for Scientific Computing (PP24), Baltimore, USA, March 5 - 8}, - abstract = {FROSch (Fast and Robust Overlapping Schwarz) is a framework for parallel Schwarz domain decomposition preconditioners in Trilinos. It is applicable to a wide range of problems due to its algebraic approach, which allows the preconditioners to be constructed from a fully assembled, parallel distributed matrix. This is enabled by the use of extension-based coarse spaces instead of classical coarse spaces. FROSch also features a variety of algorithmic variants that extend its applicability and scalability. These include monolithic preconditioning for block systems and multi-level extensions. This talk will focus on recent developments in FROSch that improve the efficiency of Schwarz preconditioners for current hardware architectures. These include techniques for reducing communication and global work, lower precision preconditioning, as well as techniques for facilitating GPUs. The performance of the different techniques will be demonstrated for different application problems and using different state-of-the-art supercomputers.}, - url = {https://www.siam.org/conferences/cm/conference/pp24}, - slides = {2024/2024-heinlein-siampp24-esp/2024-heinlein-frosch.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:Geneva:DDP, - title = {Domain decomposition for physics-informed neural networks}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {Seminar}, - note = {Invited seminar talk. Séminaire d'analyse numérique, Université de Genève, Geneva, Switzerland, February 20}, - abstract = {Physics-informed neural networks (PINNs) are a class of methods for solving differential equation-based problems using a neural network as the discretization. They have been introduced by Raissi et al. and combine the pioneering collocation approach for neural network functions introduced by Lagaris et al. with the incorporation of data via an additional loss term. PINNs are very versatile as they do not require an explicit mesh, allow for the solution of parameter identification problems, and are well-suited for high-dimensional problems. However, the training of a PINN model is generally not very robust and may require a lot of hyper parameter tuning. In particular, due to the so-called spectral bias, the training of PINN models is notoriously difficult when scaling up to large computational domains as well as for multiscale problems. In this talk, overlapping domain decomposition-based techniques for PINNs are being discussed. Compared with other domain decomposition techniques for PINNs, in the finite basis physics-informed neural networks (FBPINNs) approach, the coupling is done implicitly via the overlapping regions and does not require additional loss terms. Using the classical Schwarz domain decomposition framework, a very general framework, that also allows for mult-level extensions, can be introduced. The method outperforms classical PINNs on several types of problems, including multiscale problems, both in terms of accuracy and efficiency. Furthermore, the combination of the multi-level domain decomposition strategy with multifidelity stacking PINNs for time-dependent problems will be discussed. It can be observed that the combination of multifidelity stacking PINNs with a domain decomposition in time clearly improves the reference results without a domain decomposition.}, - url = {https://www.unige.ch/math/annonces/seminaire-danalyse-numerique}, - slides = {2024/2024-heinlein-geneva-ddp/2024-heinlein-dd_pinns.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:ANCS:DDP, - title = {Domain decomposition for physics-informed neural networks}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {ANCS}, - note = {Invited seminar talk. ANCS Seminar, Laboratoire de Mathématiques, Besançon, France, February 16}, - abstract = {Physics-informed neural networks (PINNs) are a class of methods for solving differential equation-based problems using a neural network as the discretization. They have been introduced by Raissi et al. and combine the pioneering collocation approach for neural network functions introduced by Lagaris et al. with the incorporation of data via an additional loss term. PINNs are very versatile as they do not require an explicit mesh, allow for the solution of parameter identification problems, and are well-suited for high-dimensional problems. However, the training of a PINN model is generally not very robust and may require a lot of hyper parameter tuning. In particular, due to the so-called spectral bias, the training of PINN models is notoriously difficult when scaling up to large computational domains as well as for multiscale problems. In this talk, overlapping domain decomposition-based techniques for PINNs are being discussed. Compared with other domain decomposition techniques for PINNs, in the finite basis physics-informed neural networks (FBPINNs) approach, the coupling is done implicitly via the overlapping regions and does not require additional loss terms. Using the classical Schwarz domain decomposition framework, a very general framework, that also allows for mult-level extensions, can be introduced. The method outperforms classical PINNs on several types of problems, including multiscale problems, both in terms of accuracy and efficiency. Furthermore, the combination of the multi-level domain decomposition strategy with multifidelity stacking PINNs for time-dependent problems will be discussed. It can be observed that the combination of multifidelity stacking PINNs with a domain decomposition in time clearly improves the reference results without a domain decomposition.}, - slides = {2024/2024-heinlein-ancs-ddp/2024-heinlein-dd_pinns.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:DD28:SCS, - title = {Scalable coarse spaces for monolithic Schwarz preconditioners}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {DD28}, - note = {28th International Conference on Domain Decomposition Methods (DD28), King Abdullah University of Science and Technology (KAUST), Saudi Arabia, January 28 - February 1}, - abstract = {Monolithic GDSW (generalized Dryja–Smith–Wildund) preconditioners are scalable two-level Schwarz preconditioners for block systems. Compared with block domain decomposition preconditioners, monolithic domain decomposition preconditioners often yield faster convergence since they account for the coupling within the subdomain and coarse problems. In this talk, the focus is on computational fluid dynamics (CFD) simulations, in particular, saddle point problem resulting from the discretization of the (Navier-)Stokes equations. In this case, numerical results show that fast convergence and scalability of monolithic Schwarz preconditioners strongly depends on the choice of an appropriate pair of the velocity and pressure coarse spaces; in particular, there seem to be parallels to inf-sup stable discretizations. Whereas inf-sup stable Lagrangian coarse spaces, for instance, based on Taylor-Hood elements, yield scalable monolithic preconditioners, they are limited in their applicability to complicated geometries and unstructured domain decompositions. GDSW-type coarse spaces are well-suited for those cases, but, in general, an extension of the GDSW approach is required to construct appropriate pairs of velocity and pressure coarse spaces. Therefore, in this talk, a wider class of extension-based coarse spaces using various interface partitions of unity is explored. The numerical and parallel scalability for (Navier-)Stokes problems is then investigated using the parallel FROSch (Fast and Robust Overlapping Schwarz) preconditioner framework in Trilinos.}, - url = {https://dd28.kaust.edu.sa/}, - keywords = {} -} - -@misc{Heinlein:2024:DD28:MLD, - title = {Multi-level domain decomposition-based physics-informed neural networks}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {DD28}, - note = {28th International Conference on Domain Decomposition Methods (DD28), King Abdullah University of Science and Technology (KAUST), Saudi Arabia, January 28 - February 1}, - abstract = {Scientific machine learning (SciML) is a rapidly growing field that combines scientific computing and machine learning to solve complex scientific problems. A major branch of SciML is the approximation of the solutions of partial differential equations (PDEs) using neural networks. One popular example are physics-informed neural networks (PINNs), which are trained by minimizing a loss function that may include both a data error and a residual error, the latter of which enforces the governing PDE. Challenging applications, such as multiscale problems, require neural networks with high capacity and often lead to challenges in the training. In this talk, multi-level domain decomposition-based approaches for PINNs will be discussed. Therefore, on each level, the domain is decomposed into overlapping subdomains, and a separate network is constructed on each subdomain. The networks are then trained using a monolithic optimization loop, where the subdomain networks are coupled in an additive way using partition of unity functions. Numerical results for several model problems, including challenging multiscale problems, that demonstrate the robust convergence of the multi-level domain decomposition approach are presented.}, - url = {https://dd28.kaust.edu.sa/}, - slides = {2024/2024-heinlein-dd28-fbpinns/2024-heinlein-fbpinns.pdf}, - keywords = {} -} - -@misc{Heinlein:2024:DD28:ESP, - title = {Efficient Schwarz preconditioning techniques for nonlinear problems}, - author = {Alexander Heinlein}, - year = {2024}, - abbr = {DD28}, - note = {28th International Conference on Domain Decomposition Methods (DD28), King Abdullah University of Science and Technology (KAUST), Saudi Arabia, January 28 - February 1}, - abstract = {This talk discusses several techniques for efficiently solving nonlinear problems using Schwarz methods. Newton-Krylov methods are widely used to solve nonlinear problems numerically. These methods linearize the system using Newton's method and solve the resulting linearized systems using a (preconditioned) Krylov method. When using domain decomposition preconditioners, the efficiency can be enhanced if information about the preconditioner from previous linearizations is reused. This includes structural information, such as the domain decomposition, certain index sets, and symbolic factorizations of the subdomain and coarse problems, but also certain components of the preconditioner, such as the coarse space. This typically leads to a speedup in the setup phase, resulting in a dominance of the time required for the solve phase; the solve phase can then be sped up by assign computations to GPUs. As an alternative to Newton-Krylov methods, nonlinear Schwarz preconditioning techniques can be employed to speed up both the nonlinear and linear convergence. In order to facilitate numerical scalability to large numbers of subdomains, a multi-level approach has to be employed; this leads to nonlinear multi-level Schwarz methods. The aforementioned approaches are being discussed and investigated in numerical experiments.}, - url = {https://dd28.kaust.edu.sa/}, - slides = {2024/2024-heinlein-dd28-nonlinear_schwarz/2024-heinlein-nonlinear_schwarz.pdf}, - keywords = {} -} - -@misc{Heinlein:2023:SIMULA:ICP, - title = {Improving the convergence of pseudo-transient continuation for CFD simulations using neural networks}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {SIMULA}, - note = {Invited talk. SciML@Simula workshop (Hybrid), Oslo, Norway, December 1}, - abstract = {Computational fluid dynamics (CFD) simulations are highly relevant for a large range of applications, including but not restricted to the fields of aerospace, environmental, and biological engineering as well as weather predictions and medicine. Modeling Newtonian fluids involves the solution of the Navier-Stokes equations, which, depending on the Reynolds number of the flow, may exhibit a highly nonlinear behavior. The system of nonlinear equations resulting from the discretization of the Navier-Stokes equations can be solved using nonlinear iteration methods, such as Newton’s method. However, fast quadratic convergence is typically only obtained in a local neighborhood of the solution, and for many configurations, the classical Newton iteration does not converge at all. In such cases, so-called globalization techniques may help to improve convergence. In this talk, pseudo-transient continuation is employed in order to improve nonlinear convergence. The classical algorithm is enhanced by a neural network model that is trained to predict a local pseudo-time step. Generalization of the novel approach is facilitated by predicting the local pseudo-time step separately on each element using only local information on a patch of adjacent elements as input. Numerical results for standard benchmark problems, including flow through a backward facing step geometry and Couette flow, show the performance of the machine learning-enhanced globalization approach; as the software for the simulations, the CFD module of COMSOL Multiphysics® is employed.}, - keywords = {} -} - -@misc{Heinlein:2023:DOCOMS:DPI, - title = {Decomposing physics-informed neural networks}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {DUCOMS}, - note = {Dutch Computational Sciences (DUCOMS) Day 2023, Netherlands, November 11}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving field of research that combines techniques from scientific computing and machine learning. A major branch of SciML is the approximation of the solutions of partial differential equations (PDEs) using neural networks. In classical physics-informed neural networks (PINNs), simple feed-forward neural networks are employed to discretize a PDE. The loss function may include a combination of data (e.g., initial, boundary, and/or measurement data) and the residual of the PDE. Challenging applications, such as multiscale problems, require neural networks with high capacity, and the training is often not robust and may take large numbers of iterations. In this talk, domain decomposition-based network architectures for PINNs using the finite basis physics-informed neural network (FBPINN) approach will be discussed. In particular, the global network function is constructed as a combination of local network functions defined on an overlapping domain decomposition. Similar to classical domain decomposition methods, the one-level method generally lacks scalability, but scalability can be achieved by introducing a multi-level hierarchy of overlapping domain decompositions. The performance of the multi-level FBPINN method will be investigated based on numerical results for several model problems, showing robust convergence for up to 64 subdomains on the finest level and challenging multi-frequency problems.}, - url = {https://www.computationalsciencenl.nl/en/ducoms-day/}, - slides = {2023/2023-heinlein-ducoms-dpi/2023-heinlein-fbpinns-short.pdf}, - keywords = {} -} - -@misc{Heinlein:2023:TUG:FRO, - title = {Fast and Robust Overlapping Schwarz (FROSch) Preconditioners in Trilinos -- New Developments and Applications}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {TUG 2023}, - note = {Trilinos User-Developer Group Meeting 2023 (Hybrid), CSRI, Sandia National Laboratories, Albuquerque, USA, October 30-November 2}, - url = {https://trilinos.github.io/trilinos_user-developer_group_meeting_2023.html}, - slides = {2023/2023-heinlein-tug-fro/2023-heinlein-frosch.pdf}, - keywords = {} -} - -@misc{Heinlein:2023:DAMUT:MDD, - title = {Decomposing physics-informed neural networks}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {DAMUT Colloquium}, - note = {Invited talk. DAMUT Colloquium, University of Twente, Netherlands, October 4}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving field of research that combines techniques from scientific computing and machine learning. A major branch of SciML is the approximation of the solutions of partial differential equations (PDEs) using neural networks. In classical physics-informed neural networks (PINNs), simple feed-forward neural networks are employed to discretize a PDE. The loss function may include a combination of data (e.g., initial, boundary, and/or measurement data) and the residual of the PDE. Challenging applications, such as multiscale problems, require neural networks with high capacity, and the training is often not robust and may take large numbers of iterations. In this talk, domain decomposition-based network architectures for PINNs using the finite basis physics-informed neural network (FBPINN) approach will be discussed. In particular, the global network function is constructed as a combination of local network functions defined on an overlapping domain decomposition. Similar to classical domain decomposition methods, the one-level method generally lacks scalability, but scalability can be achieved by introducing a multi-level hierarchy of overlapping domain decompositions. The performance of the multi-level FBPINN method will be investigated based on numerical results for several model problems, showing robust convergence for up to 64 subdomains on the finest level and challenging multi-frequency problems. This talk is based on joint work with Victorita Dolean (University of Strathclyde, Côte d’Azur University), Siddhartha Mishra, and Ben Moseley (ETH Zürich).}, - url = {https://www.utwente.nl/en/eemcs/damut/damutcolloquium/abstracts/2023/2023-09-heinlein/}, - keywords = {} -} - -@misc{Heinlein:2023:NA:DPI, - title = {Decomposing physics-informed neural networks}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {TU Delft}, - note = {Numerical Analysis group coffee talk. Delft University of Technology, Netherlands, September 8}, - keywords = {} -} - -@misc{Heinlein:2023:ICIAM:ESP, - title = {Efficient Schwarz Preconditioning Techniques for Nonlinear Problems Using FROSch}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {ICIAM}, - note = {10th International Congress on Industrial and Applied Mathematics (ICIAM), Waseda University, Tokyo, Japan, August 20-25}, - abstract = {FROSch (Fast and Robust Overlapping Schwarz) is a framework for parallel Schwarz domain decomposition preconditioners in Trilinos. Due an algebraic approach, meaning that the preconditioners can be constructed from a fully assembled matrix, FROSch is applicable to a wide range of problems. This talk is focused on the application to nonlinear problems, including computational fluid dynamics and land ice simulations. Techniques for improving the efficiency and the use of GPU architectures are discussed.}, - url = {https://iciam2023.org/}, - slides = {2023/2023-heinlein-iciam-fro/2023-heinlein-frosch_nonlinear.pdf}, - keywords = {} -} - -@misc{Heinlein:2023:UM:MDD, - title = {Multilevel domain decomposition-based architectures for physics-informed neural networks}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {Workshop}, - note = {Invited talk. Workshop on Scientific Learning and Computing, University of Macau, Macao, China, August 17-18}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving field of research that combines techniques from scientific computing and machine learning. A major branch of SciML is the approximation of the solutions of partial differential equations (PDEs) using neural networks. In classical physics-informed neural networks (PINNs), simple feed-forward neural networks are employed to discretize a PDE. The loss function may include a combination of data (e.g., initial, boundary, and/or measurement data) and the residual of the PDE. Challenging applications, such as multiscale problems, require neural networks with high capacity, and the training is often not robust and may take large numbers of iterations. In this talk, domain decomposition-based network architectures for PINNs using the finite basis physics-informed neural network (FBPINN) approach will be discussed. In particular, the global network function is constructed as a combination of local network functions defined on an overlapping domain decomposition. Similar to classical domain decomposition methods, the one-level method generally lacks scalability, but scalability can be achieved by introducing a multi-level hierarchy of overlapping domain decompositions. The performance of the multi-level FBPINN method will be investigated based on numerical results for several model problems, showing robust convergence for up to 64 subdomains on the finest level and challenging multi-frequency problems. This talk is based on joint work with Victorita Dolean (University of Strathclyde, Côte d’Azur University), Siddhartha Mishra, and Ben Moseley (ETH Zürich).}, - url = {https://cam.fst.um.edu.mo/workshop-on-scientific-computing-and-learning/}, - slides = {2023/2023-heinlein-um-fbpinns/2023-heinlein-fbpinns.pdf}, - keywords = {} -} - -@misc{Heinlein:2023:DLR:NNP, - title = {Neural networks with physical constraints -- Domain decomposition-based network architectures, and model order reduction}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {DLR}, - note = {Invited seminar talk, German Aerospace Center (DLR), July 18}, - keywords = {} -} - -@misc{Heinlein:2023:TUM:NNP, - title = {Neural networks with physical constraints -- Domain decomposition-based network architectures, and model order reduction}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {TUM}, - note = {Invited seminar talk, Technical University of Munich, July 13}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving field of research that combines techniques from scientific computing and machine learning. A major branch of SciML is the approximation of the solutions of partial differential equations (PDEs) using neural networks. The network models be can trained in a data-driven and/or physics-informed way, that is, using reference data (from simulations or measurements) or a loss function based on the PDE, respectively. In physics-informed neural networks (PINNs), simple feedforward neural networks are employed to discretize the PDEs, and a single network is trained to approximate the solution of one specific boundary value problem. The loss function may include a combination of data and the residual of the PDE. Challenging applications, such as multiscale problems, require neural networks with high capacity, and the training is often not robust and may take large iteration counts. Therefore, in the first part of the talk, domain decomposition-based network architectures improving the training performance using the finite basis physics-informed neural network (FBPINN) approach will be discussed. It is based on joint work with Victorita Dolean (University of Strathclyde, Côte d’Azur University), Siddhartha Mishra, and Ben Moseley (ETH Zürich). In the second part of the talk, surrogate models for computational fluid dynamics (CFD) simulations based on convolutional neural networks (CNNs) will be discussed. In particular, the network is trained to approximate a solution operator, taking a representation of the geometry as input and the solution field(s) as output. In contrast to the classical PINN approach, a single network is trained to approximate a variety of boundary value problems. This makes the approach potentially very efficient. As in the PINN approach, data as well as the residual of the PDE may be used in the loss function for training the network. The second part of the talk is based on joint work with Matthias Eichinger, Viktor Grimm, and Axel Klawonn (University of Cologne).}, - slides = {2023/2023-heinlein-tum-sciml/2023-heinlein-sciml.pdf}, - keywords = {} -} - -@misc{Heinlein:2023:EURODYN:THP, - title = {Temporal homogenisation and parallelisation for the numerical simulation of atherosclerotic plaque growth}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {EURODYN}, - note = {XII International Conference on Structural Dynamics (EURODYN 2023), Delft University of Technology, Delft, The Netherlands, July 2-5}, - abstract = {The numerical simulation of atherosclerotic plaque growth is computationally prohibitive since it involves a complex cardiovascular fluid-structure interaction (FSI) problem with a characteristic time scale of milliseconds to seconds as well as a plaque growth process governed by reaction-diffusion equations, which takes place over several months. A resolution of the fast (micro) scale over this period can easily require more than a billion time steps, each corresponding to the solution of a computationally expensive FSI problem. To tackle this problem, we combine a temporal homogenization approach with parallel time-stepping. First, a temporal homogenization approach is developed, which separates the problem in an FSI problem on the micro scale and a reaction-diffusion problem on the macro scale. The approach is analyzed in detail for a simplified flow problem and estimates for the homogenization error and the discretization errors on both time scales are given. Second, a parallel time-stepping approach based on the parareal algorithm is applied on the macro scale of the homogenized system. We investigate modifications in the coarse propagator of the parareal algorithm to further reduce the number of expensive micro problems to be solved and test the numerical algorithms in detailed numerical studies.}, - url = {https://eurodyn2023.dryfta.com/}, - keywords = {} -} - -@misc{Heinlein:2023:EUROTUG:TT, - title = {Trilinos Tutorial}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {EuroTUG2023}, - note = {European Trilinos User Group Meeting 2023 (EuroTUG2023), TU Delft, June 28}, - url = {https://eurotug.github.io/}, - slides = {2023/2023-heinlein-eurotug-tt/2023-heinlein-trilinos.pdf}, - keywords = {} -} - -@misc{Heinlein:2023:4TUAMI:SRI, - title = {SRI Bridging numerical analysis and machine learninge}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {4TU.AMI}, - note = {4TU.AMI summer event 2023, TU Delft, June 27}, - url = {https://www.4tu.nl/ami/Agenda-Events/summer-event-2023/}, - keywords = {} -} - -@misc{Heinlein:2023:MATH+:MDD, - title = {Multilevel domain decomposition-based architectures for physics-informed neural networks}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {COMINDS}, - note = {Invited talk. Optimization Workshop (Thematic Einstein Semester on Optimization and Machine Learning), Humboldt Universität zu Berlin, Berlin, June 14-16}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving field of research that combines techniques from scientific computing and machine learning. A major branch of SciML is the approximation of the solutions of partial differential equations (PDEs) using neural networks. In classical physics-informed neural networks (PINNs), simple feed-forward neural networks are employed to discretize a PDE. The loss function may include a combination of data (e.g., initial, boundary, and/or measurement data) and the residual of the PDE. Challenging applications, such as multiscale problems, require neural networks with high capacity, and the training is often not robust and may take large numbers of iterations. In this talk, domain decomposition-based network architectures for PINNs using the finite basis physics-informed neural network (FBPINN) approach will be discussed. In particular, the global network function is constructed as a combination of local network functions defined on an overlapping domain decomposition. Similar to classical domain decomposition methods, the one-level method generally lacks scalability, but scalability can be achieved by introducing a multi-level hierarchy of overlapping domain decompositions. The performance of the multi-level FBPINN method will be investigated based on numerical results for several model problems, showing robust convergence for up to 64 subdomains on the finest level and challenging multi-frequency problems. This talk is based on joint work with Victorita Dolean (University of Strathclyde, Côte d’Azur University), Siddhartha Mishra, and Ben Moseley (ETH Zürich).}, - url = {https://mathplus.de/topic-development-lab/tes-summer-2023/workshop-optimization/}, - keywords = {} -} - -@misc{Heinlein:2023:DCSE:ADD, - title = {Advanced Domain Decomposition Methods -- Parallel Schwarz Preconditioning and an Introduction to FROSch}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {HPC Summer School}, - note = {DCSE Summerschool: Numerical Linear Algebra on High Performance Computers, TU Delft, June 5-9}, - url = {https://www.aanmelder.nl/143287}, - slides = {2023/2023-heinlein-dcse-fro/2023-heinlein-frosch.pdf}, - keywords = {} -} - -@misc{Heinlein:2023:COMINDS:NNP, - title = {Neural networks with physical constraints -- Domain decomposition-based network architectures, and model order reduction}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {COMINDS}, - note = {Invited talk. GAMM Workshop on Computational and Mathematical Methods in Data Science, Center for Data and Simulation Science, University of Cologne, Cologne, Germany, May 4-5}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving field of research that combines techniques from scientific computing and machine learning. A major branch of SciML is the approximation of the solutions of partial differential equations (PDEs) using neural networks. The network models be can trained in a data-driven and/or physics-informed way, that is, using reference data (from simulations or measurements) or a loss function based on the PDE, respectively. In physics-informed neural networks (PINNs), simple feedforward neural networks are employed to discretize the PDEs, and a single network is trained to approximate the solution of one specific boundary value problem. The loss function may include a combination of data and the residual of the PDE. Challenging applications, such as multiscale problems, require neural networks with high capacity, and the training is often not robust and may take large iteration counts. Therefore, in the first part of the talk, domain decomposition-based network architectures improving the training performance using the finite basis physics-informed neural network (FBPINN) approach will be discussed. It is based on joint work with Victorita Dolean (University of Strathclyde, Côte d’Azur University), Siddhartha Mishra, and Ben Moseley (ETH Zürich). In the second part of the talk, surrogate models for computational fluid dynamics (CFD) simulations based on convolutional neural networks (CNNs) will be discussed. In particular, the network is trained to approximate a solution operator, taking a representation of the geometry as input and the solution field(s) as output. In contrast to the classical PINN approach, a single network is trained to approximate a variety of boundary value problems. This makes the approach potentially very efficient. As in the PINN approach, data as well as the residual of the PDE may be used in the loss function for training the network. The second part of the talk is based on joint work with Matthias Eichinger, Viktor Grimm, and Axel Klawonn (University of Cologne).}, - url = {https://cds.uni-koeln.de/en/workshops/cominds-2023/home}, - keywords = {} -} - -@misc{Heinlein:2023:CFC:PDD, - title = {Parallel Domain Decomposition Preconditioning Techniques for Incompressible Fluid Flow Problems}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {CFC 2023}, - note = {22nd IACM Computational Fluids Conference (CFC 2023), Cannes, France, April 25-28}, - abstract = {Monolithic GDSW (generalized Dryja–Smith–Wildund) preconditioners are two-level Schwarz domain decomposition preconditioners for block systems. They are robust because they account for the coupling terms in the system matrix on both levels, that is, in the local and coarse problems. Block preconditioners, mostly based on block-diagonal and block-triangular preconditioners, such as the famous SIMPLE (semi-implicit method for pressure linked equations) preconditioner, often yield higher iteration counts wile coming at a lower setup cost compared to monolithic approaches. In this talk, the parallel performance of the different preconditioning techniques for incompressible fluid flow problems is investigated and compared using a finite element implementation based on the FEDDLib finite element software and Schwarz preconditioners from the Trilinos package FROSch.}, - url = {https://cfc2023.iacm.info/about_cfc_2023}, - keywords = {} -} - -@misc{Heinlein:2023:CFC:SMC, - title = {Surrogate Models for CFD Simulations Based on Convolutional Neural Networks}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {CFC 2023}, - note = {22nd IACM Computational Fluids Conference (CFC 2023), Cannes, France, April 25-38}, - abstract = {Computational fluid dynamics (CFD) simulations are important in many application areas, such as civil and mechanical engineering, meteorology, geosciences, or medical science. However, accurate simulation results come at high computational costs, and they require high-quality meshes describing the computational domain. In this talk, a machine learning-based model order reduction approach for predicting flow fields is presented. After an expensive offline phase, where a surrogate model based on a convolutional neural network (U-Net type architecture) is trained using simulation data, the predictions can be performed much faster than classical numerical simulations. Moreover, the predictions do not require the generation of a complex computational mesh. The surrogate model can be 100 or 10,000 times faster on a CPU or GPU, respectively, of a normal workstation. Numerical results investigating the accuracy and efficiency for varying types of geometries from different application areas are presented. Moreover, different aspects to improve the performance such as the choice of more sophisticated loss functions are discussed.}, - url = {https://cfc2023.iacm.info/about_cfc_2023}, - keywords = {} -} - -@misc{Heinlein:2023:Sandia:NNP, - title = {Neural networks with physical constraints, domain decomposition-based network architectures, and model order reduction}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {Sandia}, - note = {Seminar talk, Sandia National Laboratories, USA, April 4}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving field of research that combines techniques from scientific computing and machine learning. A major branch of SciML is the approximation of the solutions of partial differential equations (PDEs) using neural networks. The network models be can trained in a data-driven and/or physics-informed way, that is, using reference data (from simulations or measurements) or a loss function based on the PDE, respectively. In physics-informed neural networks (PINNs), simple feedforward neural networks are employed to discretize the PDEs, and a single network is trained to approximate the solution of one specific boundary value problem. The loss function may include a combination of data and the residual of the PDE. Challenging applications, such as multiscale problems, require neural networks with high capacity, and the training is often not robust and may take large iteration counts. Therefore, in the first part of the talk, domain decomposition-based training strategies improving the training performance using the finite basis physics-informed neural network (FBPINN) approach will be discussed. In the second part of the talk, surrogate models for computational fluid dynamics (CFD) simulations based on convolutional neural networks (CNNs) will be discussed. In particular, the network is trained to approximate a solution operator, taking a representation of the geometry as input and the solution field(s) as output. In contrast to the classical PINN approach, a single network is trained to approximate a variety of boundary value problems. This makes the approach potentially very efficient. As in the PINN approach, data as well as PDE may be used in the loss function for training the network.}, - keywords = {} -} - -@misc{Heinlein:2023:IGCM:NNP, - title = {Neural networks with physical constraints, domain decomposition-based training strategies, and model order reduction}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {IGCM 2023}, - note = {Invited plenary lecture. Indo-German Conference on Computational Mathematics 2023 (IGCM-2023), Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, India, March 27-30}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving field of research that combines techniques from scientific computing and machine learning. A major branch of SciML is the approximation of the solutions of partial differential equations (PDEs) using neural networks. The network models be can trained in a data-driven and/or physics-informed way, that is, using reference data (from simulations or measurements) or a loss function based on the PDE, respectively. In physics-informed neural networks (PINNs), simple feedforward neural networks are employed to discretize the PDEs, and a single network is trained to approximate the solution of one specific boundary value problem. The loss function may include a combination of data and the residual of the PDE. Challenging applications, such as multiscale problems, require neural networks with high capacity, and the training is often not robust and may take large iteration counts. Therefore, in the first part of the talk, domain decomposition-based training strategies improving the training performance using the finite basis physics-informed neural network (FBPINN) approach will be discussed. In the second part of the talk, surrogate models for computational fluid dynamics (CFD) simulations based on convolutional neural networks (CNNs) will be discussed. In particular, the network is trained to approximate a solution operator, taking a representation of the geometry as input and the solution field(s) as output. In contrast to the classical PINN approach, a single network is trained to approximate a variety of boundary value problems. This makes the approach potentially very efficient. As in the PINN approach, data as well as PDE may be used in the loss function for training the network.}, - url = {https://cmg.cds.iisc.ac.in/igcm/}, - keywords = {selected} -} - -@misc{Heinlein:2023:HLRS:NNP, - title = {Neural networks with physical constraints, domain decomposition-based network architectures, and model order reduction}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {NVIDIA/HLRS}, - note = {Invited talk. NVIDIA/HLRS SciML GPU Bootcamp, Stuttgart (virtual), Germany, April 26-27}, - url = {https://www.hlrs.de/training/2023/bc-sciml-nv}, - slides = {2023/2023-heinlein-hlrs-nnp/2023-heinlein-sciml.pdf}, - video = {https://drive.google.com/file/d/1cugT822xUH6f8ru-olNOKDJ_fzmvy75m/view}, - keywords = {} -} - -@misc{Heinlein:2023:SIAMCSE:DDM, - title = {Domain Decomposition Training Strategies for Physics-Informed Neural Networks}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {SIAM CSE23}, - note = {SIAM Conference on Computational Science and Engineering (CSE23). RAI Congress Centre, Amsterdam, The Netherlands, February 26 - March 3}, - abstract = {Two-level domain decomposition methods, such as two-level Schwarz, finite element tearing and interconnecting - dual primal (FETI-DP), or balancing domain decomposition by constraints (BDDC) methods, are scalable for a large class of homogeneous problems. However, in the presence of highly-heterogeneous coefficients, convergence generally deteriorates. If the coarse space is enhanced by adapted coarse basis functions, robustness can be regained. Similar observations can be made for highly-heterogeneous nonlinear problems, where both the linear and the nonlinear convergence maybe affected; in this context, a combination of nonlinear domain decomposition methods and robust coarse spaces can recover good linear and nonlinear solver performance. In this talk, preconditioning techniques for highly-heterogeneous linear and nonlinear problems will be discussed and numerical results for various problems will be reported; the focus is on Schwarz domain decomposition methods, but many approaches can be - with small modifications - applied to other domain decomposition methods as well.}, - url = {https://www.siam.org/conferences/cm/conference/cse23}, - keywords = {} -} - -@misc{Heinlein:2023:CTU:DDM, - title = {Domain decomposition methods for highly heterogeneous problems - Robust coarse spaces and nonlinear preconditioning}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {CTU}, - note = {Invited seminar talk. Czech Technical University in Prague, Prague, Czech Republic, February 13}, - abstract = {Two-level domain decomposition methods, such as two-level Schwarz, finite element tearing and interconnecting - dual primal (FETI-DP), or balancing domain decomposition by constraints (BDDC) methods, are scalable for a large class of homogeneous problems. However, in the presence of highly-heterogeneous coefficients, convergence generally deteriorates. If the coarse space is enhanced by adapted coarse basis functions, robustness can be regained. Similar observations can be made for highly-heterogeneous nonlinear problems, where both the linear and the nonlinear convergence maybe affected; in this context, a combination of nonlinear domain decomposition methods and robust coarse spaces can recover good linear and nonlinear solver performance. In this talk, preconditioning techniques for highly-heterogeneous linear and nonlinear problems will be discussed and numerical results for various problems will be reported; the focus is on Schwarz domain decomposition methods, but many approaches can be - with small modifications - applied to other domain decomposition methods as well.}, - slides = {/2023-heinlein-ctu-ddm/2023-heinlein-heterogeneous.pdf}, - video = {https://youtu.be/DbOPyYk6IHQ}, - keywords = {} -} - -@misc{Heinlein:2023:CDS:FRO, - title = {Fast and Robust Overlapping Schwarz Preconditioners in Trilinos -- Highly Scalable Algorithms and Their Efficient Implementation}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {CDS}, - note = {Invited seminar talk. Center for Data and Simulation Science (CDS), Universit\"at zu K\"oln, K\"oln, Germany, January 18}, - abstract = {The Trilinos library is an object-oriented software framework for the solution of large-scale, complex multi-physics engineering and scientific problems on new and emerging high-performance computing (HPC) architectures. It provides a collection of interoperable software packages enabling the development of algorithms reaching parallel scalability up to the largest supercomputers available. This talk will discuss different aspects of Trilinos for the example of the FROSch (Fast and Robust Overlapping Schwarz) preconditioning framework, which is part of the Trilinos package ShyLU. FROSch implements multilevel Schwarz preconditioners, which are algebraic, i.e., which can be constructed using only the fully assembled parallel distributed system matrix. Making use of the software infrastructure of Trilinos, FROSch allows for the parallel solution of extremely large problems. Numerical results for various problems indicating parallel scalability up to more than 200,000 MPI ranks will be presented. Moreover, node-level parallelization on CPUs as well as GPUs using the Kokkos programming model through the Tpetra linear algebra framework will be discussed.}, - url = {https://cds.uni-koeln.de/en/labs/hpc/hpc-seminar-series/talk20230118}, - slides = {2023/2023-heinlein-cds-fro/2023-heinlein-trilinos_frosch.pdf}, - keywords = {} -} - -@misc{Heinlein:2023:SimTech:NNP, - title = {Neural networks with physical constraints, domain decomposition-based training strategies, and model order reduction}, - author = {Alexander Heinlein}, - year = {2023}, - abbr = {SimTech}, - note = {Invited seminar talk. SimTech ML-Session, Universit\"at Stuttgart, Stuttgart, Germany, January 11}, - abstract = {Scientific machine learning (SciML) is a rapidly evolving field of research that combines techniques from scientific computing and machine learning. One major branch of SciML is the approximation of the solutions of partial differential equations (PDEs) using machine learning models and, in particular, neural networks. The network models be can trained in a data-driven or physics-informed way, that is, using reference data (from simulations or measurements) or a loss function based on the PDE, respectively. In this talk, two approaches for approximating the solutions of PDEs using neural networks are discussed: physics-informed neural networks (PINNs) and surrogate models based on convolutional neural networks (CNNs). In PINNs, simple feedforward neural networks are employed to discretize the PDEs, and a single network is trained to approximate the solution of one specific boundary value problem. The loss function may include a combination of reference data and the residual of the PDE. Challenging applications, such as multiscale problems, require the use of neural networks with high capacity, and the training of the models is often not robust and may take large iteration counts. Therefore, domain decomposition-based training strategies improving the training performance using the finite basis physics-informed neural network (FBPINN) approach will be discussed. In the second part of the talk, surrogate models for computational fluid dynamics (CFD) simulations based on CNNs are discussed. In particular, the network is trained to approximate a solution operator, taking a representation of the geometry as input and the solution field(s) as output. In contrast to the classical PINN approach and similar to other operator learning approaches, a single network is therefore trained to approximate a variety of boundary value problems. This makes the surrogate modeling approach potentially very efficient. As in the PINN approach, data as well as physics may be used in the loss function for training the network.}, - slides = {2023/2023-heinlein-simtech-nnp/2023-heinlein-pinns.pdf}, - keywords = {} -} - -@misc{Heinlein:2022:Glasgow:NNP, - title = {Neural networks with physical constraints, domain decomposition-based training strategies, and model order reduction}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {Seminar}, - note = {Invited talk. Scientific Machine Learning seminar series, University of Strathclyde, Glasgow, UK, December 6}, - abstract = {One major branch of scientific machine learning (SciML) is the approximation of the solutions of partial differential equations (PDEs) using neural networks. This can be done in a data-driven or physics-informed way, that is, using reference data from simulations or measurements or by optimizing with respect to the residual of the PDE, respectively. In this talk, two approaches for approximating the solutions of PDEs using neural networks are discussed: domain decomposition techniques for improving the training of physics-informed neural networks and model order reduction techniques based on convolutional neural networks. Both approaches allow for training using a combination of data and physics.}, - keywords = {} -} - -@misc{Heinlein:2022:LUH:TBA, - title = {Robust, algebraic, and scalable Schwarz preconditioners with extension-based coarse spaces}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {LUH2022}, - note = {Seminar talk. Leibniz Universit\"at Hannover, Hannover, Germany, December 1}, - abstract = {Coarse spaces are an important component in domain decomposition preconditioners since they are, in general, necessary to obtain numerical scalability and robustness. This talk will focus on presenting an algorithmic framework for the construction of coarse spaces for Schwarz preconditioners which is based on the generalized Dryja--Smith--Widlund (GDSW) coarse space. In particular, the coarse basis functions are extensions from the interface into the interior of a corresponding nonoverlapping domain decomposition by solving the homogeneous partial differential equation (PDE) with a given trace on the interface. This makes the coarse spaces very practical since they can be constructed in an algebraic way, that is, using only the fully assembled system matrix. This algorithmic framework is the basis for the highly-scalable FROSch (Fast and Robust Schwarz) solver package, which is part of the Trilinos software library. The FROSch package provides a parallel software framework to construct algebraic Schwarz preconditioners that are robust as well as numerically and parallel scalable for a wide range of problems. It provides a multi-level implementation to extend parallel scalability. Moreover, using extension-based coarse spaces, robust monolithic solvers for saddle-point problems, such as the (Navier--)Stokes equations and multi-physics problems in land ice simulations, can be constructed. Solving appropriate local eigenvalue problems on a partition of the interface to compute the traces of the coarse basis yields provably robust extension-based coarse spaces, even for highly heterogeneous model problems with large coefficient jumps. These adaptive coarse spaces are generally not algebraic since the eigenvalue problems require local Neumann matrices. However, by solving two local eigenvalue problems for each interface component instead, an algebraic and adaptive coarse space can be obtained. Finally, the framework can also be employed in nonlinear Schwarz preconditioning.}, - keywords = {} -} - -@misc{Heinlein:2022:HLRS:NNP, - title = {Neural networks with physical constraints, domain decomposition-based training strategies, and model order reduction}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {NVIDIA/HLRS}, - note = {Invited talk. NVIDIA/HLRS SciML GPU Bootcamp, Stuttgart (virtual), Germany, October 24-25}, - url = {https://www.hlrs.de/training/2022/bc-sciml-nv}, - slides = {2022/2022-heinlein-hlrs-nnp/2022-heinlein-pinns.pdf}, - video = {https://drive.google.com/file/d/1J25FL21A89zcWy-ZQF0rssHqJOcTv6LN/view}, - keywords = {selected} -} - -@misc{Heinlein:2022:SIAMDSE:SMC, - title = {Surrogate Models for Computational Fluid Dynamics Simulations Using Convolutional Autoencoder Neural Networks and Physical Constraints}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {SIAM MDS22}, - note = {SIAM Conference on Mathematics of Data Science, SIAM MDS22, San Diego (Hybrid), USA, September 26 - 30}, - abstract = {Simulations of fluid flow are generally very costly because high grid resolutions are not only required to obtain quantitatively accurate results, but too low grid resolutions may also lead to qualitatively incorrect results. In applications, however, one is often not interested in accurate approximations of the complete flow field but only in the qualitative behavior of the flow or in individual quantities. In this talk, the use of convolutional autoencoder neural networks to construct efficient reduced order surrogate models for high fidelity computational fluid dynamics (CFD) simulations is discussed. In particular, the geometry of the computational domain is the input of the neural network, and the flow and pressure fields are the output. In order to construct accurate surrogate models, U-Net type convolutional neural networks are employed and the architecture and hyper parameters are optimized to this application. As a first step, a fully supervised approach, which requires the availability of simulation results as the training data, is presented. After that, a novel approach is introduced, which does not require CFD simulation results but is based on introducing physical constraints via the loss function. As a testbed for the surrogate models, the flow around obstacles with varying shape and size within a channel is considered. Moreover, results for the application to geometries of arteries with aneurysms are presented.}, - url = {https://www.siam.org/conferences/cm/conference/mds22}, - keywords = {} -} - -@misc{Heinlein:2022:UDE:RAS, - title = {Robust, algebraic, and scalable solvers based on Schwarz domain decomposition methods}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {UDE2022}, - note = {Kolloquium Ingenieurmathematik, Universit\"at Duisburg-Essen, Essen, Germany, September 15}, - keywords = {} -} - -@misc{Heinlein:2022:GACM:SMC, - title = {Surrogate Models for CFD Simulations Based on Convolutional Neural Networks}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {GACM2022}, - note = {9th GACM Colloquium on Computational Mechanics 2022, Essen, Germany, September 21-23}, - abstract = {CFD simulations are very costly to compute and have to be repeated if the geometry changes even slightly. Recently there have been a number of attempts to speed up this process using neural networks. Among these is the use of Convolutional Neural Networks (CNN) as surrogate models for CFD simulations with varying geometries. Here, the model is trained on images of high-fidelity simulation results. However, the generation of training data is expensive and this approach usually requires a large data set. Thus, it is of interest to be able to train a CNN in the absence of abundant training data with the help of physical constraints. First results have already been achieved for the heat equation on a fixed geometry and flow problems in parameterizable geometries. In this talk, we present a physics-aware approach to train CNNs as surrogate models for CFD simulations in varying geometries. The employed CNN takes an imags of the geometry as input and returns images of the associated CFD simulation results, i.e., velocity and pressure, as output. Our CNN architecture is based on the structure of U-Net. Since the model is trained on pixel images, it can be applied to a variety of different geometries. We show results for two-dimensional flows around obstacles of varying size and placement and in non-rectangular geometries, esp. arteries and aneurysms.}, - url = {https://colloquia.gacm.de/organisation}, - keywords = {} -} - -@misc{Heinlein:2022:GAMM:PCF, - title = {Predicting Cardiovascular Flow Using Convolutional Autoencoder Neural Networks and Physical Constraints}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {GAMM2022}, - note = {92nd GAMM Annual Meeting, Aachen, Germany, August 15-19}, - abstract = {Simulations of fluid flow are generally very costly because high grid resolutions are not only required to obtain quantitatively accurate results, but too low grid resolutions may also lead to qualitatively incorrect results. In cardiovascular applications, however, one is often not interested in accurate approximations of the complete flow field but only in the qualitative behavior of the flow or in individual quantities, such as the maximum velocity or the wall shear stresses at certain locations. In this talk, the use of convolutional autoencoder neural networks to construct efficient reduced order surrogate models for high fidelity computational fluid dynamics (CFD) simulations is discussed. Using this approach, it is possible to build surrogate models for varying geometries. In particular, the geometry is the input of the neural network, and the flow and pressure fields are the output. In order to construct accurate surrogate models, U-Net type convolutional neural networks, which are very successful in image recognition and segmentation tasks, are employed, and the architecture and hyper parameters are optimized to this application. Two different approaches are compared: a fully supervised approach, where the model is trained using high fidelity simulation data, and a novel approach, where the model is trained based on introducing physical constraints via the loss function. As a testbed for the surrogate models, the flow around obstacles with varying shape and size within a channel is considered. Then, the framework is applied to geometries of arteries with aneurysms are presented. The results show that the surrogate models provide good predictions of the flow and pressure fields while being computationally much cheaper compared to classical CFD codes.}, - url = {https://jahrestagung.gamm.org/annual-meeting-2022/annual-meeting/}, - keywords = {} -} - -@misc{Heinlein:2022:DD27:RAS, - title = {Robust, algebraic, and scalable Schwarz preconditioners with extension-based coarse spaces}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {DD XXVII}, - note = {Invited plenary lecture. 27th International Conference on Domain Decomposition Methods, Prague, Czech Republic, July 25-29}, - abstract = {Coarse spaces are an important component in domain decomposition preconditioners since they are, in general, necessary to obtain numerical scalability and robustness. This talk will focus on presenting an algorithmic framework for the construction of coarse spaces for Schwarz preconditioners which is based on the generalized Dryja--Smith--Widlund (GDSW) coarse space. In particular, the coarse basis functions are extensions from the interface into the interior of a corresponding nonoverlapping domain decomposition by solving the homogeneous partial differential equation (PDE) with a given trace on the interface. This makes the coarse spaces very practical since they can be constructed in an algebraic way, that is, using only the fully assembled system matrix. This algorithmic framework is the basis for the highly-scalable FROSch (Fast and Robust Schwarz) solver package, which is part of the Trilinos software library. The FROSch package provides a parallel software framework to construct algebraic Schwarz preconditioners that are robust as well as numerically and parallel scalable for a wide range of problems. It provides a multi-level implementation to extend parallel scalability. Moreover, using extension-based coarse spaces, robust monolithic solvers for saddle-point problems, such as the (Navier--)Stokes equations and multi-physics problems in land ice simulations, can be constructed. Solving appropriate local eigenvalue problems on a partition of the interface to compute the traces of the coarse basis yields provably robust extension-based coarse spaces, even for highly heterogeneous model problems with large coefficient jumps. These adaptive coarse spaces are generally not algebraic since the eigenvalue problems require local Neumann matrices. However, by solving two local eigenvalue problems for each interface component instead, an algebraic and adaptive coarse space can be obtained. Finally, the framework can also be employed in nonlinear Schwarz preconditioning.}, - url = {https://www.dd27.cz/}, - slides = {2022/2022-heinlein-dd27-ras/2022-heinlein-schwarz.pdf}, - video = {https://drive.google.com/file/d/1_cTipqycwK9YiXP5K7urXcomKVRh8ECJ/view?usp=sharing}, - keywords = {selected} -} - -@misc{Heinlein:2022:DD27:RCS, - title = {Robust Coarse Spaces for Nonlinear Schwarz Methods}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {DD XXVII}, - note = {27th International Conference on Domain Decomposition Methods, Prague, Czech Republic, July 25-29}, - abstract = {In this talk, nonlinear left-preconditioning by nonlinear Schwarz domain decomposition methods is considered. In particular, the focus is on the restricted additive Schwarz preconditioned exact Newton (RASPEN) method. It is based on additive Schwarz preconditioned Newton (ASPEN) method, which has been introduced together with the corresponding inexact method, ASPIN. Nonlinear domain decomposition methods can improve nonlinear as well as linear convergence. However, as in linear domain decomposition methods, scalability and robustness for difficult problems, such as highly heterogeneous problems, generally requires adding a coarse space. The coarse space can be integrated in an additive or multiplicative way using a Galerkin projection. This approach has proven to be very flexible, allowing for the use of different types of coarse spaces, such as classical Lagrangian or multiscale finite element method (MsFEM) type coarse spaces. Furthermore, to obtain robustness for heterogeneous problems, spectral coarse spaces, such as the adaptive generalized Dryja–Smith–Wildund (GDSW) coarse space can be employed. The main goal of this talk is to investigate the effectiveness of different coarse spaces, including GDSW, MsFEM, adaptive GDSW, and approximate component mode synthesis-based (OS-ACMS) adaptive coarse spaces for different nonlinear model problems and depending on the domain decomposition as well as heterogeneity of the problem.}, - url = {https://www.dd27.cz/}, - keywords = {} -} - -@misc{Heinlein:2022:DD27:SMC, - title = {Surrogate Models for Computational Fluid Dynamics Simulations Using Convolutional Autoencoder Neural Networks and Physical Constraints}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {DD XXVII}, - note = {27th International Conference on Domain Decomposition Methods, Prague, Czech Republic, July 25-29}, - abstract = {Simulations of fluid flow are generally very costly because high grid resolutions are not only required to obtain quantitatively accurate results, but too low grid resolutions may also lead to qualitatively incorrect results. In applications, however, one is often not interested in accurate approximations of the complete flow field but only in the qualitative behavior of the flow or in individual quantities (e.g., maximum velocity, pressure drop within a section of a pipe, or wall shear stresses at certain locations). In this talk, the use of convolutional autoencoder neural networks to construct efficient reduced order surrogate models for high fidelity computational fluid dynamics (CFD) simulations is discussed. Using this approach, it is possible to build surrogate models for varying geometries. In particular, the geometry is the input of the neural network, and the flow and pressure fields are the output. In order to construct accurate surrogate models, U-Net type convolutional neural networks, which are very successful in image recognition and segmentation tasks, are employed and the architecture and hyper parameters are optimized to this application. As a first step, a fully supervised approach, which requires the availability of simulation results as the training data, is presented. After that, a novel approach is introduced, which does not require CFD simulation results but is based on introducing physical constraints via the loss function. As a test-bed for the surrogate models, flow around obstacles with varying shape and size within a channel is considered. Moreover, results for the application to geometries of arteries with aneurysms are presented. The results show that the surrogate models provide good predictions of the flow and pressure fields while being computationally much cheaper compared to classical CFD codes.}, - url = {https://www.dd27.cz/}, - keywords = {} -} - -@misc{Heinlein:2022:MarburgKolloquium:RAS, - title = {Algebraic Schwarz Domain Decomposition Preconditioners – Parallel Scalability and Robustness}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {Colloquium}, - note = {Kolloquium des Fachbereichs Mathematik und Informatik, Universit\"at Marburg, Marburg, Germany, July 18}, - keywords = {} -} - -@misc{Heinlein:2022:EQUADIFF:SMC, - title = {Surrogate Models for Computational Fluid Dynamics Simulations Using Convolutional Autoencoder Neural Networks and Physical Constraints}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {EQUADIFF 15}, - note = {Equadiff 15, Brno, Czech Republic, July 11-15}, - abstract = {Simulations of fluid flow are generally very costly because high grid resolutions are not only required to obtain quantitatively accurate results, but too low grid resolutions may also lead to qualitatively incorrect results. In applications, however, one is often not interested in accurate approximations of the complete flow field but only in the qualitative behavior of the flow or in individual quantities (e.g., maximum velocity, pressure drop within a section of a pipe, or wall shear stresses at certain locations). In this talk, the use of convolutional autoencoder neural networks to construct efficient reduced order surrogate models for high fidelity computational fluid dynamics (CFD) simulations is discussed. Using this approach, it is possible to build surrogate models for varying geometries. In particular, the geometry is the input of the neural network, and the flow and pressure fields are the output. In order to construct accurate surrogate models, U-Net type convolutional neural networks, which are very successful in image recognition and segmentation tasks, are employed and the architecture and hyper parameters are optimized to this application. As a first step, a fully supervised approach, which requires the availability of simulation results as the training data, is presented. After that, a novel approach is introduced, which does not require CFD simulation results but is based on introducing physical constraints via the loss function. As a test-bed for the surrogate models, flow around obstacles with varying shape and size within a channel is considered. Moreover, results for the application to geometries of arteries with aneurysms are presented. The results show that the surrogate models provide good predictions of the flow and pressure fields while being computationally much cheaper compared to classical CFD codes.}, - url = {https://conference.math.muni.cz/equadiff15/}, - keywords = {} -} - -@misc{Heinlein:2022:4TUAMI:PDD, - title = {Parallel Domain Decomposition Solvers & Scientific Machine Learning}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {4TU.AMI}, - note = {4TU.AMI summer event 2022, Eindhoven, The Netherlands, July 5}, - url = {https://www.4tu.nl/ami/Agenda-Events/summer-event-2022/}, - keywords = {} -} - -@misc{Heinlein:2022:ICMS:FAS, - title = {A fully algebraic spectral coarse space for overlapping Schwarz methods}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {ICMS@Strathclyde}, - note = {Invited talk. ICMS@Strathclyde: Solvers for frequency-domain wave problems and applications, Glasgow, UK, June 20-24}, - abstract = {Discretizing partial differential equations often results in sparse systems of linear equations. High spatial resolutions lead to large systems, which can be solved efficiently using iterative methods. A suitable class of solvers are Krylov methods preconditioned by domain decomposition preconditioners, which are scalable and robust for a wide range of problems. Unfortunately, highly heterogeneous problems arising, for instance, in the simulation of composite materials or porous media generally lead to unfavorable distributions of the eigenvalues of the system matrix that cause slow convergence for many solvers, including classical domain decomposition preconditioners. In order to retain robustness of domain decomposition methods, the coarse space can be enriched by additional coarse basis functions computed from eigenmodes of local generalized eigenvalue problems, leading to so-called spectral or adaptive coarse spaces. The development of spectral coarse spaces for domain decomposition methods has been a very active topic within the last decade. However, until recently, the algebraic construction of robust spectral coarse spaces, that is, using only the fully assembled system matrix without additional Neumann matrices or geometrical information, has still been on open problem. This talk deals with a specific class of adaptive coarse spaces for overlapping Schwarz methods which are based on a partition of the interface of the corresponding nonoverlapping domain decomposition. An algebraic and robust spectral coarse space is then constructed by solving two eigenvalue problems on each edge of a two-dimensional domain decomposition. One of them is based on optimal local approximation spaces that are also successfully employed in the construction of multiscale discretizations. The resulting condition number bound is independent of the contrast of the coefficient function, indicating the robustness of the method. In order investigate the robustness of this new method numerically, numerical results for different coefficient distributions with large jumps are presented, including typical examples with channels, random distributions, and coefficient distributions generated from the SPE10 benchmark.}, - url = {https://www.icms.org.uk/workshops/2022/icmsstrathclyde-solvers-frequency-domain-wave-problems-and-applications}, - slides = {2022/2022-heinlein-icms-fas/2022-heinlein-adaptive.pdf}, - keywords = {selected} -} - -@misc{Heinlein:2022:ECCOMAS:PSD, - title = {Parallel Schwarz domain decomposition preconditioning and an introduction to FROSch}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {ECCOMAS2022}, - note = {Introductory lecture. 8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2022), Oslo, Norway, June 5-9}, - url = {https://www.eccomas2022.org/frontal/}, - slides = {2022/2022-heinlein-eccomas-psd/2022-heinlein-frosch.pdf}, - keywords = {} -} - -@misc{Heinlein:2022:ECCOMAS:SMC, - title = {Surrogate Models for CFD Simulations Based on Convolutional Neural Networks}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {ECCOMAS2022}, - note = {8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2022), Oslo, Norway, June 5-9}, - abstract = {Computational fluid dynamics (CFD) simulations are important in many application areas, such as civil and mechanical engineering, meteorology, geosciences, or medical science. However, accurate simulation results come at high computational costs, and they require high-quality meshes describing the computational domain. In this talk, a machine learning-based model order reduction approach for predicting flow fields is presented. After an expensive offline phase, where a surrogate model based on a convolutional neural network (U-Net type architecture) is trained using simulation data, the predictions can be performed much faster than classical numerical simulations. Moreover, the predictions do not require the generation of a complex computational mesh. The surrogate model can be 10^2 or 10^4 times faster on a CPU or GPU, respectively, of a normal workstation. Numerical results investigating the accuracy and efficiency for varying types of geometries from different application areas are presented. Moreover, different aspects to improve the performance such as the choice of more sophisticated loss functions are discussed.}, - url = {https://www.eccomas2022.org/frontal/}, - keywords = {} -} - -@misc{Heinlein:2022:CM:FAS, - title = {A fully algebraic spectral coarse space for overlapping Schwarz methods}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {CM2022}, - note = {17th Copper Mountain Conference On Iterative Methods (Virtual), April 4 - April 8}, - abstract = {Discretizing partial differential equations often results in sparse systems of linear equations. High spatial resolutions lead to large systems, which can be solved efficiently using iterative methods. A suitable class of solvers are Krylov methods preconditioned by domain decomposition preconditioners, which are scalable and robust for a wide range of problems. Unfortunately, highly heterogeneous problems arising, for instance, in the simulation of composite materials or porous media generally lead to unfavorable distributions of the eigenvalues of the system matrix that cause slow convergence for many solvers, including classical domain decomposition preconditioners. In order to retain robustness of domain decomposition methods, the coarse space can be enriched by additional coarse basis functions computed from eigenmodes of local generalized eigenvalue problems, leading to so-called spectral or adaptive coarse spaces. The development of spectral coarse spaces for domain decomposition methods has been a very active topic within the last decade. However, until recently, the algebraic construction of robust spectral coarse spaces, that is, using only the fully assembled system matrix without additional Neumann matrices or geometrical information, has still been on open problem. This talk deals with a specific class of adaptive coarse spaces for overlapping Schwarz methods which are based on a partition of the interface of the corresponding nonoverlapping domain decomposition. An algebraic and robust spectral coarse space is then constructed by solving two eigenvalue problems on each edge of a two-dimensional domain decomposition. One of them is based on optimal local approximation spaces that are also successfully employed in the construction of multiscale discretizations. The resulting condition number bound is independent of the contrast of the coefficient function, indicating the robustness of the method. In order investigate the robustness of this new method numerically, numerical results for different coefficient distributions with large jumps are presented, including typical examples with channels, random distributions, and coefficient distributions generated from the SPE10 benchmark. Furthermore, randomized eigensolvers are employed to improve the efficiency of solving the eigenvalue problems.}, - url = {https://grandmaster.colorado.edu/copper/2022/}, - keywords = {} -} - -@misc{Heinlein:2022:SIAMPP:NDF, - title = {New Developments of the FROSch Domain Decomposition Solver Package}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {SIAM PP22}, - note = {SIAM Conference on Parallel Processing for Scientific Computing, SIAM PP22, Virtual, February 23-26}, - abstract = {Schwarz methods are an algorithmic framework for a large class of domain decomposition methods. The software FROSch (Fast and Robust Overlapping Schwarz), which is part of the Trilinos package ShyLU, provides a highly scalable implementation of the Schwarz framework, and the resulting solvers are based on the construction and combination of the relevant Schwarz operators. FROSch currently focusses on Schwarz operators that are algebraic in the sense that they can be constructed from a fully assembled, parallel distributed matrix. This is facilitated by the use of extension-based coarse spaces, such as generalized Dryja-Smith-Wildund (GDSW) type coarse spaces. This talk gives an overview of the FROSch software framework as well as current developments in improving the performance of the solvers, for instance, due to the use of inexact subdomain and coarse solvers. Moreover, recent parallel results for challenging applications, such as coupled multiphysics simulations of land ice in Greenland and Antarctica, are presented.}, - url = {https://www.siam.org/conferences/cm/conference/pp22}, - keywords = {} -} - -@misc{Heinlein:2022:RUB:SCS, - title = {Spectral coarse spaces for overlapping Schwarz methods based on energy-minimizing extensions}, - author = {Alexander Heinlein}, - year = {2022}, - abbr = {Seminar}, - note = {Seminar, Ruhr-Universit\"at Bochum, January 13}, - abstract = {Discretizing partial differential equations often results in sparse linear equation systems, and high spatial resolutions lead to large systems, which can be solved efficiently using iterative methods. A suitable class of solvers are Krylov methods preconditioned by domain decomposition preconditioners, which are scalable and robust for a wide range of problems. Unfortunately, highly heterogeneous problems arising, e.g., in the simulation of composite materials or porous media generally lead to unfavorable distributions of the eigenvalues of the system matrix that cause slow convergence for many solvers, including classical domain decomposition preconditioners. In order to retain robustness of domain decomposition methods, the coarse space can be enriched by additional coarse basis functions computed from eigenmodes of local generalized eigenvalue problems, leading to so-called spectral or adaptive coarse spaces. This talk deals with a specific class of adaptive coarse spaces for overlapping Schwarz methods which are based on a partition of the interface of the corresponding nonoverlapping domain decomposition. In particular, the generalized eigenvalue problems are based on energy-minimizing extensions corresponding to the interface components. The presented methods have a provable condition number bound, which is independent of the contrast of the coefficient functions. A great challenge is to construct adaptive coarse spaces that are robust but can be built algebraically, that is, using only the fully assembled system matrix without additional Neumann matrices or geometrical information. In this talk, a novel adaptive coarse space that is both robust and algebraic is introduced. Furthermore, approaches for combining adaptive coarse spaces with nonlinear preconditioning as well as machine learning techniques are discussed. The talk is based on joint work with Axel Klawonn, Jascha Knepper, Martin Lanser, Janine Weber (University of Cologne), Oliver Rheinbach (TU Bergakademie Freiberg), Kathrin Smetana (Stevens Institute of Technology), and Olof Widlund (New York University).}, - keywords = {} -} - -@misc{Heinlein:2021:PPS:SMC, - title = {Surrogate Models for Computational Fluid Dynamics Simulations Using Convolutional Autoencoder Neural Networks and Physical Constraints}, - author = {Alexander Heinlein}, - year = {2021}, - abbr = {PPS Lecture}, - note = {Pretty Porous Science Lecture, Universit\"at Stuttgart, December 7}, - abstract = {Simulations of fluid flow are generally very costly because high grid resolutions are not only required to obtain quantitatively accurate results, but too low grid resolutions may also lead to qualitatively incorrect results. In applications, however, one is often not interested in accurate approximations of the complete flow field but only in the qualitative behavior of the flow or in individual quantities (e.g., maximum velocity, pressure drop within a section of a pipe, or wall shear stresses at certain locations). In this talk, the use of convolutional autoencoder neural networks to construct efficient reduced order surrogate models for high fidelity computational fluid dynamics (CFD) simulations is discussed; cf. [Eichinger et al., 2021] and [Eichinger et al., submitted 2020]. Using this approach, which is inspired by [Guo et al., 2016], it is possible to build surrogate models for varying geometries. In particular, the geometry is the input of the neural network, and the flow and pressure fields are the output. The proposed framework is very general since the geometry and solution fields are simply encoded as pixel images, which allows the application to various types of geometries; also the extension to other physics is, in principle, straight forward. In order to construct accurate surrogate models, U-Net [Ronneberger et al., 2015] type convolutional neural networks, which are very successful in image recognition and segmentation tasks, are employed and the architecture and hyper parameters are optimized to this application. As a first step, a fully supervised approach, which requires the availability of simulation results as the training data, is presented. Here, the choice of an appropriate loss function is crucial to obtain good results. After that, results for a newer unsupervised approach, which does not require CFD simulation results but is based on introducing physical constraints via the loss function. As a testbed for the surrogate models, the flow around obstacles with varying shape and size within a channel is considered. Moreover, results for the application to geometries of arteries with aneurysms are presented. In both cases, only two-dimensional configurations are considered for now. The results show that the surrogate models provide good predictions of the flow and pressure fields while being computationally much cheaper compared to classical CFD codes. In particular, the predictions can be performed on a workstation within a fraction of a second, without requiring the generation of a computational mesh. When evaluated on GPUs, the prediction time can be further reduced by factor of more than ten. The talk is based on joint work with Matthias Eichinger, Viktor Grimm, and Axel Klawonn (University of Cologne).}, - keywords = {} -} - -@misc{Heinlein:2021:TUG:FRO, - title = {FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica}, - author = {Alexander Heinlein}, - year = {2021}, - abbr = {TUG 2021}, - note = {Trilinos User-Developer Group Meeting 2021 (Virtual), November 30-December 2}, - url = {https://trilinos.github.io/trilinos_user-developer_group_meeting_2021.html}, - slides = {2021/2021-heinlein-tug-fro/2021-heinlein-frosch_land_ice_simulations.pdf}, - keywords = {selected} -} - -@misc{Heinlein:2021:DDSS:ESF, - title = {Exercise session: FROSch}, - author = {Alexander Heinlein}, - year = {2021}, - abbr = {DD Summer School}, - note = {Summer school on advanced DD methods, Politecnico di Milano, Milano, Italy, November 24-26}, - abstract = {Schwarz methods are an algorithmic framework for a large class of domain decomposition methods. The software FROSch (Fast and Robust Overlapping Schwarz), which is part of the Trilinos package ShyLU, provides a highly scalable implementation of the Schwarz framework, and the resulting solvers are based on the construction and combination of the relevant Schwarz operators. FROSch currently focusses on Schwarz operators that are algebraic in the sense that they can be constructed from a fully assembled, parallel distributed matrix. This is facilitated by the use of extension-based coarse spaces, such as generalized Dryja-Smith-Widlund (GDSW) type coarse spaces. In this lab session, the FROSch software framework will be introduced, and its usage will be explained based on simple model problems. The examples provided will allow investigating the influence of important algorithmic aspects of Schwarz methods, such as the variation of the width of the overlap or adding a coarse level, on the convergence of a preconditioned Krylov solver.}, - url = {https://gciara.wordpress.com/summer-school-on-dd-methods/}, - slides = {2021/2021-heinlein-ddss-esf/2021-heinlein-frosch.pdf}, - keywords = {} -} - -@misc{Heinlein:2021:CIRM:SMC, - title = {Surrogate Models for Computational Fluid Dynamics Simulations Using Convolutional Autoencoder Neural Networks and Physical Constraints}, - author = {Alexander Heinlein}, - year = {2021}, - abbr = {CIRM 2021}, - note = {Invited Lecture. CIRM Conference ``Analysis, Control and Numerics for PDE Models of Interest to Physical and Life Sciences'', Levico Terme, Italy, September 20-24}, - abstract = {Simulations of fluid flow are generally very costly because high grid resolutions are not only required to obtain quantitatively accurate results, but too low grid resolutions may also lead to qualitatively incorrect results. In applications, however, one is often not interested in accurate approximations of the complete flow field but only in the qualitative behavior of the flow or in individual quantities (e.g., maximum velocity, pressure drop within a section of a pipe, or wall shear stresses at certain locations). In this talk, the use of convolutional autoencoder neural networks to construct efficient reduced order surrogate models for high fidelity computational fluid dynamics (CFD) simulations is discussed; cf. [Eichinger et al., 2021] and [Eichinger et al., submitted 2020]. Using this approach, which is inspired by [Guo et al., 2016], it is possible to build surrogate models for varying geometries. In particular, the geometry is the input of the neural network, and the flow and pressure fields are the output. The proposed framework is very general since the geometry and solution fields are simply encoded as pixel images, which allows the application to various types of geometries; also the extension to other physics is, in principle, straight forward. In order to construct accurate surrogate models, U-Net [Ronneberger et al., 2015] type convolutional neural networks, which are very successful in image recognition and segmentation tasks, are employed and the architecture and hyper parameters are optimized to this application. As a first step, a fully supervised approach, which requires the availability of simulation results as the training data, is presented. Here, the choice of an appropriate loss function is crucial to obtain good results. After that, results for a newer unsupervised approach, which does not require CFD simulation results but is based on introducing physical constraints via the loss function. As a testbed for the surrogate models, the flow around obstacles with varying shape and size within a channel is considered. Moreover, results for the application to geometries of arteries with aneurysms are presented. In both cases, only two-dimensional configurations are considered for now. The results show that the surrogate models provide good predictions of the flow and pressure fields while being computationally much cheaper compared to classical CFD codes. In particular, the predictions can be performed on a workstation within a fraction of a second, without requiring the generation of a computational mesh. When evaluated on GPUs, the prediction time can be further reduced by factor of more than ten. The talk is based on joint work with Matthias Eichinger, Viktor Grimm, and Axel Klawonn (University of Cologne).}, - url = {https://pde-levico21.fbk.eu}, - keywords = {selected} -} - -@misc{Heinlein:2021:YIC:UIS, - title = {Using inexact subdomain and coarse solvers in FROSch preconditioners}, - author = {Alexander Heinlein}, - year = {2021}, - abbr = {YIC 2021}, - note = {YIC 2021 (Virtual), July 7-9}, - abstract = {FROSch (Fast and Robust Overlapping Schwarz) is a framework for parallel Schwarz domain decomposition preconditioners, which is part of Trilinos. Although being a general framework for the construction and combination of Schwarz operators, FROSch currently focusses on preconditioners that are algebraic in the sense that they can be constructed from a fully assembled, parallel distributed matrix. The computation of the first level is based on the construction of overlapping subdomains, which can be carried out based on the sparsity pattern of the matrix. In addition to that, robust and scalable coarse spaces are constructed from a partition of unity on the domain decomposition interface and energy-minimizing extensions, without the need for additional information. In particular, GDSW (Generalized Dryja-Smith-Widlund) type coarse spaces are considered. In this talk, the use of inexact solvers for the local overlapping problems and the global coarse problem will be investigated. For this purpose, inexact solvers from different packages from the Trilinos framework will be employed, e.g, from Ifpack2, MueLu, or FROSch itself.}, - url = {https://yic2021.upv.es}, - keywords = {} -} - -@misc{Heinlein:2021:Coupled:FRO, - title = {FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica}, - author = {Alexander Heinlein}, - year = {2021}, - abbr = {COUPLED 2021}, - note = {9th International Conference on Computational Methods for Coupled Problems in Science and Engineering (Virtual), June 14-16}, - abstract = {Greenland and Antarctic ice sheets store most of the fresh water on earth and mass loss from these ice sheets significantly contributes to sea-level rise. The simulation of temperature and velocity of the ice sheets gives rise to large highly nonlinear systems of equations. The solution of the associated tangent problems, arising in Newton’s method, is challenging also because of the strong anisotropy of the meshes. We first consider simulations of the ice velocity of Antarctica and the ice temperature of Greenland. We use one-level Schwarz preconditioners as well as GDSW (Generalized Dryja-Smith-Widlund) type preconditioners from the Trilinos package FROSch (Fast and Robust Schwarz), scaling up to 32 k processor cores (8 k MPI ranks and 4 OpenMP threads) for the finest Antarctica mesh; the corresponding velocity problem contains 566 M degrees of freedom. We then study the coupled velocity and temperature problem for the Greenland ice sheet. To the best of our knowledge, it is the first time that a scalable monolithic two-level preconditioner has been used for this multiphysics problem. We present strong scaling results, up to 4 k MPI ranks, using a monolithic GDSW type preconditioner with decoupled extensions from the FROSch package.}, - url = {https://congress.cimne.com/coupled2021}, - keywords = {} -} - -@misc{Heinlein:2021:BaNaNa:T, - title = {Trilinos}, - author = {Alexander Heinlein}, - year = {2021}, - abbr = {BaNaNa}, - note = {BaNaNa talk, SIAM Student Chapter Delft, May 19}, - abstract = {Trilinos is a collection of more than 50 open-source software packages that can be used as building blocks for all kinds of scientific applications. For example, packages exist for iterative solvers, PDE-constrained optimization problems and automatic differentiation. This talk will give a brief introduction to Trilinos. Special attention is paid to the Tpetra package that facilitates parallel sparse linear algebra.}, - url = {https://projectbanana.github.io/lecture/2021/05/19/Trilinos.html}, - keywords = {} -} - -@misc{Heinlein:2021:CM:FRO, - title = {FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica}, - author = {Alexander Heinlein}, - year = {2021}, - abbr = {CM2021}, - note = {20th Copper Mountain Conference On Multigrid Methods (Virtual), March 29 - April 2}, - abstract = {Greenland and Antarctic ice sheets store most of the fresh water on earth and mass loss from these ice sheets significantly contributes to sea-level rise. The simulation of temperature and velocity of the ice sheets gives rise to large highly nonlinear systems of equations. The solution of the associated tangent problems, arising in Newton’s method, is challenging also because of the strong anisotropy of the meshes. We first consider simulations of the ice velocity of Antarctica and the ice temperature of Greenland. We use one-level Schwarz preconditioners as well as GDSW (Generalized Dryja-Smith-Widlund) type preconditioners from the Trilinos package FROSch (Fast and Robust Schwarz), scaling up to 32 k processor cores (8 k MPI ranks and 4 OpenMP threads) for the finest Antarctica mesh; the corresponding velocity problem contains 566 M degrees of freedom. We then study the coupled velocity and temperature problem for the Greenland ice sheet. To the best of our knowledge, it is the first time that a scalable monolithic two-level preconditioner has been used for this multiphysics problem. We present strong scaling results, up to 4 k MPI ranks, using a monolithic GDSW type preconditioner with decoupled extensions from the FROSch package.}, - url = {https://grandmaster.colorado.edu/copper/2021/}, - keywords = {} -} - -@misc{Heinlein:2021:GAMM:CAW, - title = {Comparing Arterial Wall Models for the Curved Tube Fluid-Structure Interaction Benchmark}, - author = {Alexander Heinlein}, - year = {2021}, - abbr = {GAMM 2020@21}, - note = {91st GAMM Annual Meeting (Virtual), Kassel, Germany, March 15-19}, - abstract = {Stress distributions in walls of in vivo arteries (transmural stresses) are a major factor for the course of cardiac diseases; for instance, they are a driving force for the process of arteriosclerosis and arteriogenesis. In order to make accurate predictions of realistic stress distributions using numerical fluid-structure interaction (FSI) simulations, the use of appropriate material models for the arterial walls is essential. In the literature, a wide range of material models is used for this purpose. In this talk, several existing material models for arterial walls are compared based on the curved tube FSI benchmark. In the benchmark configuration, the geometry corresponds to a bended idealized coronary artery with only one material layer. Furthermore, two phases are considered: first, the artery is brought to a physiological pressure of 80 mmHg, and second, the inflow profile of one heartbeat is imposed. As material models, linear elasticity, isotropic hyperelasticity, i.e., a Neo-Hookean material model, as well as the nonlinear anisotropic hyperelastic material models are taken into account. Numerical results for both linear elasticity and Neo-Hookean material models differ significantly from the results obtained with nonlinear anisotropic hyperelastic material models, which have been fitted to experimental data of real arteries. Moreover, the performance of the parallel FSI simulations using different material models is investigated.}, - url = {https://jahrestagung.gamm-ev.de/index.php/2020/2020-annual-meeting}, - keywords = {} -} - -@misc{Heinlein:2021:DelftNA:FRO, - title = {Fast and Robust Overlapping Schwarz Methods -- New Developments and an Efficient Parallel Implementation in Trilinos}, - author = {Alexander Heinlein}, - year = {2021}, - abbr = {Seminar}, - note = {Numerical Analysis Seminar, TU Delft, Online, February 19}, - abstract = {FROSch (Fast and Robust Overlapping Schwarz) is a framework for parallel Schwarz domain decomposition preconditioners, which is part of the Trilinos package ShyLU. Although being a general framework for the construction and combination of Schwarz operators, FROSch currently focusses on preconditioners that are algebraic in the sense that they can be constructed from a fully assembled, parallel distributed matrix. This is facilitated by the use of extension based coarse spaces, such as GDSW (Generalized Dryja-Smith-Widlund) type coarse spaces. This talk will cover several Schwarz preconditioning techniques which are currently being developed based on the FROSch package: reduced dimension coarse spaces, multilevel GDSW coarse spaces, and monolithic preconditioners for block systems. These approaches are introduced and applied to different problems ranging from a Poisson equation to a coupled multi physics simulations of land ice in Antarctica. Furthermore, a brief overview of some related Schwarz preconditioning techniques, which are not implemented in FROSch yet, will be given. This includes nonlinear two-level Schwarz preconditioning techniques based on Galerkin projections, adaptive coarse spaces for highly heterogeneous problems, as well as the application of machine learning techniques in order to improve the efficiency of these adaptive coarse spaces.}, - url = {https://www.tudelft.nl/cse/events/dcse-conferences/numerical-analysis-seminars}, - keywords = {} -} - -@misc{Heinlein:2021:StuttgartKolloquium:FRO, - title = {Fast and Robust Overlapping Schwarz Methods -- New Developments and an Efficient Parallel Implementation in Trilinos}, - author = {Alexander Heinlein}, - year = {2021}, - abbr = {Colloquium}, - note = {Mathematisches Kolloquium, Universit\"at Stuttgart, Online, February 16}, - abstract = {Schwarz methods are an algorithmic framework for a large class of domain decomposition methods. The software FROSch (Fast and Robust Overlapping Schwarz), which is part of the Trilinos package ShyLU, provides a highly scalable implementation of the Schwarz framework, and the resulting solvers are based on the construction and combination of the relevant Schwarz operators. FROSch currently focusses on Schwarz operators that are algebraic in the sense that they can be constructed from a fully assembled, parallel distributed matrix. This is facilitated by the use of extension-based coarse spaces, such as generalized Dryja-Smith-Widlund (GDSW) type coarse spaces. This talk will cover several Schwarz preconditioning techniques which are currently being developed based on the FROSch package: reduced dimension coarse spaces, multilevel GDSW preconditioners, and monolithic preconditioners for block systems. These approaches are introduced and applied to different problems ranging from a simple Poisson equation to a coupled multiphysics simulations of land ice in Greenland and Antarctica. Furthermore, a brief overview of related Schwarz preconditioning techniques which are currently being developed but not implemented in FROSch yet will be given. This includes nonlinear two-level Schwarz preconditioning techniques based on Galerkin projections, adaptive coarse spaces for highly heterogeneous problems, as well as novel hybrid preconditioning algorithms combining adaptive coarse spaces and machine learning techniques.}, - keywords = {} -} - -@misc{Heinlein:2021:GAMMCSE:FPC, - title = {Flow Predictions Using Convolutional Neural Networks}, - author = {Alexander Heinlein}, - year = {2021}, - abbr = {Workshop}, - note = {GAMM CSE Workshop 2021, Online, January 15, 22, and 29}, - abstract = {Simulations of fluid flow are generally very costly because too low grid resolutions may even lead to qualitatively incorrect solutions. In applications, however, one is often not interested in accurate approximations of the complete flow field but only in the qualitative behavior of the flow or in individual quantities (e.g., maximum velocity, pressure drop within a section of a pipe, or wall shear stresses at certain locations). In this talk, the use of Convolutional Neural Networks (CNNs) to predict fluid flow fields is investigated. Therefore, U-Net [Ronneberger et al., 2015] type convolutional neural networks, which are successfully used for image recognition and segmentation tasks, are applied in this context. As a model problem, the flow around obstacles with varying shape and size within a channel is considered. Obstacles of certain type are used as training data, and the generalization of the models to other obstacle geometries and sizes is analyzed. Even though, the training of a neural network is expensive, its evaluation is quite cheap compared to fully resolved Computational Fluid Dynamics (CFD) simulations. This results in a multitude of application possibilities for neural networks in this context, especially in time critical settings.}, - url = {https://www.mb.uni-siegen.de/nm/workshops/gamm-cse-2021/}, - keywords = {} -} - -@misc{Heinlein:2020:DD26:FRO, - title = {FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica}, - author = {Alexander Heinlein}, - year = {2020}, - abbr = {DD XXVI}, - note = {26th International Conference on Domain Decomposition Methods (Virtual), Hong Kong, China, December 7-12}, - url = {https://www.math.cuhk.edu.hk/conference/dd26/?Conference-Home}, - keywords = {} -} - -@misc{Heinlein:2020:DD26:FPC, - title = {Flow Predictions Using Convolutional Neural Networks}, - author = {Alexander Heinlein}, - year = {2020}, - abbr = {DD XXVI}, - note = {26th International Conference on Domain Decomposition Methods (Virtual), Hong Kong, China, December 7-12}, - url = {https://www.math.cuhk.edu.hk/conference/dd26/?Conference-Home}, - keywords = {} -} - -@misc{Heinlein:2020:Stuttgart:IL, - title = {Inaugural Lecture}, - author = {Alexander Heinlein}, - year = {2020}, - abbr = {Seminar}, - note = {IANS Highlight Seminar, Universit\"at Stuttgart, Germany, October 26}, - keywords = {} -} - -@misc{Heinlein:2020:Stuttgart:SQ, - title = {SimTech Quickie}, - author = {Alexander Heinlein}, - year = {2020}, - abbr = {SimTech}, - note = {Universit\"at Stuttgart, Germany, October 19}, - keywords = {} -} - -@misc{Heinlein:2020:GAMMBioMech:CAW, - title = {Comparing Arterial Wall Models for the Curved Tube Fluid-Structure Interaction Benchmark}, - author = {Alexander Heinlein}, - year = {2020}, - abbr = {Workshop}, - note = {Jahrestreffen GAMM Fachausschuss “Computational Biomechanics” 2020, Bildungszentrum Kloster Banz, Germany, September 21-22}, - keywords = {} -} - -@misc{Heinlein:2020:Kevelaer:CAW, - title = {Comparing Arterial Wall Models for the Curved Tube Fluid-Structure Interaction Benchmark}, - author = {Alexander Heinlein}, - year = {2020}, - abbr = {Workshop}, - note = {Workshop on Numerical Mathematics and Mechanics, Kevelaer, Germany, February 3-6}, - keywords = {} -} - -@misc{Heinlein:2020:HUB:OSP, - title = {Overlapping Schwarz preconditioning techniques for nonlinear problems}, - author = {Alexander Heinlein}, - year = {2020}, - abbr = {Seminar}, - note = {Seminar, Humboldt-Universit\"at zu Berlin, Germany, January 29}, - keywords = {} -} - -@misc{Heinlein:2020:SciML:FPC, - title = {Flow Predictions Using Convolutional Neural Networks}, - author = {Alexander Heinlein}, - year = {2020}, - abbr = {Workshop}, - note = {International Workshop on Scientific Machine Learning, Universit\"at zu Köln, Germany, January 8-10}, - url = {https://cds.uni-koeln.de/en/workshops/international-workshop-on-scientific-machine-learning-2019/home}, - keywords = {} -} - -@misc{Heinlein:2019:ENUMATH2019:FPC, - title = {Flow predictions using convolutional neural network}, - author = {Alexander Heinlein}, - year = {2019}, - abbr = {ENUMATH 2019}, - note = {ENUMATH Conference 2019, Egmond aan Zee, Netherlands, October 2}, - url = {https://www.enumath2019.eu/}, - keywords = {} -} - -@misc{Heinlein:2019:ENUMATH2019:FRO, - title = {FROSch – A framework for parallel Schwarz preconditioners in Trilinos}, - author = {Alexander Heinlein}, - year = {2019}, - abbr = {ENUMATH 2019}, - note = {ENUMATH Conference 2019, Egmond aan Zee, Netherlands, October 2}, - url = {https://www.enumath2019.eu/}, - keywords = {} -} - -@misc{Heinlein:2019:Sandia:FRO, - title = {FROSch – A framework for parallel Schwarz preconditioners in Trilinos}, - author = {Alexander Heinlein}, - year = {2019}, - abbr = {Seminar}, - note = {Seminar, Sandia National Laboratories, USA, September 3}, - keywords = {} -} - -@misc{Heinlein:2019:Mafelap:FRO, - title = {The FROSch (Fast and Robust Overlapping Schwarz) Package in Cardiovascular Simulations}, - author = {Alexander Heinlein}, - year = {2019}, - abbr = {MAFELAP 2019}, - note = {MAFELAP 2019, Brunel University London, England, June 19}, - url = {http://people.brunel.ac.uk/~icsrsss/bicom/mafelap/}, - keywords = {} -} - -@misc{Heinlein:2019:EuroTUG:FRO, - title = {Fast and Robust Overlapping Schwarz: FROSch}, - author = {Alexander Heinlein}, - year = {2019}, - abbr = {EuroTUG}, - note = {European Trilinos User Group Meeting 2019, ETH Zürich, Switzerland, June 11}, - url = {https://trilinos.github.io/european_trilinos_user_group_meeting_2019.html}, - keywords = {} -} - -@misc{Heinlein:2019:DAMUT:DRE, - title = {Designing robust and efficient domain decomposition methods for highly heterogeneous problems using local spectral information and machine learning techniques}, - author = {Alexander Heinlein}, - year = {2019}, - abbr = {DAMUT Colloquium}, - note = {Invited talk. DAMUT Colloquium, University of Twente, Netherlands, May 8}, - url = {https://www.utwente.nl/en/eemcs/damut/damutcolloquium/abstracts/2019/2019-01b-08may}, - keywords = {selected} -} - -@misc{Heinlein:2019:GAMM:FRO, - title = {FROSch – A Parallel Implementation of the GDSW Domain Decomposition Preconditioner in Trilinos}, - author = {Alexander Heinlein}, - year = {2019}, - abbr = {GAMM 2019}, - note = {90th GAMM Annual Meeting, Vienna, Austria, February 18-22}, - url = {https://jahrestagung.gamm.org/year-2019/annual-meeting/}, - keywords = {} -} - -@misc{Heinlein:2018:WorkshopCardio:FRO, - title = {The FROSch Package in Cardiovascular Simulations}, - author = {Alexander Heinlein}, - year = {2018}, - abbr = {Workshop}, - note = {Workshop on Modeling, Simulation and Optimization of the Cardiovascular System, Magdeburg, Germany, October 22-24}, - keywords = {} -} - -@misc{Heinlein:2018:EPFL:FRO, - title = {FROSch – A Parallel Implementation of the GDSW Domain Decomposition Preconditioner in Trilinos}, - author = {Alexander Heinlein}, - year = {2018}, - abbr = {Seminar}, - note = {Seminar, EPFL, Lausanne, Switzerland, August 30}, - keywords = {} -} - -@misc{Heinlein:2018:DD25:FRO, - title = {FROSch – A Parallel Implementation of the GDSW Domain Decomposition Preconditioner in Trilinos}, - author = {Alexander Heinlein}, - year = {2018}, - abbr = {DD XXV}, - note = {25th International Conference on Domain Decomposition Methods, St. John’s, Newfoundland, Canada, July 23-27}, - url = {https://www.math.mun.ca/dd25/}, - keywords = {} -} - -@misc{Heinlein:2018:DD25:TLE, - title = {Three-Level Extensions of the GDSW Overlapping Schwarz Preconditioner}, - author = {Alexander Heinlein}, - year = {2018}, - abbr = {DD XXV}, - note = {25th International Conference on Domain Decomposition Methods, St. John’s, Canada, July 23-27}, - url = {https://www.math.mun.ca/dd25/}, - keywords = {} -} - -@misc{Heinlein:2018:DD25:MDC, - title = {Multiscale Discretizations and Coarse Spaces Based on ACMS}, - author = {Alexander Heinlein}, - year = {2018}, - abbr = {DD XXV}, - note = {25th International Conference on Domain Decomposition Methods, St. John’s, Canada, July 23-27}, - url = {https://www.math.mun.ca/dd25/}, - keywords = {} -} - -@misc{Heinlein:2018:ECCM:FRO, - title = {FROSch – A Parallel Implementation of the GDSW Domain Decomposition Preconditioner in Trilinos}, - author = {Alexander Heinlein}, - year = {2018}, - abbr = {ECCM 6}, - note = {6th European Conference on Computational Mechanics and 7th European Conference on Computational Fluid Dynamics, Glasgow, UK, June 11-15}, - url = {http://congress.cimne.com/eccm_ecfd2018/frontal/introduction.asp}, - keywords = {} -} - -@misc{Heinlein:2018:GAMM:FRO, - title = {FROSch – A Parallel Implementation of the GDSW Domain Decomposition Preconditioner in Trilinos}, - author = {Alexander Heinlein}, - year = {2018}, - abbr = {GAMM 2018}, - note = {89th GAMM Annual Meeting, Munich, Germany, March 19-23}, - url = {https://jahrestagung.gamm.org/year-2018/annual-meeting/}, - keywords = {} -} - -@misc{Heinlein:2017:Sandia:FRO, - title = {FROSch – A Parallel Implementation of the GDSW Domain Decomposition Preconditioner in Trilinos}, - author = {Alexander Heinlein}, - year = {2017}, - abbr = {SNL}, - note = {Seminar, Sandia National Laboratories, USA, October 9}, - keywords = {} -} - -@misc{Heinlein:2017:PASC:DDB, - title = {Domain-Decomposition-Based Fluid-Structure Interaction Methods Using Nonlinear Anisotropic Arterial Wall Models}, - author = {Alexander Heinlein}, - year = {2017}, - abbr = {PASC17}, - note = {PASC17 Conference, Lugano, Switzerland, Juni 26-28}, - url = {https://pasc17.pasc-conference.org/}, - keywords = {} -} - -@misc{Heinlein:2017:DLR:ACS, - title = {An Adaptive Coarse Space for the GDSW Algorithm}, - author = {Alexander Heinlein}, - year = {2017}, - abbr = {DLR}, - note = {Workshop of the German Center for Aerospace and the Mathematical Institute at the Universit\"at zu K\"oln, Cologne, Germany, March 24}, - keywords = {} -} - -@misc{Heinlein:2017:GAMM:DDB, - title = {Domain-Decomposition-Based Fluid-Structure Interaction Methods Using Nonlinear Anisotropic Arterial Wall Models}, - author = {Alexander Heinlein}, - year = {2017}, - abbr = {GAMM 2017}, - note = {88th GAMM Annual Meeting, Weimar, Germany, March 6-10}, - url = {https://jahrestagung.gamm.org/year-2017/annual-meeting/}, - keywords = {} -} - -@misc{Heinlein:2017:Kevelaer:DDB, - title = {Domain-Decomposition-Based Fluid-Structure Interaction Methods Using Nonlinear Anisotropic Arterial Wall Models}, - author = {Alexander Heinlein}, - year = {2017}, - abbr = {NMM}, - note = {Workshop on Numerical Mathematics and Mechanics, Kevelaer, Germany, February 13-15}, - keywords = {} -} - -@misc{Heinlein:2017:DD24:ACS, - title = {An Adaptive Coarse Space for the GDSW Algorithm}, - author = {Alexander Heinlein}, - year = {2017}, - abbr = {DD XIV}, - note = {24th International Conference on Domain Decomposition Methods, Svalbard, Norway, February 6-10}, - url = {http://www.ddm.org/dd24/home.html}, - keywords = {} -} - -@misc{Heinlein:2016:GAMMCSE:DDB, - title = {Domain-Decomposition-Based Fluid-Structure Interaction Methods Using Nonlinear Anisotropic Arterial Wall Models}, - author = {Alexander Heinlein}, - year = {2016}, - abbr = {GAMM CSE}, - note = {GAMM CSE Workshop 2016, Kassel, September 8-9}, - keywords = {} -} - -@misc{Heinlein:2016:DLR:ACS, - title = {An Adaptive Coarse Space for the GDSW Algorithm}, - author = {Alexander Heinlein}, - year = {2016}, - abbr = {DLR}, - note = {Workshop of the German Center for Aerospace and the Mathematical Institute at the Universit\"at zu K\"oln, Cologne, March 14}, - keywords = {} -} - -@misc{Heinlein:2016:GAMM:PIA, - title = {A parallel implementation of the approximate component mode synthesis special finite element method in 2D}, - author = {Alexander Heinlein}, - year = {2016}, - abbr = {GAMM 2016}, - note = {Joint Annual Meeting of DMV and GAMM, Braunschweig, Germany, March 7-11}, - url = {https://jahrestagung.gamm.org/annual-meeting-2016/annual-meeting/}, - keywords = {} -} - -@misc{Heinlein:2016:Kevelaer:PIA, - title = {A parallel implementation of the approximate component mode synthesis special finite element method in 2D}, - author = {Alexander Heinlein}, - year = {2016}, - abbr = {NMM}, - note = {Workshop on Numerical Mathematics and Mechanics, Kevelaer, Germany, February 22-25}, - keywords = {} -} - -@misc{Heinlein:2015:PredMedicine:DDB, - title = {Domain-Decomposition-Based Fluid-Structure Interaction Methods using Nonlinear Anisotropic Arterial Wall Models}, - author = {Alexander Heinlein}, - year = {2015}, - abbr = {IST}, - note = {Workshop on Innovative Modeling Techniques for Predictive Medicine, Lisbon, Portugal, November 12}, - keywords = {} -} - -@misc{Heinlein:2015:ENUMATH2015:DDB, - title = {Domain-Decomposition-Based Fluid-Structure Interaction Methods using Nonlinear Anisotropic Arterial Wall Models}, - author = {Alexander Heinlein}, - year = {2015}, - abbr = {ENUMATH 2015}, - note = {ENUMATH Conference 2015, Ankara, Turkey, September 14-18}, - keywords = {} -} - -@misc{Heinlein:2015:DD23:DDB, - title = {Domain-Decomposition-Based Fluid-Structure Interaction Methods using Nonlinear Anisotropic Arterial Wall Models}, - author = {Alexander Heinlein}, - year = {2015}, - abbr = {DD XXIII}, - note = {23rd International Conference on Domain Decomposition Methods, Jeju Island, Korea, July 6-10}, - url = {https://dd23.kaist.ac.kr/}, - keywords = {} -} - -@misc{Heinlein:2015:GAMM:FSI, - title = {Fluid-Structure Interaction in Hemodynamics Using Nonlinear, Anisotropic Hyperelastic Wall Models}, - author = {Alexander Heinlein}, - year = {2015}, - abbr = {GAMM 2015}, - note = {86th GAMM Annual Meeting, Lecce, Italy, March 23-27}, - url = {https://jahrestagung.gamm.org/annual-meeting-2015/annual-meeting/}, - keywords = {} -} - -@misc{Heinlein:2015:Kevelaer:FSI, - title = {Fluid-Structure Interaction in Hemodynamics Using Nonlinear, Anisotropic Hyperelastic Wall Models}, - author = {Alexander Heinlein}, - year = {2015}, - abbr = {NMM}, - note = {Workshop on Numerical Mathematics and Mechanics, Kevelaer, Germany, February 23-25}, - keywords = {} -} - -@misc{Heinlein:2014:GAMMBioMech:DDB, - title = {Fluid-Structure Interaction in Hemodynamics Using Nonlinear, Anisotropic Hyperelastic Wall Models}, - author = {Alexander Heinlein}, - year = {2014}, - abbr = {Graz}, - note = {International Workshop on Modelling and Simulation in Biomechanics, Graz, Austria, September 15-17}, - keywords = {selected} -} - -@misc{Heinlein:2014:Kevelaer:GDSW, - title = {GDSW - Domain Decomposition for Fluid-Structure Interaction}, - author = {Alexander Heinlein}, - year = {2014}, - abbr = {NMM}, - note = {Workshop on Numerical Mathematics and Mechanics, Kevelaer, Germany, February 10-12}, - keywords = {} -} diff --git a/_bibliography/theses.bib b/_bibliography/theses.bib deleted file mode 100644 index 8f2a0758032b..000000000000 --- a/_bibliography/theses.bib +++ /dev/null @@ -1,681 +0,0 @@ ---- ---- -References -========== - -# phd - -@phdthesis{Grimm:PFP, - author = {Viktor Grimm}, - title = {Predicting the Flow in Patient-Specific Aneurysm Geometries Using Convolutional Neural Networks}, - school = {Universit{\"a}t zu K{\"o}ln}, - year = {2023}, - url = {}, - abbr = {PhD Thesis}, - abstract = {}, - note = {Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {phd, supervised} -} - -@phdthesis{Roever:2022:MGD, - author = {Friederike R\"over}, - title = {Multi-Level Extensions for the {F}ast and {R}obust {O}verlapping {S}chwarz Preconditioners}, - school = {Technische Universit\"at Bergakademie Freiberg}, - year = {2023}, - url = {}, - abbr = {PhD Thesis}, - abstract = {}, - note = {Supervision by Prof.\ Dr.\ Oliver Rheinbach and Dr.\ Alexander Heinlein}, - keywords = {phd, supervised} -} - -@phdthesis{Knepper:2022:ACS, - author = {Jascha Knepper}, - title = {Adaptive Coarse Spaces for the Overlapping Schwarz Method and Multiscale Elliptic Problems}, - school = {Universit{\"a}t zu K{\"o}ln}, - year = {2022}, - url = {https://kups.ub.uni-koeln.de/62002}, - abbr = {PhD Thesis}, - abstract = {}, - note = {Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {phd, supervised} -} - -@phdthesis{Weber:2022:ERF, - author = {Janine Weber}, - title = {Efficient and Robust FETI-DP and BDDC Methods -- Approximate Coarse Spaces and Deep Learning-Based Adaptive Coarse Spaces}, - school = {Universit{\"a}t zu K{\"o}ln}, - year = {2022}, - url = {https://kups.ub.uni-koeln.de/55179/}, - abbr = {PhD Thesis}, - abstract = {}, - note = {Supervision by Prof.\ Dr.\ Axel Klawonn, Dr.\ Alexander Heinlein, and Dr.\ Martin Lanser}, - keywords = {phd, supervised} -} - -@phdthesis{Hochmuth:2021:POS, - author = {Christian Hochmuth}, - title = {Parallel Overlapping Schwarz Preconditioners for Incompressible Fluid Flow and Fluid-Structure Interaction Problems}, - school = {Universit{\"a}t zu K{\"o}ln}, - year = {2021}, - url = {https://kups.ub.uni-koeln.de/11345}, - abbr = {PhD Thesis}, - abstract = {Efficient methods for the approximation of solutions to incompressible fluid flow and fluid-structure interaction problems are presented. In particular, partial differential equations (PDEs) are derived from basic conservation principles. First, the incompressible Navier-Stokes equations for Newtonian fluids are introduced. This is followed by a consideration of solid mechanical problems. Both, the fluid equations and the equation for solid problems are then coupled and a fluid-structure interaction problem is constructed. Furthermore, a discretization by the finite element method for weak formulations of these problems is described. This spatial discretization of variables is followed by a discretization of the remaining time-dependent parts. An implementation of the discretizations and problems in a parallel C++ software environment is described. This implementation is based on the software package Trilinos. The parallel execution of a program is the essence of High Performance Computing (HPC). HPC clusters are, in general, machines with several tens of thousands of cores. The fastest current machine, as of the TOP500 list from November 2019, has over 2.4 million cores, while the largest machine possesses over 10 million cores. To achieve sufficient accuracy of the approximate solutions, a fine spatial discretization must be used. In particular, fine spatial discretizations lead to systems with large sparse matrices that have to be solved. Iterative preconditioned Krylov methods are among the most widely used and efficient solution strategies for these systems. Robust and efficient preconditioners which possess good scaling behavior for a parallel execution on several thousand cores are the main component. In this thesis, the focus is on parallel algebraic preconditioners for fluid and fluid-structure interaction problems. Therefore, monolithic overlapping Schwarz preconditioners for saddle point problems of Stokes and Navier-Stokes problems are presented. Monolithic preconditioners for incompressible fluid flow problems can significantly improve the convergence speed compared to preconditioners based on block factorizations. In order to obtain numerically scalable algorithms, coarse spaces obtained from the Generalized Dryja-Smith-Widlund (GDSW) and the Reduced dimension GDSW (RGDSW) approach are used. These coarse spaces can be constructed in an essentially algebraic way. Numerical results of the parallel implementation are presented for various incompressible fluid flow problems. Good scalability for up to 11 979 MPI ranks, which corresponds to the largest problem configuration fitting on the employed supercomputer, were achieved. A comparison of these monolithic approaches and commonly used block preconditioners with respect to time-to-solution is made. Similarly, the most efficient construction of two-level overlapping Schwarz preconditioners with GDSW and RGDSW coarse spaces for solid problems is reported. These techniques are then combined to efficiently solve fully coupled monolithic fluid-structure interaction problems.}, - note = {Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {phd, supervised} -} - -@unpublished{Cumaru:ASN, - author = {Filipe Cumaru Silva Alves}, - title = {Accurate and scalable numerical simulation of underground hydrogen storage in depleted geological reservoirs}, - school = {Delft University of Technology}, - abbr = {PhD Thesis}, - note = {Ongoing PhD thesis. Supervision by Dr.\ Alexander Heinlein and Prof.\ Hadi Hajibeygi}, - keywords = {phd, supervised, ongoing} -} - -@unpublished{Slepova:ASN, - author = {Ksenia Slepova}, - title = {PDE-based segmentation methods for noisy MRI scans}, - school = {Delft University of Technology}, - abbr = {PhD Thesis}, - note = {Ongoing PhD thesis. Supervision by Prof.\ Martin van Gijzen and Dr.\ Alexander Heinlein}, - keywords = {phd, supervised, ongoing} -} - -@unpublished{Verburg:ASN, - author = {Corné Verburg}, - title = {Physiology-informed data-supported modeling of potato crop resilience}, - school = {Delft University of Technology}, - abbr = {PhD Thesis}, - note = {Ongoing PhD thesis. Supervision by Dr.\ Neil Budko and Dr.\ Alexander Heinlein}, - keywords = {phd, supervised, ongoing} -} - -@unpublished{Medricky:ACS, - author = {Tomáš Medřický}, - title = {Adaptive coarse spaces for domain decomposition methods for modular topology optimization}, - school = {Czech Technical University in Prague}, - abbr = {PhD Thesis}, - note = {Ongoing PhD thesis. Supervision by Dr.\ Martin Doškář and Dr.\ Alexander Heinlein}, - keywords = {phd, supervised, ongoing} -} - -@unpublished{Meng:MLE, - author = {Yuhuang Meng}, - title = {Machine learning-enhanced numerical solvers for the shallow water equations}, - school = {Delft University of Technology}, - abbr = {PhD Thesis}, - note = {Ongoing PhD thesis. Supervision by Dr.\ Alexander Heinlein and Dr.\ Jing Zhao}, - keywords = {phd, supervised, ongoing} -} - -@unpublished{Kevopoulos:CSM, - author = {Konstantinos Kevopoulos}, - title = {Cardiac surrogate models}, - school = {Delft University of Technology}, - abbr = {PhD Thesis}, - note = {Ongoing PhD thesis. Supervision by Dr.\ Mathias Peirlinck and Dr.\ Alexander Heinlein}, - keywords = {phd, supervised, ongoing} -} - -# diploma - -@thesis{Grigoleit:2017:FSI, - author = {Nicole Grigoleit}, - title = {Fluid-Struktur Interaktion mit LifeV -- Eine Sensitivit\"atsuntersuchung am Beispiel von gef\"a\ss lumeneinengenden Prozessen}, - school = {Technische Universit\"at Bergakademie Freiberg}, - year = {2017}, - abbr = {Diploma Thesis}, - note = {Diploma thesis. Supervision by Prof.\ Dr.\ Oliver Rheinbach and Dr.\ Alexander Heinlein}, - keywords = {diploma, supervised} -} - -# master - -@unpublished{Kielhofer:2024:DPI, - author = {Marius Kielhöfer}, - title = {Developing a physics-informed machine learning model to classify sensor data quality}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Ongoing master thesis. Supervision by Dr.\ Alexander Heinlein and Oscar van der Ven (Boskalis)}, - keywords = {master, supervised, ongoing} -} - -@unpublished{Chen:2024:DDN, - author = {Wanxin Chen}, - title = {Domain decomposition-based neural networks for complex shaped domains}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Ongoing master thesis. Supervision by Dr.\ Alexander Heinlein and Dr.\ Amanda Howard (Pacific Northwest National Laboratory)}, - keywords = {master, supervised, ongoing} -} - -@unpublished{Wu:2024:DGN, - author = {Yuhan Wu}, - title = {Blending Neural Operators and Relaxation Methods in PDE Numerical Solvers}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Ongoing master thesis. Supervision by Dr.\ Alexander Heinlein and Prof.\ Victorita Dolean (TU Eindhoven)}, - keywords = {master, supervised, ongoing} -} - -@unpublished{Varnas:2024:TBA, - author = {Laurynas Varnas}, - title = {TBA}, - school = {Università della Svizzera italiana}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Ongoing master thesis. Supervision by Dr.\ Alena Kopaničáková (University of Toulouse, IRIT Laboratory, Artificial and Natural Intelligence Toulouse Institute) and Dr.\ Alexander Heinlein}, - keywords = {master, supervised, ongoing} -} - -@unpublished{Taraz:2024:TBA, - author = {Johannes Taraz}, - title = {TBA}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Ongoing master thesis. Supervision by Dr.\ Alexander Heinlein}, - keywords = {master, supervised, ongoing} -} - -@unpublished{Soliman:2024:TBA, - author = {Philip Soliman}, - title = {TBA}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Ongoing master thesis. Supervision by Filipe A.\ C.\ S.\ Alves and Dr.\ Alexander Heinlein}, - keywords = {master, supervised, ongoing} -} - -@unpublished{vandenBrink:2024:CFD, - author = {Mitchell Maassen van den Brink}, - title = {CFD surrogate models based on graph neural networks}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Ongoing master thesis. Supervision by Dr.\ Richard Dwight and Dr.\ Alexander Heinlein}, - keywords = {master, supervised, ongoing} -} - -@unpublished{Ouadah:2024:GLC, - author = {Ikhlasse Ouadah}, - title = {Geometry Learning for Complex Shaped Cells}, - school = {Vrije Universiteit Amsterdam}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Ongoing master thesis. Supervision by Dr.\ Alexander Heinlein and Dr.\ Qiyao Peng (Vrije Universiteit Amsterdam)}, - keywords = {master, supervised, ongoing} -} - -@unpublished{Prashanth:2024:DDM, - author = {Shreyas Prashanth}, - title = {Block Preconditioners for Monolithic Solvers of Very Large Floating Structures}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Ongoing master thesis. Supervision by Dr.\ Alexander Heinlein and Dr.\ Oriol Colom\'es}, - keywords = {master, supervised, ongoing} -} - -@unpublished{Xia:2024:DDM, - author = {Hangyu Xia}, - title = {Operator learning for periodic systems with partially hidden physics}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Ongoing master thesis. Supervision by Dr.\ Alexander Heinlein and Dr.\ Birupaksha Pal (Bosch)}, - keywords = {master, supervised, ongoing} -} - -@unpublished{Aldorf:2024:DDM, - author = {Michael Aldorf}, - title = {Data-driven methods for machine-induced metrology errors}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Ongoing master thesis. Supervision by Dr.\ Alexander Heinlein and Giulio Bottegal (ASML)}, - keywords = {master, supervised, ongoing} -} - -@unpublished{Oudenes:2024:DDM, - author = {Derby Oudenes}, - title = {Integrating Component Simulations in Digital Twins with Machine Learning}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Master thesis in Hydraulic Engineering. Supervision by José Antonio Álvarez Antolínez, PhD, Dr.ir.\ Renske Gelderloos, and Dr.\ Alexander Heinlein}, - keywords = {master, supervised, ongoing} -} - -@thesis{Daxecker:2024:MLS, - author = {Felix Daxecker}, - title = {Machine-Learning Surrogate Models for CFD -- Predicting Turbulence in the Wake of Perforated Monopiles}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Master thesis in Offshore and Dredging Engineering. Supervision by Dr.\ Oriol Colom\'es, Dr.\ Alexander Heinlein, and Ir.\ J.\ Modderman}, - keywords = {master, supervised} -} - -@thesis{Kamminga:2024:DDM, - author = {Thomas Kamminga}, - title = {A machine learning-based outlier removal algorithm incorporating a priori knowledge of the physics}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Dr.\ Alexander Heinlein and Lucas Bekker (ASML)}, - keywords = {master, supervised} -} - -@thesis{Saha:2024:DDM, - author = {Tirtho Sarathi Saha}, - title = {Separating longtime behavior and learning of mechanics by machine learning}, - school = {Technische Universit\"{a}t Braunschweig}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Dr.\ Alexander Heinlein and Dr.\ Cordula Reisch (TU Braunschweig)}, - keywords = {master, supervised} -} - -@thesis{Bonilla:2024:DDT, - author = {Gonzalo Bonilla Moreno}, - title = {Data-driven turbulence modeling of two-phase flows in nuclear reactors}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Dr.ir.\ Edo Frederix (NRG), Dr.\ Deepesh Toshniwal, and Dr.\ Alexander Heinlein}, - keywords = {master, supervised} -} - -@thesis{Verburg:2024:DDM, - author = {Corné Verburg}, - title = {A Domain Decomposition-based CNN Architecture for High-Resolution Image Segmentation}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Dr.\ Alexander Heinlein and Eric Cyr (Sandia)}, - keywords = {master, supervised} -} - -@thesis{Meijssen:2024:EGT, - author = {Vosse Meijssen}, - title = {Estimating congestion and traffic patterns when planning road work}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Dr.\ Alexander Heinlein, Leonoor Portengen, and Henk van Haaster (CGI)}, - keywords = {master, supervised} -} - -@thesis{Analikwu:2024:ESI, - author = {Brendan Analikwu}, - title = {Enhancing Sea Ice Dynamics in the Climate System by Machine Learning}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Ongoing master thesis. Supervision by Dr.\ Alexander Heinlein and Dr.\ Carolin Mehlmann (Otto von Guericke University Magdeburg)}, - keywords = {master, supervised} -} - -@thesis{Husanovic:2024:SMC, - author = {Selma Husanović}, - title = {The Application of Neural Networks to Predict Skin Evolution After Burn Trauma}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Dr.\ Alexander Heinlein and Prof.\ Dr.\ Fred Vermolen (Hasselt University)}, - keywords = {master, supervised} -} - -@thesis{vanAsselt:2023:MLP, - author = {Koen van Asselt}, - title = {Machine learning for post-storm profile predictions}, - school = {Delft University of Technology}, - year = {2023}, - url = {}, - abbr = {Master Thesis}, - note = {Master thesis in Hydraulic Engineering. Supervision by José Antonio Álvarez Antolínez, PhD, Prof.\ Dr.ir.\ Ad Reniers Reniers, Dr.\ Alexander Heinlein, Dr.ir.\ Panos Athanasiou (Deltares), and Robert McCall, PhD (Deltares)}, - keywords = {master, supervised} -} - -@thesis{Dekeyser:2023:MLC, - author = {Ruben Dekeyser}, - title = {Machine Learning for Computational Cost Reduction of Computational Fluid Dynamics for Perforated Monopiles}, - school = {Delft University of Technology}, - year = {2023}, - url = {https://repository.tudelft.nl/islandora/object/uuid:bfec0be5-11c9-4570-9c93-66952fadd0a0}, - abbr = {Master Thesis}, - note = {Master thesis in Offshore and Dredging Engineering. Supervision by Dr.\ Oriol Colom\'es and Dr.\ Alexander Heinlein}, - keywords = {master, supervised} -} - -@thesis{Zandbergen:2022:POC, - author = {Anouk Zandbergen}, - title = {Predicting the optimal {CFL} number for pseudo time-stepping: with machine learning in the {COMSOL} {CFD} module}, - school = {Delft University of Technology}, - year = {2022}, - url = {https://repository.tudelft.nl/islandora/object/uuid%3Ab3343bea-1270-4280-8192-7f08d162fbb0}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Dr.\ Alexander Heinlein and Dr.\ Tycho van Noorden (COMSOL)}, - keywords = {master, supervised} -} - -@thesis{Hoogeveen:2022:PFP, - author = {Sylle Hoogeveen}, - title = {Convolutional Neural Networks for Time-Dependent Fluid Flow}, - school = {Delft University of Technology}, - year = {2022}, - url = {https://repository.tudelft.nl/islandora/object/uuid%3A45bffaf0-5ae0-48a2-9fe7-5ebfe2594cb5}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Dr.\ Alexander Heinlein}, - keywords = {master, supervised} -} - -@thesis{Leeuwen:2022:MLF, - author = {Elske van Leeuwen}, - title = {Machine Learning for Turbulent Flows}, - school = {Delft University of Technology}, - year = {2022}, - url = {https://repository.tudelft.nl/islandora/object/uuid%3A52480fee-a585-4bbe-8785-319b94367ca0}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Dr.\ Alexander Heinlein and Dr.\ Werner Lazeroms (Sioux)}, - keywords = {master, supervised} -} - -@thesis{Sieburgh:2022:DDT, - author = {Erik Sieburgh}, - title = {Domain Decomposition Techniques for the Helmholtz Equation}, - school = {Delft University of Technology}, - year = {2022}, - url = {https://repository.tudelft.nl/islandora/object/uuid%3A32f4b716-6f83-4a95-b8b5-c3d35a32349f}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Dr.\ Alexander Heinlein and Vandana Dwarka}, - keywords = {master, supervised} -} - -@thesis{Kemna:2022:ROM, - author = {Mirko Kemna}, - title = {Reduced Order Models for Fluid Flow with Generative Adversarial Networks}, - school = {Delft University of Technology}, - year = {2022}, - url = {https://repository.tudelft.nl/islandora/object/uuid%3A25663ba2-3cdb-4581-be68-d4fd0a7a4dca}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Dr.\ Alexander Heinlein and Prof.\ Dr.\ Kees Vuik}, - keywords = {master, supervised} -} - -@thesis{Star:2022:SMC, - author = {Quinten Star}, - title = {Surrogate models for the characterization of hydrodynamic loads on perforated monopiles}, - school = {Delft University of Technology}, - year = {2022}, - url = {https://repository.tudelft.nl/islandora/object/uuid:2874787e-27ac-4c2e-a1d4-d1ddedf3f87f}, - abbr = {Master Thesis}, - note = {Master thesis in Offshore and Dredging Engineering. Supervision by Dr.\ Oriol Colom\'es and Dr.\ Alexander Heinlein}, - keywords = {master, supervised} -} - -@thesis{Sassmannshausen:2021:AFE, - author = {Lea Sa{\ss}mannshausen}, - title = {Adaptive Finite Elemente in 2D und 3D --- Fehlersch\"atzer, Verfeinerung und parallele Implementierung}, - school = {Universit\"at zu K\"oln}, - year = {2021}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {master, supervised} -} - -@thesis{Wuensch:2021:HMV, - author = {Hendrik W\"unsch}, - title = {Evaluierung und Adaption von Parallelisierungsstrategien f\"ur Markov Chain Monte Carlo Methoden zur Parameteridentifikation bei hierarchischen physiologiebasierten pharmakokinetischen Modellen -}, - school = {Universit\"at zu K\"oln}, - year = {2021}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {master, supervised} -} - -@thesis{Rettemeier:2020:HMV, - author = {Giuliana Rettemeier}, - title = {Hybride Modellierung und die Vorhersagevon Plastizit\"atsparametern von Stahl}, - school = {Universit\"at zu K\"oln}, - year = {2020}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Prof.\ Dr.\ Axel Klawonn, Dr.\ Christian Hochmuth, and Dr.\ Alexander Heinlein}, - keywords = {master, supervised} -} - -@thesis{Cevik:2020:PIM, - author = {Deniz Cevik}, - title = {Eine parallele Implementierung monolithischer Fluid-Struktur-Interaktion in ALE-For\-mulierung}, - school = {Universit\"at zu K\"oln}, - year = {2020}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Prof.\ Dr.\ Axel Klawonn, Dr.\ Christian Hochmuth, and Dr.\ Alexander Heinlein}, - keywords = {master, supervised} -} - -@thesis{Diepgrond:2020:GMF, - author = {Jennifer Diepgrond}, - title = {GMsFEM: Eine verallgemeinerte Multiskalen Finite-Elemente-Methode und deren Konvergenzanalyse}, - school = {Universit\"at zu K\"oln}, - year = {2020}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Prof.\ Dr.\ Axel Klawonn, Dr.\ Christian Hochmuth, and Dr.\ Alexander Heinlein}, - keywords = {master, supervised} -} - -@thesis{Mueller:2018:GZP, - author = {Manuel M\"uller}, - title = {Gebietszerlegungsverfahren f\"ur zeitabh\"angige Probleme mit Anwendung in der Strukturdynamik}, - school = {Universit\"at zu K\"oln}, - year = {2018}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {master, supervised} -} - -@thesis{Hoeller:2018:ACM, - author = {Laura H\"oller}, - title = {Die ACMS-Methode in drei Dimensionen: Ein spezielles Finite-Elemente-Verfahren für elliptische partielle Differentialgleichungen mit stark oszillierenden Koeffizienten}, - school = {Universit\"at zu K\"oln}, - year = {2018}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {master, supervised} -} - -@thesis{Knepper:2016:MGU, - author = {Jascha Knepper}, - title = {Multiskalen-Grobgitterr\"aume f\"ur \"Uberlappende Schwarz-Gebietszerlegungsverfahren}, - school = {Universit\"at zu K\"oln}, - year = {2016}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {master, supervised} -} - -@thesis{Knepper:2014:GEM, - author = {Katharina Wendel}, - title = {Gebietszerlegungsverfahren f\"ur ein elliptisches Multiskalen-Problem}, - school = {Universit\"at zu K\"oln}, - year = {2014}, - abbr = {Master Thesis}, - note = {Master thesis. Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {master, supervised} -} - -# bachelor - -@thesis{Gimbergh:2024:DLN, - author = {Karel Gimbergh}, - title = {Leveraging Parallel Schwarz Domain Decomposition -- Using Node-Level Parallelism for the Implementation of the Parallel Schwarz Method}, - school = {Delft University of Technology}, - year = {2024}, - url = {}, - abbr = {Bachelor Thesis}, - note = {Bachelor thesis. Supervision by Dr.\ Alexander Heinlein}, - keywords = {bachelor, supervised} -} - -@thesis{Wigmans:2023:DLN, - author = {Bram Wigmans}, - title = {Deep Learning the Nonlinear Dynamics of Mechanical Systems}, - school = {Delft University of Technology}, - year = {2023}, - url = {}, - abbr = {Bachelor Thesis}, - note = {Bachelor thesis. Supervision by Dr.\ Shobhit Jain and Dr.\ Alexander Heinlein}, - keywords = {bachelor, supervised} -} - -@thesis{Abutan:2022:PCF, - author = {Lisanne Abutan}, - title = {Photonic crystal fiber}, - school = {Delft University of Technology}, - year = {2022}, - url = {https://repository.tudelft.nl/islandora/object/uuid%3Ac3e83917-9239-48fa-ab32-aa3d2a85e005}, - abbr = {Bachelor Thesis}, - note = {Bachelor thesis. Supervision by Dr.\ Aur\`ele Adam and Dr.\ Alexander Heinlein}, - keywords = {bachelor, supervised} -} - -@thesis{Halevy:2022:EEF, - author = {Avi Halevy}, - title = {Error Estimates for Finite Element Simulations Using Neural Networks}, - school = {Delft University of Technology}, - year = {2022}, - url = {https://repository.tudelft.nl/islandora/object/uuid%3A31084250-25ee-4901-a3f0-258a6436be29}, - abbr = {Bachelor Thesis}, - note = {Bachelor thesis. Supervision by Dr.\ Alexander Heinlein and Dr.\ Deepesh Toshniwal}, - keywords = {bachelor, supervised} -} - -@thesis{Sperber:2022:DAC, - author = {Daniel Sperber}, - title = {Dimensionsreduktion mit Autoencodern basierend auf Convolutional Neuronal Networks und Principal Component Analysis}, - school = {Universit\"at Stuttgart}, - year = {2022}, - abbr = {Bachelor Thesis}, - abbr = {Bachelor Thesis. Supervision by Dr.\ Alexander Heinlein}, - keywords = {bachelor, supervised} -} - -@thesis{Dammrath:2018:SFE, - author = {Martin Dammrath}, - title = {Unblackboxing Neuronaler Netze mit der Deep Taylor Decomposition}, - school = {Universit\"at zu K\"oln}, - year = {2018}, - abbr = {Bachelor Thesis}, - note = {Bachelor thesis. Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {bachelor, supervised} -} - -@thesis{Platner:2017:BCG, - author = {Sebastian Platner}, - title = {Bi-CGSTAB}, - school = {Universit\"at zu K\"oln}, - year = {2017}, - abbr = {Bachelor Thesis}, - note = {Bachelor thesis. Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {bachelor, supervised} -} - -@thesis{Juergenson:2016:RAF, - author = {Alexander J\"urgenson}, - title = {Ein Residualer a posteriori Fehlersch\"atzer und Rot-Gr\"un Verfeinerung}, - school = {Universit\"at zu K\"oln}, - year = {2016}, - abbr = {Bachelor Thesis}, - note = {Bachelor thesis. Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {bachelor, supervised} -} - -@thesis{Kerp:2016:AGR, - author = {Dennis Kerp}, - title = {Adaptive Gitterverfeinerung mit residualen Fehlersch\"atzern und Bisektion}, - school = {Universit\"at zu K\"oln}, - year = {2016}, - abbr = {Bachelor Thesis}, - note = {Bachelor thesis. Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {bachelor, supervised} -} - -@thesis{Dembek:2016:FKU, - author = {Marcel Dembek}, - title = {Ein flexibles Krylow-Unterraum-Verfahren f\"ur nicht-symmetrische Probleme}, - school = {Universit\"at zu K\"oln}, - year = {2016}, - abbr = {Bachelor Thesis}, - note = {Bachelor thesis. Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {bachelor, supervised} -} - -@thesis{Reinsch:2016:FVG, - author = {Jannis Reinsch}, - title = {Flexibel vorkonditioniertes GMRES Verfahren}, - school = {Universit\"at zu K\"oln}, - year = {2016}, - abbr = {Bachelor Thesis}, - note = {Bachelor thesis. Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {bachelor, supervised} -} - -@thesis{Temme:2013:NUR, - author = {G\"orge Temme}, - title = {Numerische Untersuchung von Reaktions-Diffusionsgleichungen und Modellierung der Atherosklerose als Entz\"undungsprozess}, - school = {Universit\"at zu K\"oln}, - year = {2013}, - abbr = {Bachelor Thesis}, - note = {Bachelor thesis. Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {bachelor, supervised} -} - -@thesis{Baedorf:2013:NUR, - author = {Mascha Baedorf}, - title = {Eine numerische Einf\"uhrung in die Fluid-Struktur-Interaktion in 1D}, - school = {Universit\"at zu K\"oln}, - year = {2013}, - abbr = {Bachelor Thesis}, - note = {Bachelor thesis. Supervision by Prof.\ Dr.\ Axel Klawonn and Dr.\ Alexander Heinlein}, - keywords = {bachelor, supervised} -} - -# own - -@thesis{Heinlein:2011:SFE, - author = {Alexander Heinlein}, - title = {Spezielle Finite-Elemente-Methoden f\"ur stark heterogene Probleme}, - school = {Universit{\"a}t Duisburg-Essen}, - year = {2011}, - abbr = {Diploma Thesis}, - note = {Diploma thesis. Supervision by Prof.\ Dr.\ Axel Klawonn and Prof.\ Dr.\ Oliver Rheinbach}, - keywords = {diploma} -} diff --git a/_config.yml b/_config.yml deleted file mode 100644 index 94a82df51e1f..000000000000 --- a/_config.yml +++ /dev/null @@ -1,423 +0,0 @@ -# ----------------------------------------------------------------------------- -# Site settings -# ----------------------------------------------------------------------------- - -title: blank # the website title (if blank, full name will be used instead) -first_name: Alexander -middle_name: -last_name: Heinlein -email: a.heinlein@tudelft.nl -description: > # the ">" symbol means to ignore newlines until "footer_text:" - Personal website of Alexander Heinlein. -# A simple, whitespace theme for academics. Based on [*folio](https://github.com/bogoli/-folio) design. - -footer_text: - Powered by Jekyll with al-folio theme. - Hosted by GitHub Pages. -# Photos from Unsplash. -keywords: numerical analysis, scientific computing, high-performance computing, scientific machine learning # add your own keywords or leave empty - -lang: en # the language of your site (for example: en, fr, cn, ru, etc.) -icon: /assets/img/favicon.ico # the emoji used as the favicon - -url: https://searhein.github.io # the base hostname & protocol for your site -baseurl: #/al-folio # the subpath of your site, e.g. /blog/ -last_updated: true # set to true if you want to display last updated in the footer -impressum_path: # set to path to include impressum link in the footer, use the same path as permalink in a page, helps to conform with EU GDPR - -# ----------------------------------------------------------------------------- -# Theme -# ----------------------------------------------------------------------------- - -# code highlighter theme -highlight_theme_light: github # https://github.com/jwarby/jekyll-pygments-themes -highlight_theme_dark: native # https://github.com/jwarby/jekyll-pygments-themes - -# repo color theme -repo_theme_light: default # https://github.com/anuraghazra/github-readme-stats/blob/master/themes/README.md -repo_theme_dark: dark # https://github.com/anuraghazra/github-readme-stats/blob/master/themes/README.md -repo_trophies: - enabled: true - theme_light: flat # https://github.com/ryo-ma/github-profile-trophy - theme_dark: gitdimmed # https://github.com/ryo-ma/github-profile-trophy - -# ----------------------------------------------------------------------------- -# RSS Feed -# ----------------------------------------------------------------------------- -# will use title and url fields -# Take a look to https://github.com/jekyll/jekyll-feed for more customization - -rss_icon: false - -# ----------------------------------------------------------------------------- -# Layout -# ----------------------------------------------------------------------------- - -navbar_fixed: true -footer_fixed: true - -# Dimensions -max_width: 800px - -# TODO: add layout settings (single page vs. multi-page) - -# ----------------------------------------------------------------------------- -# Open Graph & Schema.org -# ----------------------------------------------------------------------------- -# Display links to the page with a preview object on social media. -serve_og_meta: false # Include Open Graph meta tags in the HTML head -serve_schema_org: false # Include Schema.org in the HTML head -og_image: # The site-wide (default for all links) Open Graph preview image - -# ----------------------------------------------------------------------------- -# Social integration -# ----------------------------------------------------------------------------- - -github_username: searhein # your GitHub user name -gitlab_username: # your GitLab user name -twitter_username: # your Twitter handle -mastodon_username: # your mastodon instance+username in the format instance.tld/@username -linkedin_username: alexander-heinlein-9b569380 # your LinkedIn user name -telegram_username: # your Telegram user name -scholar_userid: Pb5ZhSIAAAAJ # your Google Scholar ID -semanticscholar_id: # your Semantic Scholar ID -whatsapp_number: # your WhatsApp number (full phone number in international format. Omit any zeroes, brackets, or dashes when adding the phone number in international format.) -orcid_id: 0000-0003-1578-8104 # your ORCID ID -medium_username: # your Medium username -quora_username: # your Quora username -publons_id: # your ID on Publons -lattes_id: # your ID on Lattes (Brazilian Lattes CV) -osf_id: # your OSF ID -research_gate_profile: Alexander_Heinlein # your profile on ResearchGate -scopus_id: # your profile on Scopus -arxiv: a/heinlein_a_1.html -blogger_url: # your blogger URL -work_url: https://www.tudelft.nl/ewi/over-de-faculteit/afdelingen/applied-mathematics/people/dr-a-alexander-heinlein?0%5BL%5D=&cHash=bc6a6a5da90ef761e4b0899ba6d39442 # work page URL -keybase_username: # your keybase user name -wikidata_id: # your wikidata id -wikipedia_id: # your wikipedia id (Case sensitive) -dblp_url: # your DBLP profile url -stackoverflow_id: # your stackoverflow id -kaggle_id: # your kaggle id -lastfm_id: # your lastfm id -spotify_id: # your spotify id -pinterest_id: # your pinterest id -unsplash_id: # your unsplash id -instagram_id: # your instagram id -facebook_id: # your facebook id -youtube_id: # your youtube channel id (youtube.com/@) -discord_id: # your discord id (18-digit unique numerical identifier) - -contact_note: > -# You can even add a little note about which of these is the best way to reach you. - -# ----------------------------------------------------------------------------- -# Analytics and search engine verification -# ----------------------------------------------------------------------------- - -google_analytics: # your Google Analytics measurement ID (format: G-XXXXXXXXXX) -panelbear_analytics: # panelbear analytics site ID (format: XXXXXXXXX) - -google_site_verification: # your google-site-verification ID (Google Search Console) -bing_site_verification: # out your bing-site-verification ID (Bing Webmaster) - -# ----------------------------------------------------------------------------- -# Blog -# ----------------------------------------------------------------------------- - -blog_name: numblog # your blog must have a name for it to show up in the nav bar -blog_nav_title: blog # your blog must have a title for it to be displayed in the nav bar -blog_description: # a simple whitespace theme for academics -permalink: /blog/:year/:title/ - -# Pagination -pagination: - enabled: true - -related_blog_posts: - enabled: true - max_related: 5 - -# Giscus comments (RECOMMENDED) -# Follow instructions on https://giscus.app/ to setup for your repo to fill out -# the information below. -giscus: - repo: searhein/searhein.github.io # / - repo_id: MDEwOlJlcG9zaXRvcnkyOTQ1MDAxMzU= - category: Comments # name of the category under which discussions will be created - category_id: DIC_kwDOEY23J84CXsIt - mapping: title # identify discussions by post title - strict: 1 # use strict identification mode - reactions_enabled: 1 # enable (1) or disable (0) emoji reactions - input_position: bottom # whether to display input form below (bottom) or above (top) the comments - theme: preferred_color_scheme # name of the color scheme (preferred works well with al-folio light/dark mode) - emit_metadata: 0 - lang: en - -# Disqus comments (DEPRECATED) -disqus_shortname: #al-folio # put your disqus shortname -# https://help.disqus.com/en/articles/1717111-what-s-a-shortname - -# External sources. -# If you have blog posts published on medium.com or other external sources, -# you can display them in your blog by adding a link to the RSS feed. -external_sources: -# - name: medium.com -# rss_url: https://medium.com/@al-folio/feed - -# ----------------------------------------------------------------------------- -# Collections -# ----------------------------------------------------------------------------- - -collections: - news: - defaults: - layout: post - output: true - permalink: /news/:path/ - group_members: - output: true - permalink: /group_members/:path/ - projects: - output: true - permalink: /projects/:path/ - research: - output: true - permalink: /research/:path/ - software: - output: true - permalink: /software/:path/ - teaching: - output: true - permalink: /teaching/:path/ - -announcements: - enabled: true - scrollable: true # adds a vertical scroll bar if there are more than 3 news items - limit: 3 # leave blank to include all the news in the `_news` folder - 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A."] - url: https://www.pnnl.gov/people/amanda-howard - -"Kiefer": - - firstname: ["Björn", "B."] - url: - -"Klawonn": - - firstname: ["Axel", "A."] - url: https://numerik.uni-koeln.de - -"Knepper": - - firstname: ["Jascha", "J."] - url: https://numerik.uni-koeln.de/arbeitsgruppe/j-knepper-m-sc - -"Kemna": - - firstname: ["Mirko", "M."] - url: - -"Kühn": - - firstname: ["Martin", "M."] - url: https://www.dlr.de/sc/desktopdefault.aspx/tabid-1192/1635_read-38447/sortby-b_city/ - -"Langguth": - - firstname: ["Michael", "M."] - url: https://www.fz-juelich.de/profile/langguth_m - -"Lanser": - - firstname: ["Martin", "M."] - url: https://numerik.uni-koeln.de/arbeitsgruppe/dr-m-lanser - -"Mache": - - firstname: ["Ramiyou Karim", "R. 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N.", "Sharan", "S"] - url: - -"Rajamanickam": - - firstname: ["Sivasankaran", "Siva", "S."] - url: https://www.sandia.gov/~srajama/index.html - -"Rheinbach": - - firstname: ["Oliver", "O."] - url: https://tu-freiberg.de/fakult1/nmo/rheinbach - -"Richter": - - firstname: ["Thomas", "T."] - url: https://www.math.uni-magdeburg.de/~richter/ - -"Röver": - - firstname: ["Friederike", "F."] - url: https://tu-freiberg.de/fakult1/nmo/roever - -"Sandfeld": - - firstname: ["Stefan", "S."] - url: https://tu-freiberg.de/fakult4/imfd/mimm/mitarbeiter/stefan-sandfeld - -"Saßmannshausen": - - firstname: ["Lea", "L."] - url: https://numerik.uni-koeln.de/en/arbeitsgruppe/l-sassmannshausen-m-sc - -"Schlottbom": - - firstname: ["Matthias", "M."] - url: https://wwwhome.ewi.utwente.nl/~schlottbomm/ - -"Schröder": - - firstname: ["Jörg", "J."] - url: https://www.uni-due.de/mechanika/index.php - -"Schultz": - - firstname: ["Martin G.", "Martin", "M."] - url: https://www.fz-juelich.de/en/ias/jsc/about-us/structure/research-groups/esde - -"Sieburgh": - - firstname: ["Erik", "E."] - url: - -"Smetana": - - firstname: ["Kathrin", "K."] - url: https://faculty.stevens.edu/ksmetana - -"Stadtler": - - firstname: ["Scarlet", "S."] - url: https://www.fz-juelich.de/profile/stadtler_s - -"Steinberger": - - firstname: ["Daniel", "D."] - url: https://tu-freiberg.de/fakult4/imfd/mimm/mitarbeiter/dominik-steinberger - -"Stender": - - firstname: ["Merten", "M."] - url: https://www.tu.berlin/en/cpsme - -"Stinis": - - firstname: ["Panos", "P."] - url: https://www.pnnl.gov/people/panos-stinis - -"Uhlmann": - - firstname: ["Klemens", "K."] - url: http://www.lkm.rub.de/institut/team/uhlmann.html - -"van Noorden": - - firstname: ["Tycho", "T."] - url: - -"Verburg": - - firstname: ["Corné", "Corne", "C."] - url: - -"Vermolen": - - firstname: ["Fred", "F."] - url: https://www.uhasselt.be/en/who-is-who/fred-vermolen - -"Vuik": - - firstname: ["Cornelis", "C.", "Kees", "K."] - url: http://ta.twi.tudelft.nl/users/vuik/Welcome.html - -"Weber": - - firstname: ["Janine", "J."] - url: https://numerik.uni-koeln.de/arbeitsgruppe/j-weber-m-sc - -"Wedler": - - firstname: ["Mathies", "M."] - url: https://cgi.tu-harburg.de/~dynwww/cgi-bin/members/mathies-wedler - -"Widlund": - - firstname: ["Olof B.", "O. B.", "Olof", "O."] - url: https://cs.nyu.edu/widlund/ - -"Zandbergen": - - firstname: ["Anouk", "A."] - url: https://www.tu.berlin/en/cpsme/about/team/anouk-zandbergen-1 diff --git a/_data/cv.yml b/_data/cv.yml deleted file mode 100644 index 5da26086c0ff..000000000000 --- a/_data/cv.yml +++ /dev/null @@ -1,92 +0,0 @@ -- title: General Information - type: map - contents: - - name: Full Name - value: Alexander Heinlein - - name: Languages - value: English, German - -- title: Education - type: time_table - contents: - - title: Dr. rer. nat. - institution: University of Cologne, Germany - year: 2016 - description: - - [Thesis "Spezielle Finite-Elemente-Methoden für stark heterogene Probleme"] - - title: Dipl.-Math. - institution: University of Duisburg-Essen, Germany - year: 2011 - description: - - [Thesis "Parallel Overlapping Schwarz Preconditioners and Multiscale Discretizations -with Applications to Fluid-Structure Interaction and Highly Heterogeneous Problems"] - -- title: Experience - type: time_table - contents: - - title: Assistant Professor for Numerical Analysis - institution: Delft Institute of Applied Mathematics (DIAM), Delft University of Technology (TU Delft), The Netherlands - year: 2021 - now - - title: Acting Professor for Numerical Mathematics for High Performance Computing - institution: Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Germany - year: 2020 - 2021 - - title: Managing Coordinator - institution: Center for Data and Simulation Science, University of Cologne, Germany - year: 2018 - 2020 - - title: Postdoc - institution: Mathematical Institute, University of Cologne, Germany - year: 2016 - 2020 - -- title: Memberships - type: list - contents: - - American Mathematical Society (AMS) - - Dutch–Flemish Scientific Computing Society (SCS) - - European Mathematical Society (EMS)
Topical Activity Group Scientific Machine Learning - - German Association for Computational Mechanics (GACM) - - Gesellschaft für Angewandte Mathematik und Mechanik e.V. (GAMM e.V.)
Activity Groups Computational Science and Engineering, Computational Biomechanics, Computational and Mathematical Methods in Data Science - - Graduate School on Engineering Mechanics - - J.M. Burgerscentrum (JMBC) - - Society for Industrial and Applied Mathematics (SIAM)
Activity Group on Supercomputing - -- title: Certificates - type: time_table - contents: - - title: University Teaching Qualification - year: 2024 - description: Modules DEVELOP, TEACH, SUPERVISE, ASSESS - -# - title: Open Source Projects -# type: time_table -# contents: -# - title: al-folio -# year: 2015-now -# description: A beautiful, simple, clean, and responsive Jekyll theme for academics. -# -# - title: Honors and Awards -# type: time_table -# contents: -# - year: 1921 -# items: -# - Nobel Prize in Physics -# - Matteucci Medal -# - year: 2029 -# items: -# - Max Planck Medal -# -# - title: Academic Interests -# type: nested_list -# contents: -# - title: Topic 1. -# items: -# - Description 1. -# - Description 2. -# - title: Topic 2. -# items: -# - Description 1. -# - Description 2. -# -# - title: Other Interests -# type: list -# contents: -# - Hobbies: Hobby 1, Hobby 2, etc. diff --git a/_data/navigation.yml b/_data/navigation.yml deleted file mode 100644 index 587eecf3724b..000000000000 --- a/_data/navigation.yml +++ /dev/null @@ -1,19 +0,0 @@ -- title: projects - url: /projects/ -- title: publications - url: /publications/ -- title: research - url: /research/ -- title: software - url: /software/ -- title: teaching - url: /teaching/ - subfolderitems: - - title: courses - url: /teaching/ - - title: bachelor projects - url: /bachelor_projects/ - - title: master projects - url: /master_projects/ - - title: phd projects - url: /phd_projects/ diff --git a/_data/repositories.yml b/_data/repositories.yml deleted file mode 100644 index 3dbbaf1b3bd2..000000000000 --- a/_data/repositories.yml +++ /dev/null @@ -1,6 +0,0 @@ -github_users: - - searhein - -github_repos: - - trilinos/Trilinos - - FEDDLib/FEDDLib diff --git a/_data/venues.yml b/_data/venues.yml deleted file mode 100644 index 6c16ad5dcbdf..000000000000 --- a/_data/venues.yml +++ /dev/null @@ -1,6 +0,0 @@ -"AJP": - url: https://aapt.scitation.org/journal/ajp - color: "#00369f" - -"PhysRev": - url: https://journals.aps.org/ diff --git a/_group_members/alexander-heinlein.markdown b/_group_members/alexander-heinlein.markdown deleted file mode 100644 index 694c91ef1881..000000000000 --- a/_group_members/alexander-heinlein.markdown +++ /dev/null @@ -1,16 +0,0 @@ ---- -layout: page -first_name: Alexander -last_name: Heinlein -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: Mekelweg 4, 2628 CD Delft, The Netherlands -email: a.heinlein@tudelft.nl -website: https://searhein.github.io/ -img: assets/img/prof_pic5.jpg -project: -cv: /cv -nolink: true -redirect: -category: lead ---- diff --git a/_group_members/anouk-zandbergen.markdown b/_group_members/anouk-zandbergen.markdown deleted file mode 100644 index 1bfe76e14e77..000000000000 --- a/_group_members/anouk-zandbergen.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Anouk -last_name: Zandbergen -university: Technische Universität Berlin -department: Chair of Cyber-Physical Systems in Mechanical Engineering -address: Straße des 17. Juni 135, 10623 Berlin, Germany -email: anouk.zandbergen@tu-berlin.de -website: https://www.tu.berlin/en/cpsme/about/team/anouk-zandbergen-1 -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/ml-solver-parameters -nolink: true -redirect: -category: former members ---- diff --git a/_group_members/brendan-analikwu.markdown b/_group_members/brendan-analikwu.markdown deleted file mode 100644 index 8ac93461372e..000000000000 --- a/_group_members/brendan-analikwu.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Brendan -last_name: Analikwu -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: -email: -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/ml-sea-ice -nolink: true -redirect: -category: former members ---- diff --git a/_group_members/corne-verburg.markdown b/_group_members/corne-verburg.markdown deleted file mode 100644 index 362b047ed72f..000000000000 --- a/_group_members/corne-verburg.markdown +++ /dev/null @@ -1,16 +0,0 @@ ---- -layout: page -first_name: Corné -last_name: Verburg -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: Mekelweg 4, 2628 CD Delft, The Netherlands -email: C.Verburg@tudelft.nl -website: -img: https://filelist.tudelft.nl/_processed_/e/1/csm_verburg_c_62e9588aa4.jpg -project: -note: Main supervisor Neil Budko -nolink: true -redirect: -category: phd students ---- diff --git a/_group_members/elske-van-leeuwen.markdown b/_group_members/elske-van-leeuwen.markdown deleted file mode 100644 index 27d4e9b0fbd3..000000000000 --- a/_group_members/elske-van-leeuwen.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Elske -last_name: van Leeuwen -university: -department: -address: -email: -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/turbulence-ml -nolink: true -redirect: -category: former members ---- diff --git a/_group_members/erik-sieburgh.markdown b/_group_members/erik-sieburgh.markdown deleted file mode 100644 index 9646e5aea676..000000000000 --- a/_group_members/erik-sieburgh.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Erik -last_name: Sieburgh -university: -department: -address: -email: -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/ddm-helmholtz -nolink: true -redirect: -category: former members ---- diff --git a/_group_members/filipe-antonio-cumaru-silva-alves.markdown b/_group_members/filipe-antonio-cumaru-silva-alves.markdown deleted file mode 100644 index 6558d2448f9a..000000000000 --- a/_group_members/filipe-antonio-cumaru-silva-alves.markdown +++ /dev/null @@ -1,16 +0,0 @@ ---- -layout: page -first_name: Filipe Antônio -last_name: Cumaru Silva Alves -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: Mekelweg 4, 2628 CD Delft, The Netherlands -email: F.A.CumaruSilvaAlves@tudelft.nl -website: -img: https://filelist.tudelft.nl/_processed_/4/8/csm_cumaru_f_de4f165110.webp -project: -note: Co-supervisor Hadi Hajibeygi -nolink: true -redirect: -category: phd students ---- diff --git a/_group_members/gonzalo-bonilla-moreno.markdown b/_group_members/gonzalo-bonilla-moreno.markdown deleted file mode 100644 index 093eab5bc678..000000000000 --- a/_group_members/gonzalo-bonilla-moreno.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Gonzalo -last_name: Bonilla Moreno -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: -email: -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/turbulence-ml-part2 -nolink: true -redirect: -category: former members ---- diff --git a/_group_members/hangyu-xia.markdown b/_group_members/hangyu-xia.markdown deleted file mode 100644 index 46f89bd5b788..000000000000 --- a/_group_members/hangyu-xia.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Hangyu -last_name: Xia -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: -email: -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/spectral-neural-operators -nolink: true -redirect: -category: master students ---- diff --git a/_group_members/johannes-taraz.markdown b/_group_members/johannes-taraz.markdown deleted file mode 100644 index 25f019f27707..000000000000 --- a/_group_members/johannes-taraz.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Johannes -last_name: Taraz -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: Mekelweg 4, 2628 CD Delft, The Netherlands -email: J.J.Taraz@student.tudelft.nl -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/deeponet-convergence -nolink: true -redirect: -category: master students ---- diff --git a/_group_members/karel-gimbergh.markdown b/_group_members/karel-gimbergh.markdown deleted file mode 100644 index 58429fc62df1..000000000000 --- a/_group_members/karel-gimbergh.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Karel -last_name: Gimbergh -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: -email: -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/bsc-theses/kokkos-one-level-schwarz -nolink: true -redirect: -category: former members ---- diff --git a/_group_members/konstantinos-kevopoulos.markdown b/_group_members/konstantinos-kevopoulos.markdown deleted file mode 100644 index a9b9b860e794..000000000000 --- a/_group_members/konstantinos-kevopoulos.markdown +++ /dev/null @@ -1,16 +0,0 @@ ---- -layout: page -first_name: Konstantinos -last_name: Kevopoulos -university: Delft University of Technology -department: BioMechanical Engineering -address: Mekelweg 2, 2628 CD Delft, The Netherlands -email: K.Kevopoulos@tudelft.nl -website: -img: https://peirlincklab.com/images/people_kostas.jpg -project: -note: Main supervisor Mathias Peirlinck -nolink: true -redirect: -category: phd students ---- diff --git a/_group_members/ksenia-slepova.markdown b/_group_members/ksenia-slepova.markdown deleted file mode 100644 index bb6a06d20c21..000000000000 --- a/_group_members/ksenia-slepova.markdown +++ /dev/null @@ -1,16 +0,0 @@ ---- -layout: page -first_name: Ksenia -last_name: Slepova -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: Mekelweg 4, 2628 CD Delft, The Netherlands -email: K.Slepova@tudelft.nl -website: -img: https://filelist.tudelft.nl/_processed_/7/3/csm_wl16nq_af1236d89b.webp -project: -note: Main supervisor Martin van Gijzen -nolink: true -redirect: -category: phd students ---- diff --git a/_group_members/marius-kielhofer..markdown b/_group_members/marius-kielhofer..markdown deleted file mode 100644 index 879128e169b9..000000000000 --- a/_group_members/marius-kielhofer..markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Marius -last_name: Kielhöfer -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: Mekelweg 4, 2628 CD Delft, The Netherlands -email: M.Kielhofer@student.tudelft.nl -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/pinns-inverse-problems-sensor-data -nolink: true -redirect: -category: master students ---- diff --git a/_group_members/michael-aldorf.markdown b/_group_members/michael-aldorf.markdown deleted file mode 100644 index bfa89f348b10..000000000000 --- a/_group_members/michael-aldorf.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Michael -last_name: Aldorf -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: -email: -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/data-driven-metrology -nolink: true -redirect: -category: master students ---- diff --git a/_group_members/mirko-kemna.markdown b/_group_members/mirko-kemna.markdown deleted file mode 100644 index a9f7dccbe106..000000000000 --- a/_group_members/mirko-kemna.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Mirko -last_name: Kemna -university: Gradyent -department: -address: -email: -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/rom-fluid-flow-gans -nolink: true -redirect: -category: former members ---- diff --git a/_group_members/mirte-van-loenen.markdown b/_group_members/mirte-van-loenen.markdown deleted file mode 100644 index 16da163665fb..000000000000 --- a/_group_members/mirte-van-loenen.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Mirte -last_name: van Loenen -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: -email: -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/dd-gnns -nolink: true -redirect: -category: former members ---- diff --git a/_group_members/mitchell-maassen-van-den-brink.markdown b/_group_members/mitchell-maassen-van-den-brink.markdown deleted file mode 100644 index 7f97e7952032..000000000000 --- a/_group_members/mitchell-maassen-van-den-brink.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Mitchell -last_name: Maassen van den Brink -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: Mekelweg 4, 2628 CD Delft, The Netherlands -email: M.MaassenvandenBrink@student.tudelft.nl -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/gnn-surrogate-models -nolink: true -redirect: -category: master students ---- diff --git a/_group_members/philip-soliman.markdown b/_group_members/philip-soliman.markdown deleted file mode 100644 index 0c5698dfa90c..000000000000 --- a/_group_members/philip-soliman.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Philip -last_name: Soliman -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: Mekelweg 4, 2628 CD Delft, The Netherlands -email: P.M.Soliman@student.tudelft.nl -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/ddm-heterogeneous-problems-krylov -nolink: true -redirect: -category: master students ---- diff --git a/_group_members/selma-husanovic.markdown b/_group_members/selma-husanovic.markdown deleted file mode 100644 index 668867311aed..000000000000 --- a/_group_members/selma-husanovic.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Selma -last_name: Husanović -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: -email: -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/neural_networks_burn_injuries -nolink: true -redirect: -category: former members ---- diff --git a/_group_members/shreyas-prashanth.markdown b/_group_members/shreyas-prashanth.markdown deleted file mode 100644 index d92c7dbb7132..000000000000 --- a/_group_members/shreyas-prashanth.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Shreyas -last_name: Prashanth -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: Mekelweg 4, 2628 CD Delft, The Netherlands -email: S.Prashanth-1@tudelft.nl -website: -img: https://filelist.tudelft.nl/_processed_/5/6/csm_kkjzs6_4261a99015.webp -project: /teaching/msc-theses/block-preconditioners-very-large-floating-structures -nolink: true -redirect: -category: master students ---- diff --git a/_group_members/sylle-hoogeveen.markdown b/_group_members/sylle-hoogeveen.markdown deleted file mode 100644 index eed00f5ef1ca..000000000000 --- a/_group_members/sylle-hoogeveen.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Sylle -last_name: Hoogeveen -university: ADC Consulting -department: -address: -email: -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/rom-fluid-flow-transient -nolink: true -redirect: -category: former members ---- diff --git a/_group_members/thomas-kamminga.markdown b/_group_members/thomas-kamminga.markdown deleted file mode 100644 index c2b9e1e4f617..000000000000 --- a/_group_members/thomas-kamminga.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Thomas -last_name: Kamminga -university: ASML -department: -address: -email: -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/outlier-removal-ml -nolink: true -redirect: -category: former members ---- diff --git a/_group_members/tomas-medricky.markdown b/_group_members/tomas-medricky.markdown deleted file mode 100644 index c953e59b855d..000000000000 --- a/_group_members/tomas-medricky.markdown +++ /dev/null @@ -1,16 +0,0 @@ ---- -layout: page -first_name: Tomáš -last_name: Medřický -university: Czech Technical University in Prague -department: BioMechanical Engineering -address: Thákurova 7, 166 29 Prague 6, Czech Republic -email: tomas.medricky@fsv.cvut.cz -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: -note: Main supervisor Martin Doškář -nolink: true -redirect: -category: phd students ---- diff --git a/_group_members/vosse-meijssen.markdown b/_group_members/vosse-meijssen.markdown deleted file mode 100644 index 2033735241f1..000000000000 --- a/_group_members/vosse-meijssen.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Vosse -last_name: Meijssen -university: CGI -department: -address: -email: -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/traffic-modelling-ml -nolink: true -redirect: -category: former members ---- diff --git a/_group_members/wanxin-chen.markdown b/_group_members/wanxin-chen.markdown deleted file mode 100644 index aeed9fe10db3..000000000000 --- a/_group_members/wanxin-chen.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Wanxin -last_name: Chen -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: Mekelweg 4, 2628 CD Delft, The Netherlands -email: W.Chen-39@student.tudelft.nl -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/dd-nns-complex-shaped-domains -nolink: true -redirect: -category: master students ---- diff --git a/_group_members/yuhan-wu.markdown b/_group_members/yuhan-wu.markdown deleted file mode 100644 index dc2ffac05174..000000000000 --- a/_group_members/yuhan-wu.markdown +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -first_name: Yuhan -last_name: Wu -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: Mekelweg 4, 2628 CD Delft, The Netherlands -email: Y.Wu-81@student.tudelft.nl -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: /teaching/msc-theses/hints -nolink: true -redirect: -category: master students ---- diff --git a/_group_members/yuhuang-meng.markdown b/_group_members/yuhuang-meng.markdown deleted file mode 100644 index 14d56e2f4d49..000000000000 --- a/_group_members/yuhuang-meng.markdown +++ /dev/null @@ -1,16 +0,0 @@ ---- -layout: page -first_name: Yuhuang -last_name: Meng -university: Delft University of Technology -department: Delft Institute of Applied Mathematics -address: Mekelweg 4, 2628 CD Delft, The Netherlands -email: Y.Meng@tudelft.nl -website: -img: https://research.tudelft.nl/assets/no-portrait-473c6d005990baa1f418d9c668dcd4ec.png -project: -note: Co-supervisor Jing Zhao -nolink: true -redirect: -category: phd students ---- diff --git a/_includes/audio.html b/_includes/audio.html deleted file mode 100644 index 14c78017a2ad..000000000000 --- a/_includes/audio.html +++ /dev/null @@ -1,16 +0,0 @@ -
- -
diff --git a/_includes/courses.html b/_includes/courses.html deleted file mode 100644 index 243bd4527232..000000000000 --- a/_includes/courses.html +++ /dev/null @@ -1,104 +0,0 @@ -
- {% if teaching.redirect %} - {% unless teaching.nolink %} - - {% endunless %} - {% else %} - {% unless teaching.nolink %} - - {% endunless %} - {% endif %} - {% if teaching.nolink %} -
- {% else %} -
- {% endif %} -
-
-
-

- {% if teaching.university == "ude" %} - University of Duisburg-Essen - {% endif %} - {% if teaching.university == "uzk" %} - University of Cologne - {% endif %} - {% if teaching.university == "ust" %} - University of Stuttgart - {% endif %} - {% if teaching.university == "tud" %} - TU Delft - {% endif %} - {% if teaching.university == "tubraunschweig" %} - TU Braunschweig - {% endif %} - {% if teaching.university == "vua" %} - Vrije Universiteit Amsterdam - {% endif %} - {% if teaching.university == "usi" %} - Università della Svizzera italiana - {% endif %} -

-

{{ teaching.semester }}

-
-
-
-
-

{{ teaching.title }}

- {% if teaching.instructors %} -

Instructor(s): {{ teaching.instructors }}

- {% endif %} - - -
-
-
-
- {% unless teaching.nolink %} - - {% endunless %} -
- - - - diff --git a/_includes/cv/list.html b/_includes/cv/list.html deleted file mode 100644 index 7562585916d3..000000000000 --- a/_includes/cv/list.html +++ /dev/null @@ -1,5 +0,0 @@ -
    - {% for content in entry.contents %} -
  • {{ content }}
    • - {% endfor %} -
\ No newline at end of file diff --git a/_includes/cv/map.html b/_includes/cv/map.html deleted file mode 100644 index 83908dafd6e6..000000000000 --- a/_includes/cv/map.html +++ /dev/null @@ -1,8 +0,0 @@ - - {% for content in entry.contents %} - - - - - {% endfor %} -
{{ content.name }}{{ content.value }}
diff --git a/_includes/cv/nested_list.html b/_includes/cv/nested_list.html deleted file mode 100644 index 4778aca07ff1..000000000000 --- a/_includes/cv/nested_list.html +++ /dev/null @@ -1,14 +0,0 @@ -
    - {% for content in entry.contents %} -
  • -
    {{ content.title }}
    - {% if content.items %} -
      - {% for subitem in content.items %} -
    • {{ subitem }}
      • - {% endfor %} -
    - {% endif %} -
    • - {% endfor %} -
\ No newline at end of file diff --git a/_includes/cv/time_table.html b/_includes/cv/time_table.html deleted file mode 100644 index 123b9d099fde..000000000000 --- a/_includes/cv/time_table.html +++ /dev/null @@ -1,59 +0,0 @@ -
    - {% for content in entry.contents %} -
  • -
    - {% if content.year %} -
    - - {{ content.year }} - -
    - {% endif %} -
    - {% if content.title %} -
    {{content.title}}
    - {% endif %} - {% if content.institution %} -
    {{content.institution}}
    - {% endif %} - {% if content.description %} -
      - {% for item in content.description %} -
    • - {% if item.contents %} - {{ item.title }} -
        - {% for subitem in item.contents %} -
      • {{ subitem }}
        • - {% endfor %} -
      - {% else %} - {{ item }} - {% endif %} -
      • - {% endfor %} -
    - {% endif %} - {% if content.items %} -
      - {% for item in content.items %} -
    • - {% if item.contents %} - {{ item.title }} -
        - {% for subitem in item.contents %} -
      • {{ subitem }}
        • - {% endfor %} -
      - {% else %} - {{ item }} - {% endif %} -
      • - {% endfor %} -
    - {% endif %} -
    -
    -
    • - {% endfor %} -
\ No newline at end of file diff --git a/_includes/disqus.html b/_includes/disqus.html deleted file mode 100644 index 73fe9538d0dc..000000000000 --- a/_includes/disqus.html +++ /dev/null @@ -1,13 +0,0 @@ -
- - -
diff --git a/_includes/figure.html b/_includes/figure.html deleted file mode 100644 index e67e8043f6c4..000000000000 --- a/_includes/figure.html +++ /dev/null @@ -1,36 +0,0 @@ -{%- assign img_path = include.path | remove: ".jpg" | remove: ".jpeg" | remove: ".png" | remove: ".tiff" -%} - -
- - - {% if site.imagemagick.enabled %} - {% for i in site.imagemagick.widths -%} - - {% endfor -%} - {% endif %} - - - - - - - {%- if include.caption -%}
{{ include.caption }}
{%- endif %} - -
diff --git a/_includes/footer.html b/_includes/footer.html deleted file mode 100644 index acc4688f7cff..000000000000 --- a/_includes/footer.html +++ /dev/null @@ -1,25 +0,0 @@ - {% if site.footer_fixed %} -
-
- © Copyright {{ site.time | date: '%Y' }} {{ site.first_name }} {{ site.middle_name }} {{ site.last_name }}. {{ site.footer_text }} - {%- if site.impressum_path -%} - Impressum. - {%- endif -%} - {%- if site.last_updated -%} - Last updated: {{ "now" | date: '%B %d, %Y' }}. - {%- endif %} -
-
- {%- else -%} -
-
- © Copyright {{ site.time | date: '%Y' }} {{ site.first_name }} {{ site.middle_name }} {{ site.last_name }}. {{ site.footer_text }} - {%- if site.impressum_path -%} - Impressum. - {%- endif -%} - {%- if site.last_updated -%} - Last updated: {{ "now" | date: '%B %d, %Y' }}. - {%- endif %} -
-
- {%- endif %} \ No newline at end of file diff --git a/_includes/giscus.html b/_includes/giscus.html deleted file mode 100644 index bb504f64dbb8..000000000000 --- a/_includes/giscus.html +++ /dev/null @@ -1,27 +0,0 @@ -
- - -
diff --git a/_includes/group_members.html b/_includes/group_members.html deleted file mode 100644 index fe7e7a5405d1..000000000000 --- a/_includes/group_members.html +++ /dev/null @@ -1,73 +0,0 @@ - -
-
- {% unless group_member.nolink %} - {% if group_member.redirect -%} - - {%- else -%} - - {%- endif %} - {% endunless %} - -
-
-
- {%- if group_member.img %} - {%- include figure.html - path=group_member.img - alt="group_member thumbnail" -%} - {%- endif %} - {%- if group_member.note -%} -
-

{{ group_member.note }}

-
- {%- endif %} -
-
-
-

{{ group_member.first_name }} {{ group_member.last_name }}

- {%- if group_member.university -%} -

{{ group_member.university }}

- {% endif %} - {%- if group_member.department -%} -

{{ group_member.department }}

- {% endif %} - {%- if group_member.address -%} -

{{ group_member.address }}

- {% endif %} - {%- if group_member.email -%} -

Email:

- {% endif %} - {%- if group_member.website -%} -

Website:

- {% endif %} - {%- if group_member.project -%} -

Project

- {% endif %} - {%- if group_member.cv -%} -

CV:

- {% endif %} -
- {%- if group_member.github -%} -
-
- -
- {%- if group_member.github_stars -%} - - - - - {%- endif %} -
- {%- endif %} -
-
-
-
- -
- {% unless group_member.nolink %} - - {% endunless %} -
diff --git a/_includes/head.html b/_includes/head.html deleted file mode 100644 index e717c18c4bca..000000000000 --- a/_includes/head.html +++ /dev/null @@ -1,39 +0,0 @@ - - {% include metadata.html %} - - - - - - - - - - - - - - - - - {% if page.toc and page.toc.sidebar %} - - - {% endif %} - - - {% if site.icon.size <= 4 %} - - {% elsif site.icon != blank %} - - {% endif %} - - - - - {% if site.enable_darkmode %} - - - - - {% endif %} diff --git a/_includes/header.html b/_includes/header.html deleted file mode 100644 index 79779f6a44ff..000000000000 --- a/_includes/header.html +++ /dev/null @@ -1,119 +0,0 @@ - -
- - - -{% if site.enable_progressbar %} - - -
- -
- -{%- endif %} -
diff --git a/_includes/latest_posts.html b/_includes/latest_posts.html deleted file mode 100644 index bb82acb8dcb2..000000000000 --- a/_includes/latest_posts.html +++ /dev/null @@ -1,35 +0,0 @@ - -
- {% if site.latest_posts != blank -%} - {%- assign latest_posts_size = site.posts | size -%} -
3 %}style="max-height: 60vw"{% endif %}> - - {%- assign latest_posts = site.posts -%} - {% if site.latest_posts.limit %} - {% assign latest_posts_limit = site.latest_posts.limit %} - {% else %} - {% assign latest_posts_limit = latest_posts_size %} - {% endif %} - {% for item in latest_posts limit: latest_posts_limit %} - - - - - {%- endfor %} -
{{ item.date | date: "%b %-d, %Y" }} - {% if item.redirect == blank %} - {{ item.title }} - {% elsif item.redirect contains '://' %} - {{ item.title }} - - - - {% else %} - {{ item.title }} - {% endif %} -
-
- {%- else -%} -

No posts so far...

- {%- endif %} -
diff --git a/_includes/metadata.html b/_includes/metadata.html deleted file mode 100644 index e54f8ee5ff69..000000000000 --- a/_includes/metadata.html +++ /dev/null @@ -1,213 +0,0 @@ -{% if site.enable_google_verification or site.enable_bing_verification %} - - {% if site.enable_google_verification -%} - - {%- endif -%} - {% if site.enable_bing_verification -%} - - {%- endif -%} - - -{%- endif %} - - - - - - - {%- if site.title == "blank" -%} - {%- capture title -%}{{ site.first_name }} {{ site.middle_name }} {{ site.last_name }}{%- endcapture -%} - {%- else -%} - {%- capture title -%}{{ site.title }}{%- endcapture -%} - {%- endif -%} - {% if page.url == '/blog/index.html' %} - {{ site.blog_nav_title }} | {{ title }} - {%- elsif page.title != "blank" and page.url != "/" -%} - {%- if page.title == nil or page.title == "" -%} - {{ page.date | date: "%Y" }} | {{ title }} - {%- else -%} - {{ page.title }} | {{ title }} - {%- endif -%} - {%- else -%} - {{ title }} - {%- endif -%} - - - -{%- if page.keywords or site.keywords %} - -{%- endif %} - -{%- if site.serve_og_meta %} - - - - - - - - {% if page.og_image or site.og_image -%} - - {%- endif %} - - - - - - - {% if page.og_image or site.og_image -%} - - {%- endif %} - {% if site.twitter_username -%} - - - {%- endif %} -{%- endif %} - -{%- if site.serve_schema_org %} - - - {%- comment -%} Social links generator for "sameAs schema" {%- endcomment %} - {% assign sameaslinks = "" | split: "," %} - {%- if site.orcid_id -%} - {%- capture link -%}https://orcid.org/{{ site.orcid_id }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.scholar_userid -%} - {%- capture link -%}https://scholar.google.com/citations?user={{ site.scholar_userid }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.semanticscholar_id -%} - {%- capture link -%}https://www.semanticscholar.org/author/{{ site.semanticscholar_id }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.publons_id -%} - {%- capture link -%}https://publons.com/a/{{ site.publons_id }}/{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.research_gate_profile -%} - {%- capture link -%}https://www.researchgate.net/profile/{{site.research_gate_profile}}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.scopus_id -%} - {%- capture link -%}https://www.scopus.com/authid/detail.uri?authorId={{site.scopus_id}}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.github_username -%} - {%- capture link -%}https://github.com/{{ site.github_username }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.telegram_username -%} - {%- capture link -%}https://telegram.me/{{ site.telegram_username }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.linkedin_username -%} - {%- capture link -%}https://www.linkedin.com/in/{{ site.linkedin_username }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.twitter_username -%} - {%- capture link -%}https://twitter.com/{{ site.twitter_username }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.medium_username -%} - {%- capture link -%}https://medium.com/@{{ site.medium_username }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.quora_username -%} - {%- capture link -%}https://www.quora.com/profile/{{ site.quora_username }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.blogger_url -%} - {%- capture link -%}{{ site.blogger_url }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.work_url -%} - {%- capture link -%}{{ site.work_url }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.wikidata_id -%} - {%- capture link -%}https://www.wikidata.org/wiki/{{ site.wikidata_id }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.wikipedia_id -%} - {%- capture link -%}https://wikipedia.org/wiki/User:{{ site.wikipedia_id }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.strava_userid -%} - {%- capture link -%}https://www.strava.com/athletes/{{ site.strava_userid }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.keybase_username -%} - {%- capture link -%}https://keybase.io/{{ site.keybase_username }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.gitlab_username -%} - {%- capture link -%}https://gitlab.com/{{ site.gitlab_username }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.dblp_url -%} - {%- capture link -%}{{ site.dblp_url }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.stackoverflow_id -%} - {%- capture link -%}https://stackoverflow.com/users/{{ site.stackoverflow_id }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.kaggle_id -%} - {%- capture link -%}https://www.kaggle.com/{{ site.kaggle_id }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.lastfm_id -%} - {%- capture link -%}https://www.last.fm/user/{{ site.lastfm_id }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.spotify_id -%} - {%- capture link -%}https://open.spotify.com/user/{{ site.spotify_id }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.pinterest_id -%} - {%- capture link -%}https://www.pinterest.com/{{ site.pinterest_id }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.unsplash_id -%} - {%- capture link -%}https://unsplash.com/@{{ site.unsplash_id }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.instagram_id -%} - {%- capture link -%}https://instagram.com/{{ site.instagram_id }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.facebook_id -%} - {%- capture link -%}https://facebook.com/{{ site.facebook_id }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if site.discord_id -%} - {%- capture link -%}https://discord.com/users/{{ site.discord_id }}{%- endcapture -%} - {%- assign sameaslinks = sameaslinks | push: link -%} - {%- endif -%} - {%- if sameaslinks != blank -%} - {%- assign sameaslinks = sameaslinks | split: "" -%} - {%- endif -%} - - -{%- endif %} diff --git a/_includes/news.html b/_includes/news.html deleted file mode 100644 index 2146d885e5b4..000000000000 --- a/_includes/news.html +++ /dev/null @@ -1,29 +0,0 @@ -
- {% if site.news != blank -%} - {%- assign news_size = site.news | size -%} -
3 %}style="max-height: 60vw"{% endif %}> - - {%- assign news = site.news | reverse -%} - {% if include.limit and site.announcements.limit %} - {% assign news_limit = site.announcements.limit %} - {% else %} - {% assign news_limit = news_size %} - {% endif %} - {% for item in news limit: news_limit %} - - - - - {%- endfor %} -
{{ item.date | date: "%b %-d, %Y" }} - {% if item.inline -%} - {{ item.content | remove: '

' | remove: '

' | emojify }} - {%- else -%} - {{ item.title }} - {%- endif %} -
-
- {%- else -%} -

No news so far...

- {%- endif %} -
\ No newline at end of file diff --git a/_includes/pagination.html b/_includes/pagination.html deleted file mode 100644 index 4b8d27e3aee1..000000000000 --- a/_includes/pagination.html +++ /dev/null @@ -1,17 +0,0 @@ -{%- if paginator.total_pages > 1 -%} - -{%- endif -%} diff --git a/_includes/projects.html b/_includes/projects.html deleted file mode 100644 index 847c41f35f69..000000000000 --- a/_includes/projects.html +++ /dev/null @@ -1,36 +0,0 @@ - -
-
- {% if project.redirect -%} - - {%- else -%} - - {%- endif %} -
- {%- if project.img %} - {%- include figure.html - path=project.img - alt="project thumbnail" -%} - {%- endif %} -
-

{{ project.title }}

-

{{ project.description }}

-
- {%- if project.github -%} -
-
- -
- {%- if project.github_stars -%} - - - - - {%- endif %} -
- {%- endif %} -
-
-
- -
diff --git a/_includes/projects_horizontal.html b/_includes/projects_horizontal.html deleted file mode 100644 index e5ee32c2b744..000000000000 --- a/_includes/projects_horizontal.html +++ /dev/null @@ -1,43 +0,0 @@ -
- {%- if project.redirect -%} - - {%- else -%} - - {%- endif -%} -
-
- {%- if project.img -%} -
- {% include figure.html path=project.img alt="project thumbnail" %} -
-
- {%- else -%} -
- {%- endif -%} -
- -

{{ project.title }}

-

{{ project.description }}

- {% if project.github %} -
- {%- if project.github -%} -
-
- -
- {%- if project.github_stars -%} - - - - - {%- endif -%} -
- {%- endif -%} -
- {% endif %} -
-
-
-
- -
diff --git a/_includes/recent_papers.html b/_includes/recent_papers.html deleted file mode 100644 index c66abfd7e78d..000000000000 --- a/_includes/recent_papers.html +++ /dev/null @@ -1,4 +0,0 @@ -
- - {% bibliography -f papers -q @*[keywords ~= recent]* --group_by none %} -
diff --git a/_includes/related_posts.html b/_includes/related_posts.html deleted file mode 100644 index df6b3e5d84b5..000000000000 --- a/_includes/related_posts.html +++ /dev/null @@ -1,19 +0,0 @@ -{% assign have_related_posts = false %} - -{% for post in site.related_posts | limit: site.related_blog_posts.max_related %} - {% unless have_related_posts %} - {% assign have_related_posts = true %} -
-
-
-
    - - -

    Enjoy Reading This Article?

    -

    Here are some more articles you might like to read next:

    - {% endunless %} - -
  • - {{ post.title }} -
    • -{% endfor %} diff --git a/_includes/repository/repo.html b/_includes/repository/repo.html deleted file mode 100644 index a0881c0b022f..000000000000 --- a/_includes/repository/repo.html +++ /dev/null @@ -1,14 +0,0 @@ -{% assign repo_url = include.repository | split: '/' %} - -{% if site.data.repositories.github_users contains repo_url.first %} - {% assign show_owner = false %} -{% else %} - {% assign show_owner = true %} -{% endif %} - -
    - - {{ include.repository }} - {{ include.repository }} - -
    diff --git a/_includes/repository/repo_trophies.html b/_includes/repository/repo_trophies.html deleted file mode 100644 index 18f5273acbd1..000000000000 --- a/_includes/repository/repo_trophies.html +++ /dev/null @@ -1,6 +0,0 @@ -
    - - {{ include.username }} - {{ include.username }} - -
    diff --git a/_includes/repository/repo_user.html b/_includes/repository/repo_user.html deleted file mode 100644 index ae06a058fccc..000000000000 --- a/_includes/repository/repo_user.html +++ /dev/null @@ -1,6 +0,0 @@ -
    - - {{ include.username }} - {{ include.username }} - -
    diff --git a/_includes/scripts/analytics.html b/_includes/scripts/analytics.html deleted file mode 100644 index db2aeef96cd0..000000000000 --- a/_includes/scripts/analytics.html +++ /dev/null @@ -1,18 +0,0 @@ -{%- if site.enable_google_analytics -%} - - - -{%- endif -%} -{%- if site.enable_panelbear_analytics -%} - - - -{%- endif -%} diff --git a/_includes/scripts/badges.html b/_includes/scripts/badges.html deleted file mode 100644 index b8a3ccddec36..000000000000 --- a/_includes/scripts/badges.html +++ /dev/null @@ -1,6 +0,0 @@ -{%- if site.badges.altmetric_badge %} - -{%- endif %} -{%- if site.badges.dimensions_badge %} - -{%- endif %} diff --git a/_includes/scripts/bootstrap.html b/_includes/scripts/bootstrap.html deleted file mode 100644 index 1c213650a841..000000000000 --- a/_includes/scripts/bootstrap.html +++ /dev/null @@ -1,3 +0,0 @@ - - - diff --git a/_includes/scripts/jquery.html b/_includes/scripts/jquery.html deleted file mode 100644 index f84a2f22d5b6..000000000000 --- a/_includes/scripts/jquery.html +++ /dev/null @@ -1,2 +0,0 @@ - - diff --git a/_includes/scripts/masonry.html b/_includes/scripts/masonry.html deleted file mode 100644 index 804389d31ad3..000000000000 --- a/_includes/scripts/masonry.html +++ /dev/null @@ -1,6 +0,0 @@ - {%- if site.enable_masonry -%} - - - - - {%- endif -%} diff --git a/_includes/scripts/mathjax.html b/_includes/scripts/mathjax.html deleted file mode 100644 index c55ec056d26b..000000000000 --- a/_includes/scripts/mathjax.html +++ /dev/null @@ -1,12 +0,0 @@ - {%- if site.enable_math -%} - - - - - {%- endif %} diff --git a/_includes/scripts/misc.html b/_includes/scripts/misc.html deleted file mode 100644 index ddd6ee83f730..000000000000 --- a/_includes/scripts/misc.html +++ /dev/null @@ -1,25 +0,0 @@ -{% if site.enable_tooltips %} - - -{%- endif %} - -{%- if site.enable_medium_zoom %} - - - -{%- endif -%} - -{% if page.toc and page.toc.sidebar %} - - -{% endif %} - - - - - - - - diff --git a/_includes/scripts/progressBar.html b/_includes/scripts/progressBar.html deleted file mode 100644 index 88bb73cd35e4..000000000000 --- a/_includes/scripts/progressBar.html +++ /dev/null @@ -1,80 +0,0 @@ -{% if site.enable_progressbar %} - - - - -{%- endif %} diff --git a/_includes/selected_papers.html b/_includes/selected_papers.html deleted file mode 100644 index 2b57181e06e4..000000000000 --- a/_includes/selected_papers.html +++ /dev/null @@ -1,4 +0,0 @@ - -
    - {% bibliography -f {{ site.scholar.bibliography }} -q @*[keywords ~= selected]* %} -
    diff --git a/_includes/social.html b/_includes/social.html deleted file mode 100644 index 9b05921c3c05..000000000000 --- a/_includes/social.html +++ /dev/null @@ -1,111 +0,0 @@ - {%- if site.email -%} - - {% endif %} - {%- if site.telegram_username -%} - - {% endif %} - {%- if site.whatsapp_number -%} - - {% endif %} - {%- if site.orcid_id -%} - - {% endif %} - {%- if site.scholar_userid -%} - - {% endif %} - {%- if site.semanticscholar_id -%} - - {% endif %} - {%- if site.publons_id -%} - - {% endif %} - {%- if site.lattes_id -%} - - {% endif %} - {%- if site.osf_id -%} - - {% endif %} - {%- if site.research_gate_profile -%} - - {% endif %} - {% if site.arxiv %} - - {% endif %} - {%- if site.scopus_id -%} - - {% endif %} - {%- if site.github_username -%} - - {% endif %} - {%- if site.linkedin_username -%} - - {% endif %} - {%- if site.twitter_username -%} - - {% endif %} - {%- if site.mastodon_username -%} - - {% endif %} - {%- if site.medium_username -%} - - {% endif %} - {%- if site.quora_username -%} - - {% endif %} - {%- if site.blogger_url -%} - - {% endif %} - {%- if site.work_url -%} - - {% endif %} - {%- if site.wikidata_id -%} - - {% endif %} - {%- if site.wikipedia_id -%} - - {% endif %} - {%- if site.strava_userid -%} - - {% endif %} - {%- if site.keybase_username -%} - - {% endif %} - {%- if site.gitlab_username -%} - - {% endif %} - {%- if site.dblp_url -%} - - {% endif %} - {%- if site.stackoverflow_id -%} - - {% endif %} - {%- if site.kaggle_id -%} - - {% endif %} - {%- if site.lastfm_id -%} - - {% endif %} - {%- if site.spotify_id -%} - - {% endif %} - {%- if site.pinterest_id -%} - - {% endif %} - {%- if site.unsplash_id -%} - - {% endif %} - {%- if site.instagram_id -%} - - {% endif %} - {%- if site.facebook_id -%} - - {% endif %} - {%- if site.youtube_id -%} - - {% endif %} - {%- if site.discord_id -%} - - {% endif %} - {%- if site.rss_icon -%} - - {% endif %} diff --git a/_includes/theses.html b/_includes/theses.html deleted file mode 100644 index 29fcfe23cd88..000000000000 --- a/_includes/theses.html +++ /dev/null @@ -1,131 +0,0 @@ -
    - {% if teaching.redirect %} - {% unless teaching.nolink %} - - {% endunless %} - {% else %} - {% unless teaching.nolink %} - - {% endunless %} - {% endif %} - {% if teaching.nolink %} -
    - {% else %} -
    - {% endif %} -
    -
    -
    - {% if teaching.collaboration %} -

    - {% if teaching.university == "ude" %} - University of Duisburg-Essen - {% endif %} - {% if teaching.university == "uzk" %} - University of Cologne - {% endif %} - {% if teaching.university == "ust" %} - University of Stuttgart - {% endif %} - {% if teaching.university == "tud" %} - TU Delft - {% endif %} - {% if teaching.university == "tubraunschweig" %} - TU Braunschweig - {% endif %} - {% if teaching.university == "vua" %} - Vrije Universiteit Amsterdam - {% endif %} - {% if teaching.university == "usi" %} - Università della Svizzera italiana - {% endif %} -

    -

    {{ teaching.collaboration }}

    - {% else %} -

    - {% if teaching.university == "ude" %} - University of Duisburg-Essen - {% endif %} - {% if teaching.university == "uzk" %} - University of Cologne - {% endif %} - {% if teaching.university == "ust" %} - University of Stuttgart - {% endif %} - {% if teaching.university == "tud" %} - TU Delft - {% endif %} - {% if teaching.university == "tubraunschweig" %} - TU Braunschweig - {% endif %} - {% if teaching.university == "vua" %} - Vrije Universiteit Amsterdam - {% endif %} - {% if teaching.university == "usi" %} - Università della Svizzera italiana - {% endif %} -

    - {% endif %} -
    -
    -
    -
    -

    {{ teaching.title }}

    - {% if teaching.co-supervisor %} -

    Co-Supervisor(s): {{ teaching.co-supervisor }}

    - {% endif %} - {% if teaching.student %} -

    Student: {{ teaching.student }}

    - {% endif %} -
    -
    -
    -
    - {% unless teaching.nolink %} -     - {% endunless %} -
    - - - - diff --git a/_includes/video.html b/_includes/video.html deleted file mode 100644 index e56e05485d35..000000000000 --- a/_includes/video.html +++ /dev/null @@ -1,47 +0,0 @@ -{% assign extension = include.path | split:'.' | last %} - -
    - - {% if extension == "mp4" or extension == "webm" or extension == "ogg" %} - -