begin asa presentation

presentations/asa/main.typ

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+#import "@preview/touying:0.4.2": *
+#import "@preview/unify:0.6.0": num
+//#import "../themes/aus-beamer.typ" as theme-aus
+#import "@preview/academic-conf-pre:0.1.0" as theme-aus
+#import "@preview/cades:0.3.0": qr-code
+#import "@preview/algo:0.3.3": algo, i, d, comment, code
+
+#let s = theme-aus.register(aspect-ratio: "16-9") //4-3, 16-9
+#let s = (s.methods.info)(
+  self: s,
+  title: [Scalable Parallel-in-Time Integration],
+  short-title: [Scalable Parallel-in-Time Integration],
+  subtitle: [Acoustics in Expanding Volumes],
+  author: [Nathan Chapman#super[1], and Andy Piacsek#super[2]],
+  short-author: [Chapman \& Piacsek],
+  date: [Innovations in Computational Acoustics - ASA #datetime.today().year()],
+  institution: [#super[1]Department of Computer Science, Central Washington University\ #super[2]Department of Physics, Central Washington University],
+)
+
+#let (init, slides, touying-outline, alert, speaker-note, tblock) = utils.methods(s)
+#let (slide, empty-slide, title-slide, outline-slide, new-section-slide, ending-slide) = utils.slides(s)
+
+// #show link: underline
+#show: init
+#show: slides.with()
+
+= Introduction
+
+== Why should we care?
+- IVPs can take a long time
+- Parallelization is only becoming more accessible in many ways
+  - Hardware
+  - Effort
+  - Methods and types of problems
+- Work in Progress
+
+== Acoustics in Expanding Volumes
+// TODO: add image e.g. maybe a sequence of expanding boxes with changing waves
+// TODO: highlight each part of the equation, especially the a term describing the expansion behavior
+- Wave $psi(t, bold(x))$ defined by its density $n$ and phase $theta$ with
+$ psi(t, bold(x)) = sqrt(n_0 + Delta n(t, bold(x))) e^(i(theta_0 + Delta theta(t, bold(x)))) $
+
+- Wave equation for an expanding volume:
+$ partial_t^2 theta - dot(a)/a partial_t theta - a c_0^2 nabla^2 theta = 0 $
+
+- Spectral decomposition in space $tilde(theta)_bold(k) = cal(F)(Delta theta)(t, bold(k))$ for $k < k_c (t)$
+#tblock(title: align(center, [The Field Equation]))[
+  $ partial_t^2 tilde(theta)_bold(k) - dot(a)/a partial_t tilde(theta)_bold(k) - a c_0^2 k^2 tilde(theta)_bold(k) = 0 $
+  $ tilde(theta)_bold(k)(0) = tilde(theta)_(bold(k) 0) "    " partial_t tilde(theta)_bold(k)(0) = -U_0 n_(bold(k) 0) \/ h $
+]
+
+= Methods
+
+== The Parareal Algorithm
+
+// - What is the Parareal algorithm and how is it useful?
+// - Psuedo-code goes here
+// - Picture goes here
+
+// TODO: get algo working; addressed in github issue https://github.com/platformer/typst-algorithms/issues/22
+// #algo(
+//   title: "The Parareal Algorithm",
+//   parameters: (
+//     [Coarse Propagator $cal(C)$], 
+//     [Fine Propagator $cal(F)$], 
+//     [Initial Condition $u_0$], 
+//     [Discretized Time Domain $T = {T_0, T_1, dots, T_N}$]
+//   )
+// )[
+//   // Output: Solution ${u_0, u_1, ..., u_N}$
+
+//   #comment[INITIALIZATION]\
+//   use coarse propagator and initial values to generate ${u_0, u_1, ..., u_N}$ on the discretized time domain $T$\
+//   #comment[BEGIN PARALLEL]\
+//   #comment[parallelize over the temporal subdomains]\
+//   for $n = 0, 1, dots, N - 1$ do #i\
+//     Use the fine propagator and psuedo-initial value $u_n$ to get the data point $u_(n + 1)^cal(F)$\
+//     Use the coarse propagator and psuedo-initial value $u_n$ to get the data point $u_(n + 1)^cal(C)$\
+//     $"corrector"_(n + 1) arrow.l u_(n + 1)^cal(F) - u_(n + 1)^cal(C)$ #d\
+// ]
+
+
+== GPU Computing
+- Each subproblem can be computed in parallel on each gpu core
+
+== Distributed Computing
+- 1 wave number per gpu
+- many machines with gpus can further parallelize the calculation
+
+= Results
+== Some Basic Results
+- pictures of results
+
+= Discussion
+
+== Numerical Analysis
+- Error
+- Convergence
+- Stability
+
+== Algorithm Analysis
+- Time Complexity
+- Space Complexity
+
+= Conclusion
+== Conclusion
+// TODO: focus on what I did
+- Accessibility to parallelization is increasing
+- Problems only becoming more complex
+
+#ending-slide(title: [Thank you for your time.])[
+  #v(10%)
+  #columns(2,
+    [
+      - Code available on GitHub #sym.arrow.r.long
+      - Let's collaborate! 
+      - #link("NChapman@whatcom.edu")
+      - #link("nathanwchapman.com")
+      #colbreak()
+      #qr-code("https://github.com/NonDairyNeutrino/Thesis")
+    ]
+  )
+]
+
+// = Complex Layouts
+// == Complex Layouts 1
+// #tblock(title: [Complex Layouts])[
+//   You can easily use composer or grid func from slide to implement *complex layouts*.
+// ]
+
+// #grid(
+//   columns: (1fr, 1fr, 1fr),
+//   figure(
+//     image("figures/grid1.png"),
+//     caption: [This is the test figure],
+//   ),
+//   figure(
+//     image("figures/grid2.png"),
+//     caption: [This is the test figure],
+//   ),
+//   figure(
+//     image("figures/grid3.png"),
+//     caption: [This is the test figure],
+//   ),
+// )
+
+// == Complex Layouts 2
+
+// #slide(composer: (1.1fr, 1fr))[
+//   #set text(0.8em)
+
+//   As you can see, the composer function can be used to create *complex layouts*.
+
+//   And adjust the different layout parameters to achieve the desired result.
+// ][
+//   #figure(
+//     table(
+//     columns: 3,
+//     align: (center, center, center),
+//     [Hello], [Hello], [Hello],
+//     [A], [B], [C],
+//   ),
+//     caption: [This is the table with caption],
+//   ) <tab:gateways>
+// \
+
+//   #figure(
+//     table(
+//       columns: 4,
+//       [], [Exam 1], [Exam 2], [Exam 3],
+//       [John], [85], [96], [86],
+//       [Mary], [53], [64], [75],
+//       [Robert], [32], [86], [85],
+//     ),
+//     caption: [This is the table with caption],
+//   ) <tab:gateways>
+// ]