diff --git a/references.bib b/references.bib new file mode 100644 index 00000000000..e2417e800a3 --- /dev/null +++ b/references.bib @@ -0,0 +1,12583 @@ +@string{jcp = {J.~Comp.~Phys.}} +@string{jgr = {J.~Geophys.~Res.}} +@string{epsl = {Earth~Planet.~Sci.~Lett.}} +@string{grl = {Geophys.~Res.~Lett.}} +@string{pepi = {Phys.~Earth.~Planet.~Inter.}} +@string{g3 = {Geochem.~Geophys.~Geosyst.}} +@string{gji = {Geophy.~J.~Int.}} +@string{ijnmf = {Int.~J.~Num.~Meth.~Fluids}} +@string{ijnme = {Int.~J.~Num.~Meth.~Eng.}} +@string{se = {Solid Earth}} +@string{ajs = {American Journal of Science}} +@string{cmame = {Computer Methods in Applied Mechanics and Engineering}} +@string{pnas = {Proceedings of the National Academy of Sciences}} +@String{IWR = {IWR, Universit{\"a}t Heidelberg}} +@String{SFB = {SFB~359, Universit{\"a}t Heidelberg}} +@String{IAM = {Institut f{\"u}r Angewandte Mathematik, Universit{\"a}t Heidelberg}} +@String{UMSI = {University of Minnesota Supercomputing Institute}} +@String{IMA = {Institute for Mathematics and its Applications, Minneapolis}} +@String{EastWest = {East-West J. Numer. Math.}} +@String{LNCSE = {Lecture Notes in Computational Science and Engineering} +} + +#****************************************************************** +# Please insert publications by alphabetical order +#****************************************************************** + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% AAAA +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +@article{allken:etal:2012, +Author = {V. Allken and R. Huismans and C. Thieulot}, +Journal = g3, +Title = {Factors controlling the mode of rift interaction in brittle-ductile coupled systems: a {3D} numerical study}, +Volume = {13}, +Number = {5}, +Pages = {Q05010}, +Year = {2012}} + +@article{allken:etal:2011, +Author = {V. Allken and R. Huismans and C. Thieulot}, +Journal = jgr, +Title = {Three dimensional numerical modelling of upper crustal extensional systems}, +Pages = {B10409}, +Volume = {116}, +Year = {2011}} + + + +@article{allken:etal:2013, +title={{3D numerical modelling of graben interaction and linkage: a case study of the Canyonlands grabens, Utah}}, +author={V. Allken and R.S. Huismans and H. Fossen and C. Thieulot}, +journal={Basin Research}, +volume={25}, +pages={1--14}, +year={2013} +} + +@Article{ABC05, + author = {Anderson, M. and Bangerth, W. and Carey, G. F.}, + title = {Analysis of parameter sensitivity and experimental design + for a class of nonlinear partial differential equations}, + journal = {Int. J. Numer. Meth. Fluids}, + year = 2005, + volume = 48, + pages = {583--605} +} + +@Book{AD59, + author = {Abott, I. H. and von Doenhoff, A. E.}, + title = {Theory of Wing Sections}, + publisher = {Dover Publications, Inc., New York}, + year = 1959 +} + +@Misc{AG94, + title = {A selection of experimental Test cases for the validation of {CFD} Codes}, + key = {AGARD AR-303}, + howpublished = {AGARD Report AR-303}, + year = 1994 +} + +@Article{ASW97, + author = {Ackermann, R. V. and Schlische, R. W. and Withjack, M. O.}, + title = {Systematics of an evolving population of normal faults in + scaled physical models}, + journal = {Geological Society of America Abstracts with programs}, + year = 1997, + pages = {A-198} +} + +@Book{ABM06, + author = {Attouch, H. and Buttazzo, G. and Michaille, G.}, + title = {Variational Analysis in {S}obolev and {BV} spaces}, + publisher = {SIAM-MPS}, + year = 2060, + series = {MPS-SIAM Series on Optimization} +} + +@Article{ACWY00, + author = {Arbogast, T. and Cowsar, L. C. and Wheeler, M. F. and Yotov, I.}, + title = {Mixed finite element methods on nonmatching grids}, + journal = {SIAM J. Numer. Anal.}, + year = 2000, + volume = 37, + pages = {1295--1315} +} + +@Book{AO00, + author = {Ainsworth, M. and Oden, J. T.}, + title = {A Posteriori Error Estimation in Finite Element Analysis}, + publisher = {John Wiley and Sons}, + year = 2000 +} + +@Article{AO93, + author = {Ainsworth, M. and Oden, J. T.}, + title = {A unified approach to a posteriori error estimation using + element residual methods}, + journal = {Numer. Math.}, + year = 1993, + volume = 65, + pages = {23--50} +} + +@Book{Ada03, + author = {Adams, R. A. and Fournier, J. J. F.}, + title = {Sobolev Spaces}, + publisher = {Academic Press}, + year = 2003, + edition = {2nd}, +} + +@Book{Ada75, + author = {Adams, R. A.}, + title = {Sobolev Spaces}, + publisher = {Academic Press}, + year = {1975}, +} + +@Book{Alt85, + author = {Alt, H. W.}, + title = {Lineare Funktionalanalysis}, + publisher = {Springer}, + year = 1985, + series = {Hochschultext} +} + +@Article{Arn82, + author = {Arnold, D. N.}, + title = {An Interior Penalty Finite Element Method with Discontinuous Elements}, + journal = {SIAM J. Numer. Anal.}, + year = 1982, + volume = 19, + number = 4, + pages = {742--760} +} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% BBBB +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +@Article{burstedde:etal:2013, + author = {Burstedde, C. and Stadler, G. and Alisic, L. and Wilcox, L. C. and Tan, E. and Gurnis, M. and Ghattas, O.}, + title = {Large-scale adaptive mantle convection simulation}, + journal = {Geophysical Journal International}, + year = 2013, + volume = {192.3}, + pages = {889--906}} + +@article{buiter:2012, +title={{A review of brittle compressional wedge models}}, +author={S. J. H. Buiter}, +journal={Tectonophysics}, +volume={530}, +pages={1-17}, +year={2012} +} + +@Article{BA76, + author = {Babu{\v s}ka, I. and Aziz, A. K.}, + title = {On the Angle Condition in the Finite Element Method}, + journal = {SIAM J. Numer. Anal.}, + year = {1976}, + volume = {13}, + pages = {214--226} +} + +@Article{BB73, + author = {Boris, J. and Book, L.}, + title = {Flux-Corrected Transport --- {SHASTA}, a Fluid Transport + Algorithm That Works}, + journal = {J. Comp. Phys.}, + volume = 11, + year = 1973, + pages = {38--69} +} + +@Book{BBCDDEPRV93, + author = {Barrett, R. and Berry, M. and Chan, T. F. and Demmel, J. and Donato, J. and + Dongarra, J. and Eijkhout, V. and Pozo, R. and Romine, C. and van der Vorst, H.}, + title = {Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods}, + publisher = {SIAM}, + year = 1993 +} + +@Article{BBP81, + author = {Bardos, C. and Bercovier, M. and Pironneau, O.}, + title = {The Vortex Method with Finite Elements}, + journal = {Math. Comp.}, + volume = 36, + year = 1981, + pages = {119--136} +} + +@Article{BD04, + author = {Borcea, L. and Druskin, V.}, + title = {Optimcal finite difference grids for direct and inverse {S}turm + {L}iouville problems}, + journal = {Inverse Problems}, + year = 2004, + volume = 18, + pages = {979--1001} +} + +@Article{BD87, + author = {Bermudez, A. and Durany, J.}, + title = {La Methode des Characteristiques pour les Problemes de + Covection--Diffusion Stationnaires}, + journal = {MMAN}, + volume = 21, + number = 1, + year = 1987, + pages = {7--26} +} + +@Article{BDDF87, + author = {Brezzi, F. and Douglas, J. and Duran, R. and Fortin, M.}, + title = {Mixed finite elements for second order elliptic problems in three variables}, + journal = {Numer. Math.}, + year = 1987, + volume = 51, + pages = {237--250} +} + +@Article{BDM85, + author = {Brezzi, F. and Marini, D. and Douglas, J.}, + title = {Two families of mixed finite elements for second order elliptic problems}, + journal = {Numer. Math.}, + year = 1985, + volume = 47, + pages = {217--235} +} + +@Article{BDY88, + author = {Bank, R. E. and Dupont, T. F. and Yserentant, H.}, + title = {The Hierarchical Basis Multigrid Method}, + journal = {Numer. Math.}, + year = 1988, + volume = 52, + pages = {427--458} +} + +@Article{BF79, + author = {Boris, J. and Fritts, M.}, + title = {The {L}agrangian Solution of Transient problems in Hydrodynamics + Using a Triangular Mesh}, + journal = {J. Comp. Phys.}, + volume = 31, + year = 1979, + pages = {173--215} +} + +@Book{BF91, + author = {Brezzi, F. and Fortin, M.}, + title = {Mixed and Hybrid Finite Element Methods}, + publisher = {Springer}, + year = 1991 +} + +@InProceedings{BG99, + author = {Barnard, S. T. and Grote, M. J.}, + title = {A block version of the {SPAI} preconditioner}, + booktitle = {Proceedings of the Ninth SIAM Conference on Parallel + Processing for Scientific Computing, San Antonio, Texas, + March 1999}, + year = 1999, + publisher = {SIAM} +} + +@Article{BH82, + author = {Brooks, A. and Hughes, T.}, + title = {Streamline Upwind/{P}etrov-{G}alerkin Formulation for Convection + Dominated Flows with Particular Emphasis on the Incompressible + {N}avier-{S}tokes Equations }, + journal = {Comp. Meth. Appl. Mech. Engrg.}, + volume = 32, + year = 1982, + pages = {199--259} +} + +@Book{BHM00, + author = {Briggs, W. L. and Henson, V. E. and McCormick, S. F.}, + title = {A Multigrid Tutorial}, + publisher = {SIAM}, + year = 2000, + edition = {second} +} + +@Article{BHMS00, + author = {Brezzi, F. and Houston, P. and Marini, D. and S\"{u}li, E.}, + title = {Modeling subgrid viscosity for advection-diffusion problems}, + journal = {Comput. Meth. Appl. Mech. Engrg.}, + year = {2000}, + volume = {190}, + number = {13-14}, + pages = {1601--1610}, +} + +@Article{BJ98, + author = {Bouchut, F. and James, F.}, + title = {One-dimensional transport equations with discontinuous coefficients}, + journal = {Nonlinear Analysis TMA}, + year = 1998, + volume = 14, + pages = {255--283} +} + +@InProceedings{BJLS93, + author = {Babu{\v{s}}ka, I. and Jerina, K. and Li, Y. and Smith, P.}, + title = {Quantitative assessment of the accuracy of constitutive laws for plasticity with an emphasis on cyclic deformation}, + booktitle = {Material Parameter Estimation for Modern Constitutive Equations, presented at the 1993 ASME Winter Annual Meeting, New Orleans, LA}, + year = 1993, + editor = {Bertram, L. A. and Brown, S. B. and Freed, A. D.} +} + +@Article{becache:etal:2000, + author = {B{\'e}cache, E. and Joly, P. and Tsogka, C.}, + title = {An analysis of new mixed finite elements for the + approximation of wave propagation problems}, + journal = {SIAM J. Numer. Anal.}, + year = 2000, + volume = 37, + pages = {1053--1084} +} + +@Article{BJT02, + author = {B{\'e}cache, E. and Joly, P. and Tsogka, C.}, + title = {A new family of mixed finite elements for the linear + elastodynamic problem}, + journal = {SIAM J. Numer. Anal.}, + year = 2002, + volume = 39, + pages = {2109--2132} +} + +@InProceedings{BK00, + author = {Br{\"o}ker, O. and Grote, M. J.}, + title = {Parallel Algebraic Multigrid via Sparse Approximate Inverses}, + booktitle = {Proceedings of the 16th IMACS World Congress 2000, Lausanne, + Switzerland, 2000}, + year = 2000, + editor = {Michel Deville and Robert Owens}, + note = {{D}ocument 108-10} +} + +@Article{BKP94, + author = {Bramble, J. H. and Kwak, D. Y. and Pasciak, J. E.}, + title = {Uniform Convergence of Multigrid {V}-Cycle Iterations for + Indefinite and Nonsymmetric Problems}, + journal = {SIAM J. Num. Anal.}, + year = 1994, + volume = 31, + number = 6, + pages = {1746--1763} +} + +@Article{BL42, + author = {Buckley, J. M. and Leverett, M. C.}, + title = {Mechanism of fluid displacement in sands}, + journal = {Trans. AIME}, + year = 1942, + volume = 146, + pages = {107--116} +} + +@Article{BLP94, + author = {Bramble, J. and Leyk, Z. and Pasciak, J. E.}, + title = {The Analysis of multigrid algorithms for pseudo-differential operators of order minus one}, + journal = {Math. Comp.}, + year = 1994, + volume = 63, + pages = {461--478} +} + +@Article{BLR82, + author = {Benque, J. and Labadie, G. and Ronat, J.}, + title = {A New Finite Element Method for {N}avier-{S}tokes Equations coupled + with a Temperature Equation}, + journal = {Proc. 4th Int. Symp. on FEM}, + year = 1982, + pages = {295--302} +} + +@TechReport{BM92, + author = {Boukir, K. and Maday, Y.}, + title = {A High Order Characteristics/Finite Element Method for the + Incompressible {N}avier-{S}tokes Equations}, + institution = {Lab. Analyse Numerique}, + number = {R 92032}, + year = 1992 +} + +@Article{BP79, + author = {Bercovier, M. and Pironneau, O.}, + title = {Error Estimates for Finite Element Solution of the {S}tokes Problem + in Primitive Variables}, + journal = {Numer. Math.}, + volume = 33, + year = 1979, + pages = {211--224} +} + +@Article{BP82, + author = {Bercovier, M. and Pironneau, O.}, + title = {Characteristics and the Finite Element method}, + journal = {Proc. 4th Int. Symp. on FEM}, + year = 1982, + pages = {67--73} +} + +@Book{BP86, + author = {Barbu, V. and Precupanu, T.}, + title = {Convexity and Optimization in {B}anach Spaces}, + publisher = {Reidl Publishing, Dordrecht}, + year = 1986 +} + +@Article{BP92, + author = {Bramble, J. H. and Pasciak, J. E.}, + title = {The Analysis of Smoothers for Multigrid Algorithms}, + journal = {Math. Comp.}, + year = 1992, + volume = 58, + number = 198, + pages = {467--488} +} + +@Article{BPX91, + author = {Bramble, J. H. and Pasciak, J. E. and + Xu, J.}, + title = {The Analysis of Multigrid Algorithms with Nonnested + Spaces or Noninherited Quadratic Forms}, + journal = {Math. Comp.}, + year = 1991, + volume = 56, + number = 193, + pages = {1--34} +} + +@Article{BR78, + author = {Babu{\v s}ka, I. and Rheinboldt, W. C.}, + title = {Error estimates for adaptive finite element computations}, + journal = {SIAM J. Numer. Anal.}, + year = 1978, + volume = 15, + pages = {736--754} +} + +@Book{BS01book, + author = {Babu{\v s}ka, I. and Strouboulis, T.}, + title = {The Finite Element Method and its Reliability}, + publisher = {Clarendon Press, New York}, + year = 2001 +} + +@Book{BS02, + author = {Brenner, S. C. and Scott, R. L.}, + title = {The Mathematical Theory of Finite Elements}, + publisher = {Springer, Berlin-Heidelberg-New York}, + year = 2002, + edition = {second} +} + +@Article{BS93, + author = {Bank, R. E. and Santos, R.}, + title = {Analysis of Some Moving Space-Time Finite Elements}, + journal = {SIAM J. Numer. Anal.}, + volume = 30, + number = 1, + year = 1993, + pages = {1--18} +} + +@Book{BS94, + author = {Brenner, S. C. and Scott, R. L.}, + title = {The Mathematical Theory of Finite Elements}, + publisher = {Springer, Berlin-Heidelberg-New York}, + year = {1994} +} + +@Article{BV96, + author = {Braess, D. and Verf{\"u}rth, R.}, + title = {A posteriori error estimators for the {R}aviart-{T}homas element}, + journal = {SIAM J. Numer. Anal.}, + year = 1996, + volume = 33, + pages = {2431--2444} +} + +@Article{BW85, + author = {Bank, R. E. and Weiser, A.}, + title = {Some A Posteriori Error Estimators for Elliptic Partial + Differential Equations}, + journal = {Math. Comp.}, + year = 1985, + volume = 44, + pages = {283--301} +} + +@Article{Bab81, + author = {Babu{\v s}ka, I.}, + title = {Error estimates for the combined $h$ and $p$ version of + finite element method}, + journal = {Numer. Math.}, + year = 1981, + volume = 37, + pages = {252--277} +} + +@Article{Ben99, + author = {Belgacem, F. B.}, + title = {The mortar finite element method with {L}agrange multipliers}, + journal = {Numer. Math.}, + year = 1999, + volume = 84, + pages = {173--197} +} + +@Article{Ber91, + author = {Bermejo, R.}, + title = {Analysis of an Algorithm for the {G}alerkin-Characteristic Method}, + journal = {Numer. Math.}, + volume = 60, + year = 1991, + pages = {163--194} +} + +@PhdThesis{Blo92, + author = {Bl{\"o}mer, C.}, + title = {Eine neue {D}iskretisierung f{\"u}r zweidimensionale + {T}ransportprobleme mit dominanter {K}onvektion}, + school = {Ruhr-Universit{\"a}t Bochum}, + type = {Dissertation}, + year = 1992 +} + +@Book{Bra93, + author = {Bramble, J. H.}, + title = {Multigrid Methods}, + publisher = {Longman}, + year = 1993 +} + +@Book{Bra97, + author = {Braess, D.}, + isbn={978-0-521705189}, + title = {Finite elements}, + publisher = {Cambridge University Press}, + year = 1997 +} + +@PhdThesis{Bro01, + author = {Brooksbanks, E.}, + title = {A Numerical Investigation of Time Resolved Flows Around +Turbine Blades}, + school = {University of Leicester}, + year = 2001 +} + +@Book{BB93, + author = {Brady, B. H. G. and Brown, E. T.}, + title = {Rock mechanics for underground mining}, + publisher = {Chapman and Hall}, + year = 1993 +} + +@Article{BMHF00, + author = {Beaumont, C. and Munoz, J. A. and Hamilton, J. and Fullsack, P.}, + title = {Factors controlling the {A}lpine evolution of the central + {P}yrenees inferred from a comparison of observations and + geodynamical models}, + journal = jgr, + year = 2000, + volume = 105, +doi={10.1029/1999JB900390}, + pages = {8121--8145} +} + +@Article{BSTOL02, + author = {Babeyko, A. Y. and Sobolev, S. V. and Trumbull, R. B. and + Oncken, O. and Lavier, L. L.}, + title = {Numerical models of crustal scale convection and partial + melting beneath the {A}ltiplano-{P}una plateau}, + year = {2002}, + month = {06}, + pages = {373-388}, + volume = {199}, + journal = {Earth and Planetary Science Letters}, + doi = {10.1016/S0012-821X(02)00597-6} +} + +@Article{Bas91, + author = {Bassi, G.}, + title = {Factors controlling the style of continental + rifting: insights from numerical modeling}, + journal = {Earth Planet. Sc. Lett.}, + year = 1991, + volume = 105, +doi={10.1016/0012-821X(91)90183-I}, + pages = {430--452} +} + +@Article{Bru14, + author = {Brune, S. and Heine, C. and P\~{e}rez-Gussiny\~{e}, M and Sobolev, S. V.}, + title = {Rift migration explains continental margin asymmetry and crustal hyperextension}, + journal = {Nat. Comm.}, + year = 2014, + volume = 5, +doi={10.1038/ncomms5014}, + number = 4014 +} + +@Article{Bas95, + author = {Bassi, G.}, + title = {Relative importance of strain rate and rheology + for the mode of continental extension}, + journal = {Geoph. J. Int.}, + year = 1995, + volume = 122, +doi={10.1111/j.1365-246X.1995.tb03547.x}, + pages = {195--206} +} + +@Article{Buc91, +title={{Modes of Continental Lithospheric Extension}}, +author={W.R. Buck }, +journal=jgr, +volume={96}, +number={B2}, +pages={20,161-20,178}, +doi={10.1029/91JB01485}, +year={1991} +} + +@Article{Behn2009, + title={Implications of grain size evolution on the seismic structure of the oceanic upper mantle}, + author={Behn, Mark D and Hirth, Greg and Elsenbeck II, James R}, + journal={Earth and Planetary Science Letters}, + volume={282}, + number={1-4}, + pages={178--189}, + doi={10.1016/j.epsl.2009.03.014}, + year={2009} +} + +@Article{Buc93, + author = {Buck, W. R.}, + title = {Effect of Lithospheric thickness on the formation + of high- and low-angle normal faults}, + journal = {Geology}, + year = 1993, + volume = 21, + doi={10.1130/0091-7613(1993)021<0933:EOLTOT>2.3.CO;2}, + pages = {933--936} +} + +@Article{Bye78, + author = {Byerlee, J. D.}, + title = {Friction of rock}, + journal = {Pageoph.}, + year = 1978, + volume = 116, + pages = {515--526} +} + +@article{barcilon:richter:1986, + title={Nonlinear waves in compacting media}, + author={Barcilon, V. and Richter, F. M.}, + journal={Journal of Fluid mechanics}, + volume={164}, + pages={429--448}, + year={1986}, + publisher={Cambridge Univ Press} +} + +@Article{BR97, + author = {Bassi, F. and Rebay, S.}, + title = {High-order accurate discontinuous finite element solution of the {2D} {E}uler equations}, + journal = {J. Comput. Phys.}, + year = {1997}, + volume = {138}, + pages = {251--285}, +} + +@Article{BGP87, + author = {Bristeau, M. O. and Glowinski, R. and Periaux, J.}, + title = {Numerical methods for the {N}avier-{S}tokes equations: + {A}pplications to the simulation of compressible and incompressible + viscous flows}, + journal = {Report UH/MD-4, Univ. of Houston, in Computer Physics Report}, + year = {1987} +} + +@article{bunge:etal:1996, +title={{Effect of depth-dependent viscosity on the planform of mantle convection}}, +author={H.-P. Bunge and M.A. Richards and J.R. Baumgardner}, +journal={Nature}, +volume={379}, +number={}, +pages={436--438}, +doi={10.1038/379436a0}, +year={1996}} + +@article{busse:1975, +title={{Patterns of convection in spherical shells}}, +author={F.H. Busse}, +journal={J. Fluid Mech.}, +volume={72}, +number={1}, +pages={67--85}, +doi={10.1017/S0022112075002947}, +year={1975}} + +@article{busse:1979, +title={High {P}randtl number convection}, +author={Busse, FH}, +journal=pepi, +volume={19}, +number={2}, +pages={149--157}, +doi={10.1016/0031-9201(79)90079-7}, +year={1979}} + +@article{bunge:etal:1997, +title={{A sensitivity study of three-dimensional spherical mantle convection at $10^8$ +{R}ayleigh number: {E}ffects of depth-dependent viscosity, heating mode, and endothermic phase change}}, +author={H.-P. Bunge and M.A. Richards and J.R. Baumgardner}, +journal=jgr, +volume={102}, +number={B6}, +pages={11,991--12,007}, +doi={10.1029/96JB03806}, +year={1997}} + +@Article{p4est, + author = {Burstedde, C. and Wilcox, L. C. and Ghattas, O.}, + title = {{p4est}: {S}calable algorithms for parallel + adaptive mesh refinement on forests of octrees}, + journal = {SIAM J. Sci. Comput.}, + year = {2011}, + volume = {33}, + number = {3}, + pages = {1103--1133}, + doi = {10.1137/100791634} +} + +@article{behn:transform:fault, + title={Thermal structure of oceanic transform faults}, + author={Behn, Mark D and Boettcher, Margaret S and Hirth, Greg}, + journal={Geology}, + volume={35}, + number={4}, + pages={307--310}, + year={2007}, + publisher={Geological Society of America} +} + +@Article{badro:etal:2004, + author = {Badro, J. and Rueff, J.-P. and Vank{\'o}, G. and Monaco, G. + and G. Fiquet and F. Guyot}, + title = {Electronic Transitions in Perovskite: {P}ossible + Nonconvecting Layers in the Lower Mantle}, + journal = {Science}, + year = 2004, + volume = 305, + pages = {383--386} +} + +@Article{BBHK10, + author = {Bangerth, W. and Burstedde, C. and Heister, T. and Kronbichler, + M.}, + title = {Algorithms and Data Structures for Massively Parallel Generic + Adaptive Finite Element Codes}, + journal = {ACM Trans. Math. Softw.}, + volume = {38}, + number = {2}, + year = {2011} +} + +@Article{BCTH07, + author = {Bazilevs, Y. and Calo, V. M. and Tezduyar, T. E. and Hughes, + T. J. R.}, + title = {{YZ$\beta$ discontinuity capturing for advection-dominated processes with application to arterial drug delivery}}, + journal = {Int. J. Numer. Meth. Fluids}, + volume = {54}, + pages = {593--608}, + year = {2007} +} + +@article{bauville:baumann:2019, + title={geomIO: an open-source MATLAB toolbox to create the initial configuration of 2D/3D thermo-mechanical simulations from 2D vector drawings}, + author={Bauville, A and Baumann, TS}, + journal={Geochemistry, Geophysics, Geosystems}, + publisher={Wiley Online Library}, + year = {2019}, + doi = {10.1029/2018GC008057} +} + +@Article{BBC89, +author = {Blankenbach, B. and Busse, F. and Christensen, U. and Cserepes, + L. and Gunkel, D. and Hansen, U. and Harder, H. and Jarvis, + G. and Koch, M. and Marquart, G. and Moore, D. and Olson, + P. and Schmeling, H. and Schnaubelt, T.}, +title = {A benchmark comparison for mantle convection codes}, +journal = gji, +volume = 98, +doi={10.1111/j.1365-246X.1989.tb05511.x}, +year = 1989, +pages = {23--38} +} + + +@INPROCEEDINGS{BGG08, + author = {Burstedde, C. and Ghattas, O. and Gurnis, M. and Tan, E. and Tu, T. and Stadler, G. and Wilcox, L. C. and Zhong, S.}, + title = {Scalable adaptive mantle convection simulation on petascale + supercomputers}, + booktitle = {SC '08: Proceedings of the International Conference for High + Performance Computing, Networking, Storage, and Analysis}, + doi={10.1109/SC.2010.25}, + year = {2008}, + publisher = {ACM/IEEE} +} + +@Article{busse:etal:1993, +author= {Busse, F. and Christensen, U. and Clever, R. and Cserepes, L. and + Gable, C. and Giannandrea, E. and Guillou, L. and Houseman, + G. and Nataf, H.-C. and Ogawa, M. and Parmentier, M. and + Sotin, C. and Travis, B.}, +title= {{3D} convection at infinite {Prandtl} numbers in cartesian geometry --- a benchmark comparison}, +journal= {Geophys. Astrophys. 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Geosystems}, + year = 2011, + volume = 12, + pages = {Q07004/1--26}} + + +@InBook {donea:etal:2004, +author = {Donea, Jean and Huerta, Antonio and Ponthot, J.-Ph. and Rodr{\'i}guez-Ferran, A.}, +publisher = {American Cancer Society}, +isbn = {9780470091357}, +title = {Arbitrary Lagrangian-Eulerian Methods}, +booktitle = {Encyclopedia of Computational Mechanics}, +chapter = {14}, +pages = {}, +doi = {10.1002/0470091355.ecm009}, +url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/0470091355.ecm009}, +eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/0470091355.ecm009}, +year = {2004} +} + +@Article{deubelbeiss:kaus:2008, + author = {Y. Deubelbeiss and B. J. P. 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DiCaprio and S. Spasojevic and R. D. M{\"u}ller and J. Boyden and M. Seton and V. C. Manea and D. J. Bower}, + title = {Plate tectonic reconstructions with continuously closing plates}, + journal = {Computers \& Geosciences}, + year = 2012, + volume = 38, + pages = {35--42}} + +@Book{gerya:2010, + author = {T. Gerya}, + title = {Introduction to Numerical Geodynamic Modelling}, + publisher = {Cambridge University Press}, + year = 2010} + +@Article{GA02, + author = {Guessous, N. and Akhmouch, M.}, + title = {Higher order analytical nodal methods in + response-matrix formulation for the multigroup neutron + diffusion equations}, + journal = {Ann. Nucl. Energy}, + year = 2002, + volume = 29, + pages = {1765--1778}} + + +@Article{GB86a, + author = {Guo, B. and Babu{\v s}ka, I.}, + title = {The h-p version of the finite element method. {P}art {I}: + {T}he basic approximation results}, + journal = {Comp. 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C. + and Babu\v{s}ka, I.}, + title = {A posteriori error analysis and adaptive processes + in the finite element method: + Part {II} --- {A}daptive Mesh Refinement}, + journal = {Int. J. Num. Meth. Engrg.}, + year = {1983}, + volume = {19}, + pages = {1621--1656} +} + + +@Book{GMW81, + author = {Gill, P. E. and Murray, W. and Wright, M. H.}, + title = {Practical Optimization}, + publisher = {Academic Press}, + year = 1981 +} + +@Article{GOR99, + author = {Godlewski, E. and Olazabal, M. and Raviart, P. -A.}, + title = {On the linearization of systems of conservation laws for fluids +at a material contact discontinuity}, + journal = {J. Math. Pures Appl.}, + year = 1999, + volume = 17, + pages = {1013--1042} +} + +@Article{GP00, + author = {Gopalakrishnan, J. and Pasciak, J. E.}, + title = {Multigrid for the mortar finite element method}, + journal = {SIAM J. Numer. Anal.}, + year = 2000, + volume = 37, + pages = {1029--1052} +} + +@Book{GT83, + author = {Gilbarg, D. and Trudinger, N. S.}, + title = {Elliptic Partial Differential Equations of Second Order}, + publisher = {Springer}, + year = 1983, + address = {Heidelberg}, + edition = {Second} +} + +@Book{GV89, + author = {Golub, G. H. and Van Loan, C. F.}, + title = {Matrix Computations}, + publisher = {J. Hopkins University Press}, + year = 1989, + address = {Baltimore}, + edition = {Second} +} + +@InProceedings{GW88, + author = {Glowinski, R. and Wheeler, M. F.}, + title = {Domain decomposition and mixed finite element methods for + elliptic problems}, + booktitle = {Domain Decomposition Methods for Partial Differential + Equations}, + pages = {144--172}, + year = 1988, + publisher = {SIAM, Philadelphia} +} + + + + + + +@article{gassmoeller:etal:2023, + author = {Gassm\"{o}ller, R. and Dannberg, J. and Bangerth, W. and Puckett, E. G. and Thieulot, C.}, + title = {Benchmarking the accuracy of higher order particle methods in geodynamic models of transient flow}, + journal = {EGUsphere}, + volume = {2023}, + year = {2023}, + pages = {1--29}, + url = {https://egusphere.copernicus.org/preprints/2023/egusphere-2023-2765/}, + doi = {10.5194/egusphere-2023-2765} +} + + +@TECHREPORT{ml-guide, + Author = {Gee, M. W. and Siefert, C. M. and Hu, J. J. and Tuminaro, + R. S. and Sala, M. G.}, + Title = {ML 5.0 Smoothed Aggregation User's Guide}, + Institution = {Sandia National Laboratories}, + Number = {2006-2649}, + Year = {2006} +} + + +@ARTICLE{G09, +Author = {Geenen, T. and ur Rehman, M. and MacLachlan, S. P. and Segal, + G. and Vuik, C. and van den Berg, A. P. and Spakman, W.}, +Title = {Scalable robust solvers for unstructured {FE} geodynamic modeling + applications: Solving the {S}tokes equation for models with + large localized viscosity contrasts}, +doi={10.1029/2009GC002526}, + Journal = {Geochem. Geophys. 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Engrg.}, + volume = 58, + year = 1986, + pages = {305--328} +} + + +@Article{HM86d, + author = {Hughes, T. and Mallet, M.}, + title = {A New Finite Element Formulation for Computational Fluid + Dynamics {IV} --- A Discontinuity--Capturing Operator for + Multidimensional Advective--Diffusive Systems}, + journal = {Comput. Methods Appl. Mech. Engrg.}, + volume = 58, + year = 1986, + pages = {329--336} +} + +@Article{HMM86, + author = {Hughes, T. and Mallet, M. and Mizukami, A.}, + title = {A New Finite Element Formulation for Computational Fluid + Dynamics {II} --- Beyond {SUPG}}, + journal = {Comput. Methods Appl. Mech. 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Meth. Appl. Mech. Engrg.}, + volume = 96, + year = 1992, + pages = {239--253} +} + +@Article{Han92n, + author = {Hansbo, P.}, + title = {The Characteristic Streamline Diffusion Method for the + Time-Dependent Incompressible {N}avier-{S}tokes Equations}, + journal = {Comp. Meth. Appl. Mech. Engrg.}, + volume = 99, + year = 1992, + pages = {171--186} +} + +@Article{Har83, + author = {Harten, A.}, + title = {High Resolution Schemes for Hyperbolic Conservation Laws}, + journal = {J. Comp. 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Tackley}, + title = {Computational Methods for Geodynamics}, + publisher = {Cambridge University Press}, + year = 2010 +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% JJJJ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +@Article{JJS95, + author = {Jaffre, J. and Johnson, C. and Szepessy, A.}, + title = {Convergence of the discontinuous {G}alerkin finite element method + for hyperbolic conservation laws}, + journal = {Math. Models and Methods in Appl. Sciences}, + year = 1995, + volume = 5, + pages = {367-386} +} + +@Article{JNP84, + author = {Johnson, C. and N{\"a}vert, U. and Pitk{\"a}ranta, J.}, + title = {Finite Element Methods for Linear Hyperbolic Problems}, + journal = {Comp. Mech. in Appl. Mech. Engrg.}, + year = 1984, + volume = 45, + pages = {285--312} +} + +@Article{JP83, + author = {Johnson, C. and Pitk{\"a}ranta, J.}, + title = {Convergence of a Fully Discrete Scheme for Two-Dimensional Neutron Transport}, + journal = {SIAM J. Numer. Anal}, + year = 1983, + volume = 20, + pages = {951--966} +} + +@Article{JP86, + author = {Johnson, C. and Pitk{\"a}ranta, J.}, + title = {An Analysis of the Discontinuous {G}alerkin Method for a Scalar Hyperbolic Equation}, + journal = {Math. Comp.}, + year = 1986, + volume = 46, + number = 173, + pages = {1-26} +} + +@Article{JS86, + author = {Johnson, C. and Saranen, J.}, + title = {Streamline Diffusion Methods for the Incompressible {E}uler and + {N}avier-{S}tokes Equations}, + journal = {Math. Comp.}, + volume = 47, + year = 1986, + pages = {1--18} +} + +@Article{JS87, + author = {Johnson, C. and Szepessy, A.}, + title = {On the Convergence of a Finite Element Method for a Nonlinear + Hyperbolic Conservation Law}, + journal = {Math. Comp.}, + volume = 49, + year = 1987, + pages = {427--444} +} + + +@article{JS92, + author = {Johnson, C. and Szepessy, A.}, + title = {Adaptive finite element methods for conservation laws based on a posteriori error estimates}, + journal = {Communications on Pure and Applied Mathematics}, + volume = {48}, + number = {3}, + pages = {199-234}, + doi = {10.1002/cpa.3160480302}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.3160480302}, + eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/cpa.3160480302}, + abstract = {Abstract We prove a posteriori error estimates for a finite element method for systems of strictly hyperbolic conservation laws in one space dimension, and design corresponding adaptive methods. The proof of the a posteriori error estimates is based on a strong stability estimate for an associated dual problem, together with the Galerkin orthogonality of the finite-element method. The strong stability estimate uses the entropy condition for the system in an essential way.}, + year = {1995} +} + + +@Article{JSH90, + author = {Johnson, C. and Szepessy, A. and Hansbo, P.}, + title = {On the Convergence of Shock-Capturing Streamline Diffusion + Finite Element methods for Hyperbolic Conservation Laws}, + journal = {Math. Comp.}, + volume = 54, + year = 1990, + pages = {107--129} +} + + +@Article{Joh76, + author = {Johnson, C.}, + title = {Existence theorems for plasticity problems}, + journal = {J. Math. Pures Appl.}, + year = 1976, + volume = 55, + pages = {431--444} +} + +@Book{Joh87, + author = {Johnson, C.}, + title = {Numerical Solutions of Partial Differential + Equations by the Finite Element Method}, + publisher = {Cambridge University Press}, + year = 1987 +} + + +@Article{Joh90c, + author = {Johnson, C.}, + title = {Adaptive Finite Element Methods for Diffusion and Convection + Problems}, + journal = {Comp. Meth. Appl. Mech. Engrg.}, + volume = 82, + year = 1990, + pages = {301--322} +} + +@TechReport{Joh90f, + author = {Johnson, C.}, + title = {A New Approach to Algorithms for Convection Problems which are + Based on Exact Transport + Projection}, + institution = {Dept. of Math., Chalmers Univ., G{\"o}teborg}, + number = {1990--24}, + year = 1990 +} + +@Article{Joh90p, + author = {Johnson, C.}, + title = {The Streamline Diffusion Finite Element Method for Compressible and + Incompressible Fluid Flow}, + journal = {Pitman Res. Notes. Math. Ser.}, + volume = 228, + year = 1990, + pages = {155--181} +} + +@Article{Joh91, + author = {Johnson, C.}, + title = {The Characteristic Streamline Diffusion Method}, + journal = {Mat. Aplic. Comp.}, + volume = 10, + year = 1991, + pages = {229--242} +} + +@Book{Joh93, + author = {Johnson, C.}, + title = {Finite Element Methods for Partial Differential Equations}, + publisher = {Studentlitteratur}, + year = 1993, + address = {Lund} +} + +@Book{johnson:1993:pdes, + author = {Johnson, C.}, + title = {Finite Element Methods for Partial Differential Equations}, + publisher = {Cambridge University Press}, + year = 1993 +} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% KKKK +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +@Article{Kam05, + author = {M. Kameyama}, + title = {{ACuTEMan}: {A} multigrid-based mantle convection simulation + code and its optimization to the {E}arth simulator}, + journal = {J. Earth Simulator}, + year = 2005, + volume = 4, + pages = {2--10}} + +@Article{KZ99, + author = {P. van Keken and S. Zhong}, + title = {Mixing in a {3D} spherical model of present-day mantle convection}, + journal = {Earth Planet. Science L.}, + year = 1999, + volume = 171, + pages = {533--547}} + + +@Article{kronbichler:etal:2012, + Title = {High Accuracy Mantle Convection Simulation through Modern Numerical Methods}, + Author = {M. Kronbichler and T. Heister and W. Bangerth}, + Journal = {Geophysical Journal International}, + Year = {2012}, + Pages = {12-29}, + Volume = {191}, + doi = {10.1111/j.1365-246X.2012.05609.x}, + url = {http://dx.doi.org/10.1111/j.1365-246X.2012.05609.x} +} + +@Article{kaus:etal:2010, + title={A stabilization algorithm for geodynamic numerical simulations with a free surface}, + author={Kaus, B. J. P. and M{\"u}hlhaus, H. and May, D. A.}, + journal={Physics of the Earth and Planetary Interiors}, + volume={181}, + number={1}, + pages={12--20}, + year={2010}, + publisher={Elsevier} +} + +@article{king:etal:2010, + title={A community benchmark for 2-{D} {C}artesian compressible convection in the {E}arth's mantle}, + author={King, Scott D and Lee, Changyeol and Van Keken, Peter E and Leng, Wei and Zhong, Shijie and Tan, Eh and Tosi, Nicola and Kameyama, Masanori C}, + journal={Geophysical Journal International}, + volume={180}, + number={1}, + pages={73--87}, + year={2010} +} + +@article{keller:etal:2013, + author = {Keller, Tobias and May, Dave A. and Kaus, Boris J. 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J.}, +Title = {Finite Volume Methods for Hyberbolic Problems}, +Publisher = {Cambridge Texts in Applied Mathematics}, +Address = {Cambridge}, +Year = {2002} +} + +@Article{LB02, + author = {Lavier, L. L. and Buck, W. R.}, + title = {Half graben versus large-offset low-angle normal fault: + importance of keeping cool during normal faulting}, + journal = {J. Geoph. Res.}, + year = 2002, + volume = 107, + doi={10.1029/2001JB000513}, + pages = {ETG 8-1--ETG 8-13} +} + +@Article{LBP00, + author = {Lavier, L. L. and Buck, W. R. and Poliakov, A. B. N.}, + title = {Factors controlling normal fault offset in an ideal + brittle layer}, + journal = {J. Geoph. Res}, + year = 2000, + volume = 23, + doi={10.1029/2000JB900108}, + pages = {23431--23442} +} + +@Article{LBP99, + author = {Lavier, L. L. and Buck, W. R. and Poliakov, A. B. N.}, + title = {A self-consistent rolling-hinge model for the evolution + of large-offset low-angle normal faults}, + journal = {Geology}, + year = 1999, + volume = 27, + pages = {1127--1130} +} + +@InProceedings{LM03, + author = {Lavier, L. L. and Manatschal, G.}, + title = {Modeling of the Role of Serpentinization and Magmatism at the + Transition From Rifting to Seafloor Spreading}, + booktitle = {American Geophysical Union abstract volume}, + year = 2003, + address = {San Fransisco} +} + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +@Article{SF93, + author = {Sleijpen, G. L. G. and Fokkema, D. R.}, + title = {Bicgstab(${L}$) for Linear Equations Involving + Unsymmetric Matrices with Complex Spectrum}, + journal = {ETNA}, + year = 1993, + volume = 1, + pages = {11--32}, + month = Sep +} + + +@Inbook{SH02, + author = {S{\"u}li, E. and Houston, P.}, + editor={Barth, T. J. and Deconinck, H.}, + title ={Adaptive Finite Element Approximation of Hyperbolic Problems}, + bookTitle={Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics}, + year={2003}, + publisher={Springer Berlin Heidelberg}, + address={Berlin, Heidelberg}, + pages={269--344}, + isbn={978-3-662-05189-4}, + doi={10.1007/978-3-662-05189-4_6}, + url={https://doi.org/10.1007/978-3-662-05189-4_6} +} + + +@Article{SW81, + author = {Steger, J. L. and Warming, R. F.}, + title = {Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods.}, + journal = {J. Comput. Phys.}, + year = 1981, + pages = {263--293} +} + +@Article{SW94, + author = {Silvester, D. and Wathen, A.}, + title = {Fast iterative solution of stabilised {S}tokes systems. {P}art + {II}: {U}sing general block preconditioners}, + journal = {SIAM J. Numer. Anal.}, + year = 1994, + volume = 31, + pages = {1352--1367}} + +@Book{Saa96, + author = {Saad, Y.}, + title = {Iterative Methods for Sparse Linear Systems}, + publisher = {PWS}, + year = 1996 +} + +@Book{Sch91, + author = {Schwarz, H. R.}, + title = {Methode der finite Elemente}, + publisher = {B.G. Teubner Stuttgart}, + year = 1991 +} + +@Book{Sch98b, + author = {Schwab, C.}, + title = {$p$- and $hp$-Finite Element methods. Theory and Applications to Solid and Fluid Mechanics}, + publisher = {Oxford University Press}, + year = 1998 +} + + +@Article{Sul92, + author = {S{\"u}li, E.}, + title = {The accuracy of cell vertex finite volume methods on + quadrilateral meshes}, + journal = {Math. Comp.}, + year = 1992, + volume = 59, + pages = {359--382} +} + +@TechReport{Sul95, + author = {S{\"u}li, E.}, + title = {A posteriori error analysis and global error control + for adaptive finite element approximations of + hyperbolic problems}, + institution = {University of Oxford}, + year = 1995, + month = jun +} + + + +@InCollection{Sul98, + author = {S{\"u}li, E.}, + title = {A posteriori error analysis and adaptivity for finite element + approximations of hyperbolic problems}, + booktitle = {An introduction to recent developments in theory and numerics + for conservation laws }, + pages = {123--194}, + publisher = {Springer}, + year = 1998, + editor = {Kr{\"o}ner, D. and Ohlberger, M. and Rhode, C.}, + volume = 5, + series = {Lecture Notes in Comput. Sciences and Engrg.} +} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +xxxxxxxxxxxxxxxxxxx +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + + + + +@InProceedings{BBR98, + author = {Becker, R. and Braack, M. and Rannacher, R.}, + title = {Adaptive finite elements for reactive flows}, + bootitle = {ENUMATH 97}, + pages = {206--213}, + year = 1999 +} + + +@InProceedings{BBR98a, + author = {Becker, R. and Braack, M. and Rannacher, R.}, + title = {An adaptive finite element method for combustion problems}, + booktitle = {ENUMATH 97}, + pages = {206--213}, + year = 1998, + editor = {Bock, H. G. et al.}, + publisher = {World Scientific Publ., Singapure} +} + +@Article{BBR99a, + author = {Becker, R. and Braack, M. and Rannacher, R.}, + title = {Numerical simulation of laminar + flames at low {M}ach number by adaptive finite elements}, + journal = {Combust. Theory Modelling}, + year = {1999}, + volume = {3}, + pages = {503--534} +} + + +@InProceedings{BBR99b, + author = {Becker, R. and Braack, M. and Rannacher, R.}, + title = {Adaptive finite element methods for + flow problems}, + booktitle = {Proc. FoCM'99, Oxford, July 18-27}, + year = {1999}, + editor = {A. Iserles} +} + +@Article{BBRW99b, + author = {Becker, R. and Braack, M. and Rannacher, R. and Waguet, C.}, + title = {Fast and reliable + solution of the {N}avier-{S}tokes equations including chemistry}, + journal = {Comput. Visual. Sci.}, + year = {1999}, + volume = {2}, + pages = {107--122} +} + + + +@Article{BGH04, + author = {Bangerth, W. and Grote, M. and Hohenegger, C.}, + title = {Finite Element Method For Time Dependent Scattering: + Nonreflecting Boundary Condition, Adaptivity, and + Energy Decay}, + journal = {Comp. Meth. Appl. Mech. Engrg.}, + year = {2004}, + volume = {193}, + pages = {2453--2482} +} + +@TechReport{BHK06, + author = {Bangerth, W. and Hartmann, R. and Kanschat, G.}, + title = {{deal.II} -- a General Purpose Object Oriented Finite Element Library}, + institution = {Institute for Scientific Computation, Texas A\&M University}, + year = 2006, + number = {ISC-06-02-MATH} +} + + +@Article{bangerth:etal:2007, + author = {Bangerth, W. and Hartmann, R. and Kanschat, G.}, + title = {{deal.II} -- a General Purpose Object Oriented Finite Element Library}, + journal = {ACM Trans. Math. Softw.}, + year = 2007, + volume = 33, + number = 4, + pages = {24} +} + + + +@Article{BJ08, + author = {Bangerth, W. and Joshi, A.}, + title = {Adaptive finite element methods for the solution of + inverse problems in optical tomography}, + journal = {Inverse Problems}, + year = 2008, + volume = 24, + pages = {034011/1--22}} + + + +@Article{BJR95, + author = {Becker, R. and Johnson, C. and Rannacher, R.}, + title = {Adaptive error control for multigrid finite element methods}, + journal = {Computing}, + year = 1995, + volume = 55, + pages = {271-288} +} + + +@Article{BJS05, + author = {Bangerth, W. and Joshi, A. and Sevick-Muraca, E. M.}, + title = {Adaptive finite element methods for increased + resolution in fluorescence optical tomography}, + journal = {Progr. Biomed. Optics Imag.}, + year = 2005, + volume = 6, + pages = {318--329} +} + + +@InProceedings{BJS07b, + author = {Bangerth, W. and Joshi, A. and Sevick-Muraca, E. M.}, + title = {Inverse biomedical imaging using separately adapted meshes + for parameters and forward model variables}, + booktitle = {Proceedings of the IEEE International Symposium on + Biomedical Imaging, Arlington, VA, 2007}, + pages = {1368--1371}, + year = 2007, + publisher = {IEEE} +} + +@Manual{bangerth:etal:2012, + title = {{deal.{I}{I}} Differential Equations Analysis Library, + Technical Reference}, + author = {Bangerth, W. and Heister, T. and Kanschat, G.}, + year = {2012}, + note = {{http://www.dealii.org/}} +} + + +@Manual{deal.ii-publications, + author = {Bangerth W. and Kanschat, G.}, + title = {Publications based on the {deal.{I}{I}} library}, + note = {{http://www.dealii.org/developer/publications/toc.html}} +} + + +@TechReport{BK99tr, + author = {Bangerth, W. and Kanschat, G.}, + title = {Concepts for Object-Oriented Finite Element Software -- the + {deal.II} library}, + institution = {IWR Heidelberg}, + year = 1999, + type = {{P}reprint 99-43 ({SFB} 359)}, + month = oct +} + + +@Article{BKMPW05, + author = {Bangerth, W. and Klie, H. and Matossian, V. + and Parashar, M. and Wheeler, M.}, + title = {An Autonomic Reservoir Framework for the Stochastic + Optimization of Well Placement}, + journal = {Cluster Computing}, + year = 2005, + volume = 8, + pages = {255--269} +} + +@Article{BKR00, + author = {Becker, R. and Kapp, H. and Rannacher, R.}, + title = {Adaptive Finite Element Methods for Optimal Control + of Partial Differential Equations: {B}asic Concept}, + journal = {SIAM J. Contr. Optim.}, + year = 2000, + volume = 39, + pages = {113--132} +} + + + + + +@TechReport{BKS96, + author = {Becker, R. and Kanschat, G. and Suttmeier, F.-T.}, + title = {Optimality Criteria for Adaptive Finite Element + Meshes}, + institution = IWR, + year = 1996, + note = {to appear}, + nolist = 1 +} + + + +@Article{BKWSS06, + author = {Bangerth, W. and Klie, H. and Wheeler, M. F. and + Stoffa, P. and Sen, M.}, + title = {On optimization algorithms for the reservoir oil + well placement problem}, + journal = {Comp. Geosciences}, + year = 2006, + volume = {10}, + pages = {303--319} +} + +@article{BR01, + author = {Becker, R. and Rannacher, R.}, + title = {An optimal control approach to error estimation and mesh adaptation +in finite element methods}, + journal = {Acta Numerica}, + year = 2001, + volume = 10, + pages = {1-102} +} + + +@Article{BR01a, + author = {Bangerth, W. and Rannacher, R.}, + title = {Adaptive Finite Element Techniques for the Acoustic Wave Equation}, + journal = {J. Comput. Acoustics}, + year = 2001, + volume = 9, + number = 2, + pages = {575--591} +} + + + +@Book{BR03, + author = {Bangerth, W. and Rannacher, R.}, + title = {Adaptive Finite Element Methods for + Differential Equations}, + publisher = {Birkh{\"a}user Verlag}, + year = 2003 +} + + + +@InProceedings{BR95, + author = {Becker, R. and Rannacher, R.}, + title = {Weighted A Posteriori Error Control in {FE} Methods}, + booktitle = {ENUMATH 95}, + pages = {621--637}, + year = 1998, + editor = {Bock, H. G., et al.}, + address = {Paris}, + month = sep, + publisher = {World Scientific Publ., Singapure}, + note = {in \cite{enumath97}} +} + + + +@InProceedings{BR95short, + author = {Becker, R. and Rannacher, R.}, + title = {Weighted A Posteriori Error Control in {FE} Methods}, + booktitle = {Proc. of ENUMATH 95, in Proc. of ENUMATH 97}, + year = 1998, + editor = {Bock, H. G. and others}, + address = {Singapore}, + publisher = {World Scientific}, +} + +@TechReport{BR96k, + author = {B{\"o}ttcher, K. and Rannacher, R.}, + title = {Adaptive error control in solving ordinary + differential equations by the discontinuous {G}alerkin + method}, + institution = sfb, + year = {1996}, + OPTkey = {}, + type = {Preprint}, + OPTnumber = {}, + OPTaddress = {}, + OPTmonth = {}, + OPTnote = {}, + OPTannote = {} +} + + + +@Article{BR96r, + author = {Becker, R. and Rannacher, R.}, + title = {A Feed-Back Approach to Error Control in Finite + Element Methods: {B}asic Analysis and Examples}, + journal = EastWest, + year = 1996, + volume = 4, + pages = {237--264} +} + + + + +@InProceedings{BR98, + author = {Becker, R. and Rannacher, R.}, + title = {A General Concept of Adaptivity in Finite Element + Methods with Applications to Problems in Fluid and + Structural Mechanics}, + booktitle = {Grid Generation and Adaptive Algorithms}, + year = 1999, + editor = {Bern, M. and Flaherty, J. E. and Luskin, M.}, + volume = 113, + series = {IMA Volumes in Mathematics and its Applications}, + publisher = {Springer} +} + +@Article{BR99b, + author = {Bangerth, W. and Rannacher, R.}, + title = {Finite element approximation of the acoustic wave equation: {E}rror + control and mesh adaptation}, + journal = {East--West J. Numer. Math.}, + year = 1999, + volume = 7, + number = 4, + pages = {263--282} +} + + +@InProceedings{BR99c, + author = {Braack, M. and Rannacher, R.}, + title = {Adaptive finite element methods for + low-{M}ach-number flows with chemical reactions}, + booktitle = {30th Computational Fluid Dynamics}, + year = 1999, + editor = {Deconinck, H.}, + volume = 3, + series = {Lecture Series}, + publisher = {von Karman Institute of Fluid Dynamics, Brussels} +} + + +@Article{BS00, + author = {Blum, H. and Suttmeier, F.-T.}, + title = {Weighted Error Estimates for Finite Element Solutions + of Variational Inequalities}, + journal = {Computing}, + year = 2000, + volume = 65, + pages = {119--134} +} + + +@Misc{BV02, + author = {Becker, R. and Vexler, B.}, + title = {Mesh adaptation for parameter identification problems}, + howpublished = {Proceedings of ENUMATH 2001}, + year = 2002, + note = {submitted} +} + + +@Article{BV03, + author = {Becker, R. and Vexler, B.}, + title = {A posteriori error estimation for finite element + discretization of parameter identification problems}, + journal = {Numer. Math.}, + year = 2003, + volume = 96, + pages = {435--459} +} + +@MastersThesis{Bac97, + author = {Backes, E.}, + title = {{G}ewichtete a posteriori {F}ehleranalyse bei der adaptiven + {F}inite-{E}lemente-{M}ethode: Ein {V}ergleich zwischen {R}esiduen- und + {B}ank-{W}eiser-{S}ch{\"a}tzer}, + school = {Institut f{\"u}r Angewandte Mathematik, Universit{\"a}t Heidelberg}, + year = 1997, + type = {Diplomarbeit} +} + +@InProceedings{Ban00i, + author = {Bangerth, W.}, + title = {Using Modern Features of {C}++ for Adaptive Finite Element Methods: + {D}imension-Independent Programming in deal.{I}{I}}, + booktitle = {Proceedings of the 16th IMACS World Congress 2000, Lausanne, + Switzerland, 2000}, + year = 2000, + editor = {Deville, M. and Owens, R.}, + note = {{D}ocument Sessions/118-1} +} + +@TechReport{Ban00mt, + author = {Bangerth, W.}, + title = {Multi-threading support in {deal.II}}, + institution = SFB, + year = 2000, + type = {{P}reprint}, + number = {2000-11}, + month = apr +} + +@InProceedings{Ban00w, + author = {Bangerth, W.}, + title = {Mesh Adaptivity and Error Control for a Finite Element + Approximation of the Elastic Wave + Equation}, + booktitle = {Proceedings of the Fifth International Conference on Mathematical + and Numerical Aspects of Wave Propagation (Waves2000), Santiago + de Compostela, Spain, 2000}, + pages = {725--729}, + year = 2000, + editor = {Berm\'udez, A. and G\'omez, D. and Hazard, C. and + Joly, P. and Roberts, J. E.}, + publisher = {SIAM} +} + +@PhdThesis{Ban02, + author = {Bangerth, W.}, + title = {Adaptive Finite Element Methods for the Identification + of Distributed Parameters in Partial Differential + Equations}, + school = {University of Heidelberg}, + year = 2002 +} + +@Article{Ban03cuj, + author = {Bangerth, W.}, + title = {Starting threads in a {C}++ compatible fashion}, + journal = {C/C++ Users Journal}, + year = 2003, + month = Oct, + pages = {21--24} +} + + +@TechReport{Ban03ip1, + author = {Bangerth, W.}, + title = {A framework for the adaptive finite element solution of + large inverse problems. {I}. {B}asic techniques}, + institution = {Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin}, + year = 2004, + number = {2004-39} +} + + +@TechReport{Ban04, + author = {Bangerth, W.}, + title = {A framework for the adaptive finite element solution of + large inverse problems. I. Basic techniques}, + institution = {Institute for Computational Engineering and Sciences, The + University of Texas at Austin}, + year = 2004, + number = {2004-39} +} + + + + +@Article{Ban08ip, + author = {Bangerth, W.}, + title = {A framework for the adaptive finite element solution of + large inverse problems}, + journal = {SIAM J. Sc. Comput.}, + year = 2008, + volume = 30, + pages = {2965--2989} +} + + + +@MastersThesis{Ban98, + author = {Bangerth, W.}, + title = {{A}daptive {F}inite-{E}lemente-{M}ethoden zur {L}{\"o}sung der + {W}ellengleichung mit {A}nwendung in der {P}hysik der {S}onne}, + school = {Institut f{\"u}r Angewandte Mathematik, Universit{\"a}t Heidelberg}, + year = 1998, + type = {Diplomarbeit} +} + + +@Misc{Bec01, + author = {Becker, R.}, + title = {Adaptive finite elements for optimal control problems}, + howpublished = {Habilitation thesis, University of Heidelberg}, + year = 2001 +} + + +@PhdThesis{Bec95, + author = {Becker, R.}, + title = {An Adaptive Finite Element Method for the + Incompressible {N}avier-{S}tokes Equations on + Time-dependent Domains}, + school = {Universit{\"a}t Heidelberg}, + year = 1995, + type = {Dissertation} +} + + +@TechReport{Bec98, + author = {Becker, R.}, + title = {Weighted error estimators for finite element approximations of the + incompressible {N}avier-{S}tokes equations}, + institution = {SFB 359, Universit{\"a}t Heidelberg}, + year = 1998, + type = {Preprint}, + number = {98-20} +} + + + +@Article{Bel05, + author = {Bell, W.}, + title = {Good prospects}, + journal = {Access, the quarterly journal of NCSA}, + year = 2005, + volume = 18, + number = 1, + pages = {1--4}, + note = {\\This article also appeared in the \textit{GRIDSTART + Business Newsletter}, March 2005, pp. 6-8, as well + as \textit{GRID + today}, edition of March 28, 2005.} +} + + + +@InCollection{Boc81, + author = {Bock, H. 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L. and Chow, S. + and Bangerth, W.}, + title = {Modeling error and constitutive relations in simulation + of flow and transport}, + journal = {International Journal for Numerical Methods in Fluids}, + year = 2004, + volume = 46, + pages = {1211--1236} +} + + +@Article{CKPS01, + author = {Cockburn, B. and Kanschat, G. and Perugia, I. and + Sch{\"o}tzau, D.}, + title = {Superconvergence of the Local Discontinuous {G}alerkin + Method for Elliptic Problems on Cartesian Grids}, + journal = {SIAM J. Numer. Anal.}, + year = 2001, + volume = 39, + number = 1, + pages = {264--285} +} + + +@article{CKSS, + author = {Cockburn, B. and Kanschat, G. and Sch{\"o}tzau, D. and Schwab, C.}, + title = {Local discontinuous {G}alerkin methods for the {S}tokes + system}, + journal = {SIAM Journal on Numerical Analysis}, + volume = {40}, + number = {1}, + pages = {319-343}, + year = {2002}, + doi = {10.1137/S0036142900380121}, + URL = { https://doi.org/10.1137/S0036142900380121}, + eprint = { https://doi.org/10.1137/S0036142900380121} +} + + + +@Inbook{DBS01, + author = {Diehl, M. and Bock, H. G. and Schl{\"o}der, J. P.}, + editor={Di Pillo, G. and Murli, A.}, + title={Newton-Type Methods for the Approximate Solution of Nonlinear Programming Problems in Real-Time}, + bookTitle={High Performance Algorithms and Software for Nonlinear Optimization}, + year={2003}, + publisher={Springer US}, + address={Boston, MA}, + pages={177--200}, + abstract={An efficient numerical method for the real-time solution of optimal control problems in optimal feedback control is presented, which is based on the direct multiple shooting method, and the contractivity of this real-time iteration scheme is proven.}, + isbn={978-1-4613-0241-4}, + doi={10.1007/978-1-4613-0241-4_8}, + url={https://doi.org/10.1007/978-1-4613-0241-4_8} +} + + +@Manual{DEAL, + title = {{deal.II} Homepage}, + author = {Bangerth, W. and Kanschat, G.}, + address = {{{http://gaia.iwr.uni-heidelberg.de/\~{}deal/}}} +} + + + + +@PhdThesis{Die01, + author = {Dieses, A.}, + title = {Numerical Methods for Optimization Problems in Water Flow and Reactive Solute Transport Processes of Xenobiotics in Soils}, + school = {University of Heidelberg}, + year = 2001, + number = {SFB Preprint 2001-07}, + note = {Ph.D. Thesis}, + url = {http://www.ub.uni-heidelberg.de/archiv/1431}, + doi = {10.11588/heidok.00001431} +} + + + +@Article{FK97, + author = {F{\"u}hrer, C. and Kanschat, G.}, + title = {A Posteriori Error Control in Radiative Transfer}, + journal = {Computing}, + year = {1997}, + volume = {58}, + number = {4}, + pages = {317--334} +} + + +@Article{FR96, + author = {F{\"u}hrer, C. and Rannacher, R.}, + title = {Error Analysis for the Finite Element Approximation + of a Radiative Transfer Model}, + journal = {M$^2$AN}, + year = {1996}, + key = {FR94}, + volume = {30}, + number = {6}, + pages = {743--761} +} + + +@Article{FR97, + author = {F{\"u}hrer, C. and Rannacher, R.}, + title = {An adaptive streamline--diffusion finite element method for hyperbolic + conservation laws}, + journal = EastWest, + year = 1997, + volume = 5, + number = 3, + pages = {145--162} +} + + +@MastersThesis{Fuh93, + author = {F{\"u}hrer, C.}, + title = {{F}inite--{E}lemente--{D}is\-kre\-ti\-sie\-run\-gen + der {2D}--{S}trah\-lungs\-trans\-port\-gleich\-ung}, + school = {Universit{\"a}t Heidelberg}, + year = 1993, + type = {Diplomarbeit} +} + + + + +@PhdThesis{Fuh97, + author = {F{\"u}hrer, C.}, + title = {Adaptive Error Control for Hyperbolic Problems}, + school = IAM, + year = 1997, + type = {Dissertation} +} + +@Article{GK, + author = {Gopalakrishnan, J. and Kanschat, G.}, + title = {A Multilevel Discontinuous {G}alerkin Method}, + journal = {Numer. Math}, + year = {2003}, + volume = 95, + pages = {527-550}, + url = {https://doi.org/10.1007/s002110200392} +} + +@Article{hartmann:houston:2002:conservation-laws, + author = {Hartmann, R. and Houston, P.}, + title = {Adaptive Discontinuous {G}alerkin Finite Element Methods + for Nonlinear Hyperbolic Conservation Laws}, + journal = {SIAM J. Sci. Comput.}, + year = 2002, + volume = 24, + pages = {979--1004} +} + +@InProceedings{houston:hartmann:2001, + author = {Houston, P. and Hartmann, R.}, + title = {Goal--Oriented A Posteriori Error Estimation for Compressible Fluid Flows}, + booktitle = {Proceedings of ENUMATH 2001}, + note = {Submitted}, + year = 2001 +} + +@Article{hartmann:houston:2002:compressible-euler, + author = {Hartmann, R. and Houston, P.}, + title = {Adaptive Discontinuous {G}alerkin Finite Element Methods for the Compressible {E}uler Equations}, + journal = {J. Comput. Phys.}, + year = 2002, + volume = 183, + pages = {508--532} +} + +@InProceedings{HH02a, + author = {Hartmann, R. and Houston, P.}, + editor={Hou, T. Y. and Tadmor, E.}, + title={Goal-Oriented A Posteriori Error Estimation for Multiple Target Functionals}, + booktitle={Hyperbolic Problems: Theory, Numerics, Applications}, + year={2003}, + publisher={Springer Berlin Heidelberg}, + address={Berlin, Heidelberg}, + pages={579--588}, + abstract={In many applications the quantities of interest are a series of target functionals of the solution to the governing system of partial differential equations rather than the solution itself. For example, in the field of aerodynamics, examples include the drag and lift coefficients of an airfoil immersed into a fluid, the pressure difference between the leading and trailing edges of the airfoil and point evaluations of the density or pressure on the profile of the airfoil. While traditionally these quantities are measured in wind tunnel experiments, nowadays these experiments are increasingly replaced by numerical simulations aiming to predict these quantities to a high level of accuracy.}, + isbn={978-3-642-55711-8} +} + + +@Misc{HH02b, + author = {Hartmann, R. and Houston, P.}, + title = {A posteriori error estimation for nonlinear hyperbolic conservation +laws involving discontinuous solutions}, + note = {In preparation} +} + +@Article{HH06, + author = {Hartmann, R. and Houston, P.}, + title = {Symmetric Interior Penalty {DG} Methods for the Compressible {N}avier-{S}tokes Equations {II}: Goal-Oriented A Posteriori Error Estimation}, + journal = {Int. J. Numer. Anal. Model.}, + year = 2006, + volume = 3, + pages = {141--162} +} + +@InProceedings{HHS01, + author = {Houston, P. and Hartmann, R. and S{\"u}li, A.}, + title = {Adaptive Discontinuous {G}alerkin Finite Element Methods for compressible Fluid Flows.}, + booktitle = {Numerical methods for Fluid Dynamics VII, ICFD}, + pages = {347--353}, + year = 2001, + editor = {Baines, M.} +} + +@Article{HPJRBS06, + author = {Hwang, K. and Pan, T. and Joshi, A. and + Rasmussen, J. C. and Bangerth, W. and Sevick-Muraca, E. M.}, + title = {Influence of excitation light rejection on + forward model mismatch in optical + tomography}, + journal = {Phys. Med. Biol.}, + year = 2006, + volume = 51, + number = 22, + pages = {5889--5902} +} + +@Article{HR00a, + author = {Hujeirat, A. and Rannacher, R.}, + title = {Towards implicit methods in computational astrophysics}, + journal = {New Astronomy Review}, + year = {2000}, + OPTvolume = {}, + OPTnumber = {}, + OPTpages = {}, + OPTmonth = {}, + note = {to appear}, + OPTannote = {} +} + + +@Inbook{HR00b, + author= {Rannacher, Rolf and Heuveline, Vincent}, + editor= {J{\"a}ger, Willi and Krebs, Hans-Joachim}, + title = {A Numerical Tool for Flow Simulation in a Wankel Motor}, + bookTitle= {Mathematics --- Key Technology for the Future: Joint Projects between Universities and Industry}, + year= {2003}, + publisher= {Springer Berlin Heidelberg}, + address= {Berlin, Heidelberg}, + pages= {33--42}, + abstract= {We describe the main steps in the development of a new numerical tool for simulating gas flow and heat transfer in a rotary engine (``Wankel motor''). Our approach comprises a 2D/3D grid generator for the Wankel motor geometry, an implicit finite element discretization for coping with the stiff pressure-velocity coupling and robust multigrid solvers on strongly distorded meshes. These components are implemented within a new FE-software package named Hi-Flow++ which is presently under development.}, + isbn= {978-3-642-55753-8}, + doi= {10.1007/978-3-642-55753-8_3}, + url= {https://doi.org/10.1007/978-3-642-55753-8_3} +} + + +@Article{HR82, + author = {Heywood, J. G. and Rannacher, R.}, + title = {Finite Element Approximation of the Nonstationary {N}avier-{S}tokes + Problem. {I}. {R}egularity of Solutions and Second-Order Error + Estimates for Spatial Discretization}, + journal = {SIAM J. Numer. Anal.}, + year = {1982}, + volume = {19}, + pages = {275--311} +} + +@Article{HR98, + author = {Hujeirat, A. and Rannacher, R.}, + title = {A Method for Computing Compressible, Highly + Stratified Flows in Astrophysics Based on Operator + Splitting}, + journal = {Int. J. Num. Meth. Fluids}, + year = 1998, + volume = 28, + pages = {1--22} +} + + +@Article{HR99, + author = {Hebeker, F. -K. and Rannacher, R.}, + title = {An adaptive finite element method for unsteady convection--dominated flows + with stiff source terms}, + journal = {SIAM J. Sci. Comp.}, + year = {1999}, + volume = {21}, + pages = {799--818}, +} + +@Misc{HRS98, + author = {Houston, P. and Rannacher, R. and S{\"u}li, E.}, + title = {Adaptive finite + element methods for stationary conservation laws}, + OPThowpublished = {}, + OPTmonth = {}, + year = {1998}, + note = {Preprint in prep.}, + OPTannote = {} +} + + +@Article{HRS99, + author = {Houston, P. and Rannacher, R. and S{\"u}li, E.}, + title = {A posteriori error analysis for stabilised finite + element approximations of transport problems}, + journal = {Comput. Meth. Appl. Mech. Engrg.}, + year = {2000}, + volume = {190}, + number = {11-12}, + pages = {1483-1508}, +} + + +@Article{HRT96, + author = {Heywood, J. and Rannacher, R. and Turek, S.}, + title = {Artificial boundaries and Flux and Pressure + Conditions for the Incompressible {N}avier-{S}tokes + equations}, + journal = {Int. J. Comp. Fl. Mech.}, + year = 1996, + volume = 22, + pages = {325--352} +} + + +@InProceedings{Har00a, + author = {Hartmann, R.}, + title = {Adaptive {FE} {M}ethods for {C}onservation {E}quations}, + booktitle = {Hyperbolic Problems: theory, numerics, applications: eighth international conference in {M}agdeburg, February, March 2000}, + year = 2001, + editor = {Freist{\"u}hler, H. and Warnecke, G.}, + volume = 2, + series = {International series of numerical mathematics; Vol. 141}, + publisher = {Birkh{\"a}user, Basel}, + pages = {495--503} +} + +@TechReport{Har00b, + author = {Hartmann, R.}, + title = {A comparison of adaptive {SDFEM} and {DG}(r) method for linear + transport problems.}, + institution = {Institut f{\"u}r Angewandte Mathematik, Universit{\"a}t + Heidelberg}, + year = 2000, + note = {In preparation} +} + +@PhdThesis{Har02, + author = {Hartmann, R.}, + title = {Adaptive Finite Element Methods for the Compressible {E}uler Equations}, + school = {University of Heidelberg}, + year = 2002 +} + +@Article{Har06, + author = {Hartmann, R.}, + title = {Adaptive discontinuous {G}alerkin methods with shock-capturing for the compressible {N}avier-{S}tokes equations}, + journal = {International Journal for Numerical Methods in Fluids}, + volume = {51}, + number = {9-10}, + pages = {1131-1156}, + keywords = {finite element methods, discontinuous Galerkin methods, compressible Navier-Stokes equations, shock-capturing}, + doi = {10.1002/fld.1134}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.1134}, + eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.1134}, + abstract = {Abstract We present the Interior Penalty discontinuous Galerkin method for the compressible Navier-Stokes equations. Shock-capturing is used to reduce over-shoots at discontinuities and sharp gradients. This stabilization introduces artificial viscosity at places of large local residuals, but preserves conservation and Galerkin orthogonality of the DG method. Based on this discretization we derive a posteriori error estimates for the error measured in terms of arbitrary target functionals, like, e.g. the drag and lift coefficients of an airfoil immersed in a viscous or inviscid fluid. The performance of the nonlinear solution process, the a posteriori error estimation and an adaptive mesh refinement specially tailored for the accurate computation of the force coefficients are demonstrated for supersonic laminar flows around the NACA0012 airfoil.}, + year = {2006} + } + +@MastersThesis{Har98, + author = {Hartmann, R.}, + title = {A posteriori {F}ehlersch{\"a}tzung und adaptive {S}chrittweiten- und + {O}rtsgittersteuerung bei {G}alerkin-{V}erfahren f{\"u}r die + {W}{\"a}rmeleitungsgleichung}, + school = {Institut f{\"u}r Angewandte Mathematik, Universit{\"a}t Heidelberg}, + year = 1998, + type = {Diplomarbeit} +} + +@Article{JBHRS06a, + author = {Joshi, A. and Bangerth, W. and Hwang, K. and Rasmussen, J. C. + and Sevick-Muraca, E. M.}, + title = {Plane wave fluorescence tomography with adaptive finite elements}, + journal = {Optics Letters}, + year = 2006, + volume = 31, + pages = {193--195} +} + +@Article{JBHRS06b, + author = {Joshi, A. and Bangerth, W. and Hwang, K. and Rasmussen, J. C. + and Sevick-Muraca, E. M.}, + title = {Fully adaptive {FEM} based fluorescence optical + tomography from time-dependent measurements with area + illumination and detection}, + journal = {Med. Phys.}, + year = 2006, + volume = 33, + number = 5, + pages = {1299--1310} +} + + +@Article{JBS04, + author = {Joshi, A. and Bangerth, W. and Sevick-Muraca, E. M.}, + title = {Adaptive finite element modeling of optical + fluorescence-enhanced tomography}, + journal = {Optics Express}, + year = 2004, + volume = 12, + number = 22, + pages = {5402--5417}, + month = nov +} + + +@InProceedings{JBS06, + author = {Joshi, A. and Bangerth, W. and Sevick-Muraca, E. M.}, + title = {Non-contact fluorescence optical tomography with scanning + area illumination}, + booktitle = {Proceedings of the IEEE International Symposium on + Biomedical Imaging, Arlington, VA, 2006}, + pages = {582--585}, + year = 2006, + publisher = {IEEE} +} + + +@Article{JBS06a, + author = {Joshi, A. and Bangerth, W. and Sevick-Muraca, E. M.}, + title = {Non-contact fluorescence + optical tomography with scanning patterned illumination}, + journal = {Optics Express}, + year = 2006, + volume = 14, + pages = {6516--6534} +} + + +@InProceedings{JBSWS07, + author = {Joshi, A. and Bangerth, W. and Sharma, R. and + Wang, W. and Sevick-Muraca, E. M.}, + title = {Molecular tomographic imaging of lymph nodes with {NIR} + fluorescence}, + booktitle = {Proceedings of the IEEE International Symposium on + Biomedical Imaging, Arlington, VA, 2007}, + pages = {564--567}, + year = 2007, + publisher = {IEEE} +} + + +@InProceedings{JBTS04, + author = {Joshi A. and + Bangerth, W. and Thompson, A. B. and Sevick-Muraca, E. M.}, + title = {Adaptive finite element methods for + fluorescence enhanced frequency domain optical + tomography: Forward imaging problem}, + booktitle={2004 2nd IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE Cat No. 04EX821)}, + year={2004}, + volume={}, + number={}, + pages={1103-1106 Vol. 2} +} + + +@Article{JBTS05, + author = {Joshi, A. and Bangerth, W. and Thompson, A. B. and + Sevick-Muraca, E. M.}, + title = {Experimental fluorescence optical tomography using + adaptive finite elements and planar illumination with + modulated excitation light}, + journal = {Progr. Biomed. Optics Imag.}, + year = 2005, + volume = 6, + pages = {351--358} +} + + +@Article{JRB95, + author = {Johnson, C. and Rannacher. R. and Boman, M.}, + title = {Numerics and Hydrodynamic Stability: Towards Error Control + in Computational Fluid Dynamics}, + journal = {SIAM J. Numer. Anal.}, + year = {1995}, + volume = {32}, + pages = {1058--1079} +} + + +@InProceedings{JTSB04, + author = {Joshi, A. and Thompson, A. B. and Sevick-Muraca, E. M. + and Bangerth, W.}, + title = {Adaptive finite element methods for forward modeling in + fluorescence enhanced frequency domain optical tomography}, + booktitle = {Proceedings of the 2004 OSA Biomedical Topical Meetings}, + year = 2004 +} + + +@Article{KBGWSSPCSK05, + author = {Klie, H. and Bangerth, W. and Gai, X. and + Wheeler, M. F. and Stoffa, P. L. and Sen, M. and + Parashar, M. and Catalyurek, U. and Saltz, J. and + Kurc, T.}, + title = {Models, methods and middleware for {G}rid-enabled + multiphysics oil reservoir management}, + year = {2006}, + month = {12}, + pages = {349-370}, + volume = {22}, + journal = {Engineering with Computers}, + doi = {10.1007/s00366-006-0035-9} +} + + +@InProceedings{KBWPM04, + author = {Klie, H. and Bangerth, W. and Wheeler, M. + and Parashar, M. and Matossian, V.}, + title = {Parallel well location optimization using stochastic + algorithms on the Grid computational framework}, + booktitle = {Proceedings of the 9th European Conference on the + Mathematics of Oil Recovery (ECMOR IX), Cannes, France}, + year = 2004 +} + + +@TechReport{KR98, + author = {Kanschat, G. and Rannacher, R.}, + title = {A posteriori error analysis for the dual-mixed discontinuous finite + element {G}alerkin approximation of transport-dominated advection-diffusion + problem}, + institution = SFB, + year = {1998}, + OPTkey = {}, + type = {Preprint}, + OPTnumber = {}, + OPTaddress = {}, + OPTmonth = {}, + note = {in prep.}, + OPTannote = {} +} + + +@InProceedings{KS00dgm, + author = {Kanschat, G. and Suttmeier, F. -T.}, + title = {A Posteriori Error Estimates in the Case of Insufficient + Regularity of the Discrete Space}, + booktitle = {Discontinuous {G}alerkin Methods: + Theory, Computation and Applications}, + pages = {349--354}, + year = 2000, + editor = {Cockburn, B. and Karniadakis, G. and Shu, C. -W.}, + volume = 11, + series = LNCSE, + publisher = {Springer} +} + +@Unpublished{kanschat:suttmeier:1992, + author = {Kanschat, G. and Suttmeier, F. T.}, + title = {{D}atenstrukturen f{\"u}r die {M}ethode der finiten {E}lemente}, + note = {unpublished, Bonn-Venusberg}, + OPTkey = {}, + OPTmonth = {}, + year = {1992}, + OPTannote = {} +} + +@Article{KS99c, + author = {Kanschat, G. and Suttmeier, F. -T.}, + title = {A Posteriori Error Estimates for Nonconforming + Finite Element Schemes}, + journal = {Calcolo}, + year = 1999, + volume = 36, + number = 3, + pages = {129--141} +} + + + +@InProceedings{Kan00ima, + author = {Kanschat, G.}, + title = {Solution of Multi-Dimensional Radiative Transfer + Problems on Parallel Computers}, + booktitle = {Parallel Solution of Partial Differential Equations}, + pages = {85--96}, + year = 2000, + editor = {Bj{\o}rstad, P. and Luskin, M.}, + volume = 120, + series = {IMA Volumes in Mathematics and its Applications}, + address = {New York}, + publisher = {Springer}, +} + + + +@InProceedings{Kan95, + author = {Kanschat, G.}, + title = {Parallel Adaptive Algorithms for Radiative Transfer + Problems}, + booktitle = {Parallel Programming and Applications}, + organization = {ZEUS}, + year = 1995, + editor = {Fritzson, P. and Finmo, L.}, + publisher = {{IOS} {P}ress}, + address = {Amsterdam}, + pages = {238--243}, + volume = 45, + series = {Transputer and OCCAM Engineering Series} +} + +@PhdThesis{Kan96, + author = {Kanschat, G.}, + title = {Parallel and Adaptive {G}alerkin Methods for Radiative + Transfer Problems}, + school = {Universit{\"a}t Heidelberg}, + year = 1996, + type = {Dissertation} +} + + + +@InProceedings{Kan97i, + author = {Kanschat G.}, + title = {New Algorithms for Radiative Transfer in Accretion + Disks and Surroundings}, + booktitle = {IAU Colloquium 163: Accretion Phenomena and Related + Outflows}, + year = {1997}, + editor = {Wickramasinghe, D. T. and Bicknell, G. V. and + Ferrario, L.}, + publisher = {Astronomical Society of the Pacific}, + address = {San Francisco, California}, + pages = {736-737} +} + +@InProceedings{Kan97m, + author = {Kanschat, G.}, + title = {Efficient and Reliable Solution of Multi-Dimensional + Radiative Transfer Problems}, + booktitle = {Multiscale Phenomena and Their Simulation}, + year = 1997, + editor = {Karsch, F. and Monien, B. and Satz, H.}, + publisher = {World Scientific}, + address = {Singapore}, + pages = {245--249} +} + +@Article{Kan98e, + author = {Kanschat, G.}, + title = {A robust finite element discretization for + radiative transfer problems with scattering}, + journal = EastWest, + year = 1998, + volume = 6, + number = 4, + pages = {265--272} +} + + +@InProceedings{Kan99f, + author = {Kanschat, G.}, + title = {Parallel Computation of Multi-dimensional Neutron + and Photon Transport in Inhomogeneous Media}, + booktitle = {High Performance Scientific and Engineering + Computing}, + pages = {431--440}, + year = 1999, + editor = {Bungartz, H.-J. and Durst, F. and Zenger, Chr.}, + volume = 8, + series = LNCSE, + publisher = {Springer} +} + +@Article{Kan04, + author = {Kanschat, G.}, + title = {Multilevel methods for discontinuous {G}alerkin {FEM} on locally refined meshes}, + number = {28}, + pages = {2437--2445}, + volume = {82}, + journal = {Computers \& structures}, + publisher = {Elsevier}, + year = {2004}, +} + +@Article{LR81, + author = {Luskin, M. and Rannacher, R.}, + title = {On the Smoothing Property of the {G}alerkin Method for + Parabolic Problems}, + journal = {SIAM J. Numer. Anal.}, + volume = 19, + year = 1981, + pages = {93--113} +} + +@Article{LR82, + author = {Luskin, M. and Rannacher, R.}, + title = {On the Smoothing Property of the {C}rank-{N}icolson + Scheme}, + journal = {Applic. Anal.}, + volume = 14, + year = 1982, + pages = {117--135} +} + +@InProceedings{MPRT95, + author = {M{\"u}ller, S. and Prohl, A. and Rannacher, R. and Turek, S.}, + title = {Implicit time-discretization of the nonstationary incompressible + {N}avier-{S}tokes equations}, + booktitle = {Fast Solvers for Flow Problems, Proceedings of the tenth + GAMM-Seminar, Kiel January 14--16, 1994}, + editor = {Hackbusch, W. and Wittum, G.}, + year = {1994}, + publisher = {F. Vieweg \& Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden} +} + +@Article{MV07, + author = {Meidner, D. and Vexler. B.}, + title = {Adaptive Space-Time Finite Element Methods for Parabolic + Optimization Problems}, + journal = {SIAM J. Contr. Optim.}, + year = 2007, + volume = 46, + pages = {116--142}} + + + +@Article{PKCKBMSW05, + author = {Parashar, M. and Klie, H. and Catalyurek, U. + and Kurc, T. and Bangerth, W. and + Matossian, V. and Saltz, J. and Wheeler, M. F.}, + title = {Application of Grid-enabled Technologies for Solving + Optimization Problems in Data-Driven Reservoir Studies}, + journal = {Future Generation Computer Systems}, + year = {2005}, + volume = {21}, + pages = {19--26} +} + + +@InProceedings{PMBKRKCSW05, + author = {Parashar, M. and Matossian, V. and Bangerth, W. + and Klie, H. and Rutt, B. and Kurc, T. and + Catalyurek, U. and Saltz, J. and Wheeler, M. F.}, + title = {Towards dynamic data-driven optimization of oil well + placement}, + booktitle = {Computational Science -- ICCS 2005: 5th International + Conference, Atlanta, GA, USA, May 22-25, 2005. + Part II}, + pages = {656--663}, + year = 2005, + editor = {Sunderam, V. S. and van Albada, G. D. and + Sloot, P. M. A. and et al.} +} + + +@InCollection{RS02, + author = {Rannacher, R. and Suttmeier, F.-T.}, + title = {Error estimation and adaptive mesh design for FE models in elasto-plasticity}, + booktitle = {Error-Controlled Adaptive FEMs in Solid Mechanics}, + publisher = {John Wiley}, + year = 2002 +} + + + +@Article{RS97, + author = {Rannacher, R. and F.-T. Suttmeier, F.-T.}, + title = {A Feed-Back Approach to Error Control in Finite + Element Methods: Application to Linear Elasticity}, + journal = {Comp. Mech.}, + year = 1997, + volume = 19, + number = 5, + pages = {434--446} +} + + +@InProceedings{RS98b, + author = {Rannacher, R. and Suttmeier, F.-T.}, + title = {An adaptive finite element method for problems in perfect plasticity}, + booktitle = {GAMM-Conference 1998, Bremen, April 6-9, 1998}, + OPTcrossref = {}, + OPTkey = {}, + OPTpages = {}, + year = {1998}, + OPTeditor = {}, + OPTvolume = {}, + OPTnumber = {}, + OPTseries = {}, + OPTaddress = {}, + OPTmonth = {}, + organization = {ZAMM}, + OPTpublisher = {}, + note = {to appear}, + OPTannote = {} +} + + +@Article{RS98c, + author = {Rannacher, R. and Suttmeier. F.-T.}, + title = {A Posteriori Error Control in Finite Element Methods + Via Duality Techniques: Application to Perfect + Plasticity}, + journal = {Comp. Mech.}, + year = {1998}, + volume = 21, + number = 2, + pages = {123--133} +} + +@InProceedings{RS98p, + author = {Rannacher, R. and Suttmeier, F.-T.}, + title = {A Posteriori Error estimation and Mesh Adaptation in + Elasticity and Elasto-Plasticity}, + booktitle = {Advances in Adaptive Computational Methods in + Mechanics}, + OPTcrossref = {}, + OPTkey = {}, + editor = {Ladev\`eze, P. and Oden, J. T.}, + volume = {176}, + OPTnumber = {}, + OPTseries = {}, + year = {1998}, + OPTorganization ={}, + publisher = {Elsevier}, + address = {Amsterdam}, + OPTmonth = {}, + pages = {275--292}, + OPTnote = {}, + OPTannote = {} +} + +@Article{RS99, + author = {Rannacher, R. and Suttmeier, F.-T.}, + title = {A Posteriori Error Control and Mesh Adaptation + for Finite Element Models in + Elasticity and Elasto-Plasticity}, + journal = {Comput. Methods Appl. Mech. Engrg.}, + year = 1999, + pages = {333--361} +} + +@Article{RSWODW96, + author = {Rannacher, R. and Segatz, J. and Wichmann, J. and + Orlemann, C. and Dreier, T. and Wolfrum, J.}, + title = {Detailed numerical simulations in flow reactors -- + A new approach in measuring absolute rate constants}, + journal = {J. Phys. Chem.}, + year = 1996, + volume = 22, + pages = {9323-9333} +} + +@Article{RT92, + author = {Rannacher, R. and Turek, S.}, + title = {Simple nonconforming Quadrilateral {S}tokes Element}, + journal = {Num. Meth. PDE}, + year = 1992, + volume = 8, + number = 2, + pages = {97--111}, + month = mar +} + + + +@InProceedings{RZ94, + author = {Rannacher, R. and Zhou, G.}, + title = {Mesh adaptation via a predictor-corrector strategy in the +streamline diffusion method for nonstationary hyperbolic systems}, + booktitle = {Proceedings Workshop Adaptive Methods}, + pages = {236--250}, + year = 1994, + editor = {Hackbusch, W. and Wittum, G.}, + volume = 46, + series = {NNFM}, + publisher = {Vieweg} +} + + +@TechReport{RZ97, + author = {Rannacher, R. and Zhou, G.}, + title = {Local {$L^2$}-error analysis and + superconvergence of the streamline-diffusion finite element method for stationary + convection--diffusion problems}, + institution = SFB, + year = {1997}, + OPTkey = {}, + OPTtype = {}, + OPTnumber = {}, + OPTaddress = {}, + OPTmonth = {}, + OPTannote = {} +} + + +@InProceedings{Ran00a, + author = {Rannacher, R.}, + title = {The dual-weighted-residual method for error control and + mesh adaptation in finite element methods}, + booktitle = {Proc. MAFELAP 1999}, + pages = {97--116}, + year = 2000, + editor = {Whiteman, J. R.}, + publisher = {Elsevier, Amsterdam} +} + +@Article{Ran00b, + author = {Rannacher, R.}, + title = {Adaptive {G}alerkin finite element methods for partial + differential equations}, + journal = {Special Millenium 2000 Issue of J. Comput. Appl. Math.}, + year = {2000}, + note = {to appear} +} + + +@InProceedings{Ran00c, + author = {Rannacher, R.}, + title = {Adaptive finite element discretization of optimization problems}, + booktitle = {Proc. Conf. Numer. Analysis 1999}, + year = 2000, + editor = {Griffiths, D. F. and Watson, G. A.}, + publisher = {Chapman\&Hall/ CRC, London} +} + +@InCollection{Ran00d, + author = {Rannacher, R.}, + title = {Numerical Methods for the Incompressible {N}avier-{S}tokes Equations}, + booktitle = {Fundamental Directions in Mathematical Fluid Mechanics}, + pages = {191--293}, + publisher = {Birkh{\"a}user, B.}, + year = 2000, + editor = {P. Galdi and J. Heywood and R. Rannacher} +} + + +@Article{Ran84, + author = {R. Rannacher}, + title = {Finite Element Solution of Diffusion Problems with + Irregular Data}, + journal = {Numer. Math.}, + volume = 43, + year = 1984, + pages = {309--327} +} + +@InCollection{Ran89, + author = {R. Rannacher}, + title = {Numerical analysis of nonstationary fluid flow. {A} survey}, + booktitle = {Applications of Mathematics in Industry and Technology}, + publisher = {B. G. Teubner, Stuttgart}, + year = {1989}, + editor = {Boffi, V. C. and Neunzert, H.}, + pages = {34--53} +} + + +@TechReport{Ran92, + author = {Rannacher, R.}, + title = {On the numerical Solution of the Incompressible + {N}avier--{S}tokes Equations}, + institution = {IWR, Univ. 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Engrg.}, + year = {1998}, + volume = {166}, + pages = {99--114}, +} + +@TechReport{Ran98d, + author = {Rannacher, R.}, + title = {A Posteriori Error Estimates for Dual-Mixed Finite + Element Approximations}, + year = 1998, + institution = SFB, + type = {Preprint}, + OPTnumber = {} +} + + + +@InProceedings{Ran99a, + author = {Rannacher, R.}, + title = {Adaptive finite element methods for flow problems}, + booktitle = {Proc. 88th Int. Symp. on Comput. Fluid Dynamics, Bremen, + Sept. 5-10, 1999}, + OPTcrossref = {}, + OPTkey = {}, + OPTpages = {}, + year = {1999}, + OPTeditor = {}, + OPTvolume = {}, + OPTnumber = {}, + OPTseries = {}, + OPTaddress = {}, + OPTmonth = {}, + OPTorganization = {}, + publisher = {J. Japan Society of CFD (CFD Journal)}, + note = {to appear}, + OPTannote = {} +} + + +@InProceedings{Ran99b, + author = {Rannacher, R.}, + title = {Adaptive {FEM}}, + booktitle = {Proc. CISM-Course ``Adaptive Finite Elements in +Linear and Nonlinear Solid and Structural Mechanics'' Udine, Oct. 4-8, 1999}, + OPTcrossref = {}, + OPTkey = {}, + OPTpages = {}, + year = {1999}, + OPTeditor = {}, + OPTvolume = {}, + OPTnumber = {}, + OPTseries = {}, + OPTaddress = {}, + OPTmonth = {}, + OPTorganization = {}, + OPTpublisher = {}, + OPTnote = {}, + OPTannote = {} +} + + +@InProceedings{SPSB04, + author = {Schulz, R. B. and Peter, J. and Semmler, W. + and Bangerth, W.}, + title = {Independent modeling of fluorescence excitation and + emission}, + booktitle = {Proceedings of the 2004 OSA Biomedical Topical Meetings}, + year = 2004 +} + + +@InProceedings{SSSKGBRW05, + author = {Stoffa, P. L. and Sen, M. K. and Seifoullaev, R. and + Klie, H. and Gai, X. and Bangerth, W. and + Rungamornrat, J. and Wheeler, M. 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Comp. Sci. Eng.}, + year = 1993, + volume = 5, + pages = {201--214} +} + + +@Article{Tur94, + author = {Turek, S.}, + title = {Tools for Simulating Non-Stationary Incompressible Flow via + Discretely Divergence-Free Finite Element Models}, + journal = {Int. J. Numer. 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W.}, + volume = 523, + series = {Lecture Notes in Physics}, + publisher = {Springer} +} + + +@TechReport{WMK99, + author = {Wehrse, R. and Meink{\"o}hn, E. and Kanschat, G.}, + title = {Recent Work in {H}eidelberg on the Solution of the Radiative Transfer}, + institution = SFB, + year = 1999, + type = {{P}reprint}, + number = {99--48} +} + + +@article{ZR94, + author = {Zhou, G. and Rannacher, R.}, + title = {Pointwise superconvergence of the streamline diffusion finite-element method}, + journal = {Numerical Methods for Partial Differential Equations}, + volume = {12}, + number = {1}, + pages = {123-145}, + doi = {10.1002/(SICI)1098-2426(199601)12:1<123::AID-NUM7>3.0.CO;2-U}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291098-2426%28199601%2912%3A1%3C123%3A%3AAID-NUM7%3E3.0.CO%3B2-U}, + eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/%28SICI%291098-2426%28199601%2912%3A1%3C123%3A%3AAID-NUM7%3E3.0.CO%3B2-U}, +abstract = {Abstract In this article, we analyze the local superconvergence property of the streamline-diffusion finite-element method (SDFEM) for scalar convection-diffusion problems with dominant convection. By orienting the mesh in the streamline direction and imposing a uniformity condition on the mesh, the theoretical order of pointwise convergence is increased from O(h11/8|log h|) to O(h2|log h|). Numerical tests show that this result cannot be extended to arbitrary quasi-uniform meshes.}, +year = {1996} +} + + + +@Article{ZR96, + author = {Zhou, G. and Rannacher, R.}, + title = {Pointwise Superconvergence of the Streamline + Diffusion Finite Element Method}, + journal = {Num. Meth. PDE}, + year = 1996, + key = {ZR94}, + volume = 12, + pages = {123--145} +} + +@Article{Zho97, + author = {Zhou, G.}, + title = {How Accurate is the Streamline Diffusion Method?}, + journal = {Math. Comp.}, + year = 1997, + volume = 66, + number = 217, + pages = {31--44} +} + +@Proceedings{enumath97, + title = {{ENUMATH 97}, Proceedings of the 2nd European Conference on Numerical Mathematics and Advanced Applications}, + year = 1998, + editor = {Bock, H. 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Hill and Zsuzsanna V\'ag\'o}, + title = {Discrete optimization via {SPSA}}, + booktitle = {Proceedings of the Americal Control Conference, + Arlington, VA, 2001}, + pages = {1503--1504}, + year = 2001 +} + +@InProceedings{GHV99, + author = {L. Gerencs\'er and S. D. Hill and Zsuzsanna V\'ag\'o}, + title = {Optimization over discrete sets via {SPSA}}, + booktitle = {Proceedings of the 38th Conference on Decision and Control, + Phoenix, AZ, 1999}, + pages = {1791--1795}, + year = 1999 +} + +@Article{GIN90, + author = {D. G. Gisser and D. Isaacson and J. C. Newell}, + title = {Electric current computed tomography and eigenvalues}, + journal = {SIAM J. Appl. Math.}, + year = 1990, + volume = 50, + pages = {1623--1634} +} + + +@Article{GK94, + author = {S. Gutman and M. V. 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Vexler}, + doi = {10.1088/0266-5611/24/2/025025}, + url = {https://doi.org/10.1088%2F0266-5611%2F24%2F2%2F025025}, + year = 2008, + month = mar, + publisher = {{IOP} Publishing}, + volume = {24}, + number = {2}, + pages = {025025}, + title = {Efficient computation of the Tikhonov regularization parameter by goal-oriented adaptive discretization}, + journal = {Inverse Problems}, + abstract = {Parameter identification problems for partial differential equations (PDEs) often lead to large-scale inverse problems. For their numerical solution it is necessary to repeatedly solve the forward and even the inverse problem, as it is required for determining the regularization parameter, e.g., according to the discrepancy principle in Tikhonov regularization. To reduce the computational effort, we use adaptive finite-element discretizations based on goal-oriented error estimators. This concept provides an estimate of the error in a so-called quantity of interest, which is a functional of the searched for parameter q and the PDE solution u. Based on this error estimate, the discretizations of q and u are locally refined. The crucial question for parameter identification problems is the choice of an appropriate quantity of interest. A convergence analysis of the Tikhonov regularization with the discrepancy principle on discretized spaces for q and u provides a possible answer: it shows, that in order to determine the correct regularization parameter, one has to guarantee sufficiently high accuracy in the squared residual norm-which is therefore our quantity of interest-whereas q and u themselves need not be computed precisely everywhere. This fact allows for relatively low dimensional adaptive meshes and hence for a considerable reduction of the computational effort. In this paper, we study an efficient inexact Newton algorithm for determining an optimal regularization parameter in Tikhonov regularization according to the discrepancy principle. With the help of error estimators we guide this algorithm and control the accuracy requirements for its convergence. This leads to a highly efficient method for determining the regularization parameter.} +} + + +@Article{GM78, + author = {P. E. Gill and W. Murray}, + title = {Algorithms for the solution of the nonlinear least-squares problem}, + journal = {SIAM J. Numer. Anal.}, + year = 1978, + volume = 15, + pages= {977--992} +} + +@Article{GMPS92, + author = {P. E. Gill and W. Murray and D. B. Ponceleon and M. A. Saunders}, + title = {Preconditioners for indefinite systems arising in optimization}, + journal = {SIAM J. Matrix Anal. Appl.}, + year = 1992, + volume = 13, + pages = {292--311} +} + +@Article{GRWN03, + author = {E. E. Graves and J. Ripoll and R. Weissleder and + V. Ntziachristos}, + title = {A submillimeter resolution fluorescence molecular imaging + system for small animal imaging}, + journal = {Med. Phys.}, + year = 2003, + volume = 30, + pages = {901--911} +} + +@Article{GS02, + author = {J. Guilbot and B. Smith}, + title = {4-{D} constrained depth conversion for reservoir compaction: + {A}pplication to {E}kofisk field}, + journal = {The Leading Edge}, + year = 2002, + pages = {302--308}, + month = mar +} + +@Article{GST95, + author = {M. Gockenbach and W. Symes and R. Tapia}, + title = {The dual regularization approach to seismic velocity + inversion}, + journal = {Inverse Problems}, + year = 1995, + volume = 11, + pages = {501--531} +} + + +@Article{GTRTMMGTRM00, + author = {M. Gurfinkel and A. B. Thompson and W. Ralston and T. L. Troy and A. L. Moore and T. A. Moore and J. D. Gust and D. Tatman and J. S. Reynolds and B. Muggenburg}, + title = {Pharmacokinetics of {ICG} and {HPPH}-car for the detection of normal and tumor tissue using fluorescence, near-infrared reflectance imaging: A case study}, + journal = {Photochem. and Photobiol.}, + year = 2000, + volume = 72, + pages = {94--102} +} + +@Article{GVB02, + author = {L. Gilles and C. R. Vogel and J. M. Bardsley}, + title = {Computational methods for a large-scale inverse + problem arising in atmospheric optics}, + journal = {Inverse Problems}, + year = 2002, + volume = 18, + pages = {237--252} +} + +@Article{GY98, + author = {M. Grasselli and M. Yamamoto}, + title = {Identifying a Spatial Body Force in Linear + Elastodynamics via Traction Measurements}, + journal = {SIAM J. Contr. Opt.}, + year = 1998, + volume = 36, + pages = {1190--1206} +} + + +@inproceedings{GYIC03, + AUTHOR = {Guven, M. and Yazici, B. and Intes, X. and Chance, B.}, + TITLE = {An adaptive multigrid algorithm for region of interest diffuse optical +tomography}, + BOOKTITLE = {Proceedings of the International Conference on Image Processing 2003}, + YEAR = 2003, + volume = 2, + PAGES = {823-826} +} + + +@Article{GYKGI07a, + author = {M. Guven and B. Yazici and K. Kwon and E. Giladi and X. Intes}, + title = {Effect of discretization error and adaptive mesh generation + in diffuse optical absorption imaging: {I}}, + journal = {Inverse Problems}, + year = 2007, + volume = 23, + pages = {1115--1134} +} + +@Article{GYKGI07b, + author = {M. Guven and B. Yazici and K. Kwon and E. Giladi and X. Intes}, + title = {Effect of discretization error and adaptive mesh generation + in diffuse optical absorption imaging: {II}}, + journal = {Inverse Problems}, + year = 2007, + volume = 23, + pages = {1124--1160} +} + +@Article{GZES04, + author = {A. Godavarty and C. Zhang and M. J. Eppstein and + E. M. Sevick-Muraca}, + title = {Fluorescence-enhanced optical imaging of large + phantoms using single and simulateous dual point illumination geometries}, + journal = {Med. Phys.}, + year = 2004, + volume = 31, + pages = {183--190} +} + + + + +@TechReport{Gil97, + author = {M. B. Giles}, + title = {Aerodynamic design optimisation for complex geometries using unstructured grids}, + institution = {Oxford University Computing Laboratory}, + year = 1997, + type = {Report}, + number = {97/08} +} + +@Article{Gut90, + author = {S. Gutman}, + title = {Identification of discontinuous parameters in flow + equations}, + journal = {SIAM J. Control Optimization}, + year = 1990, + volume = 28, + number = 5, + pages = {1049--1060} +} + +@Article{HA01, + author = {E. Haber and U. M. Ascher}, + title = {Preconditioned all-at-once methods for large, sparse + parameter estimation problems}, + journal = {Inverse Problems}, + year = {2001}, + volume = {17}, + pages = {1847--1864} +} + +@Article{HAO00, + author = {E. Haber and U. M. Ascher and D. Oldenburg}, + title = {On optimization techniques for solving nonlinear + inverse problems}, + journal = {Inverse Problems}, + year = 2000, + volume = 16, + pages = {1263--1280} +} + + + +@Article{HHT09, + author = {E. Haber and L. Horesh and L. Tenorio}, + title = {Numerical methods for experimental design of large-scale + ill-posed inverse problems}, + journal = {Inverse Problems}, + year = 2008, + volume = 24, + pages = {055012/1--17}} + +@InProceedings{HAS02, + author = {R. Hauge and O. J. Arntzen and H. Soleng}, + title = {Choosing objective function for conditioning on + production data}, + booktitle = {ECMOR VIII: 8th European Conference on the Mathematics + of Oil Recovery, Freiberg, Germany}, + pages = {E-47}, + year = 2002, + organization = {European Association of Geoscientists and + Engineers (EAGE)} +} + + + +@Article{HB01, + author = {A. Hielscher and S. Bartel}, + title = {Use of penalty terms in gradient-based iterative + reconstruction schemes for optical tomography}, + journal = {J. Biomed. Optics}, + year = 2001, + volume = 6, + pages = {183--192} +} + +@InProceedings{HGNKC03, + author = {G. M. Hoversten and E. Gasperikova and G. A. Newman and + J. Kauakihaua and N. Cuevas}, + title = {Magnetotelluric imaging of the {K}ilauea volcano, {H}awaii}, + booktitle = {Proceedings of the SEG International Exposition and + Seventy-Third Annual Meeting, October 2003, Dallas, Texas}, + year = 2003 +} + +@Article{hahner:hohage:2001, + author = {P. H{\"a}hner and T. Hohage}, + title = {New stability estimate for the inverse acoustic + inhomogeneous medium problem and applications}, + journal = {SIAM J. Math. Anal.}, + year = 2001, + volume = 33, + pages = {670--685} +} + +@Article{HH08, + author = {M. Hinterm{\"u}ller and M. Hinze}, + title = {A {SQP}-semi-smooth {N}ewton-type algorithm applied to control if the instantionary {N}avier-{S}tokes system subject to control constraints}, + number = {4}, + pages = {1177--1200}, + volume = {16}, + journal = {SIAM Journal on Optimization}, + publisher = {SIAM}, + year = {2006}, +} + + +@Article{HHA07, + author = {E. Haber and S. Heldmann and U. Ascher}, + title = {Adaptive finite volume methods for distributed + non-smooth parameter identification}, + journal = {Inverse Problems}, + year = 2007, + volume = 23, + pages = {1659--1676} +} + + +@Article{HIIS06, + author = {R. H. W. Hoppe and Y. Iliash and C. Iyyunni and N. H. Sweilam}, + title = {A posteriori error estimates for adaptive finite element discretizations of boundary control problems}, + journal = {J. Numer. Anal.}, + year = 2006, + volume = 14, + pages = {57--82}} + +@Article{HIK02, + author = {M. Hinterm{\"u}ller and K. Ito and K. Kunisch}, + title = {The Primal-Dual Active Set Strategy as a Semismooth {N}ewton Method}, + journal = {SIAM J. Optim.}, + year = 2002, + volume = 13, + pages = {865--888}} + + + +@Article{HKH99, + author = {A. H. Hielscher and A. D. Klose and K. M. Hanson}, + title = {Gradient Based Iterative Image Reconstruction for Time-Resolved Tomography}, + journal = {IEEE Trans. Medical Imaging}, + year = 1999, + volume = 18, + pages = 262 +} + +@Article{HLP06, + author = {R. H. W. Hoppe and C. Linsenmann and S. I. Petrova}, + title = {Primal-dual {N}ewton methods in structural optimization}, + journal = {Comput. Visual Sci.}, + year = 2006, + volume = 9, + pages = {71--87}} + + +@Article{HO00, + author = {E. Haber and D. Oldenburg}, + title = {A {GCV} based method for nonlinear ill-posed problems}, + journal = {Computational Geosciences}, + year = 2000, + volume = 4, + pages = {41--63} +} + + +@Article{HO97, + author = {E. Haber and D. Oldenburg}, + title = {Joint inversion: a structural approach}, + journal = {Inverse Problems}, + year = 1997, + volume = 13, + pages = {63--77} +} + + + +@Article{HP01, + author = {G. J. Hicks and R. G. Pratt}, + title = {Reflection waveform inversion using local descent methods: Estimating attenuation and velocity over a gas-sand deposit}, + journal = {GEOPHYSICS}, + volume = {66}, + number = {2}, + pages = {598-612}, + year = {2001}, + doi = {10.1190/1.1444951}, + URL = {https://doi.org/10.1190/1.1444951}, + eprint = {https://doi.org/10.1190/1.1444951}, + abstract = { Prestack seismic reflection data contain amplitudes, traveltimes, and moveout information; waveform inversion of such data has the potential to estimate attenuation levels, reflector depths and geometry, and background velocities. However, when inverting reflection data, strong nonlinearities can cause reflectors to be incorrectly imaged and can prevent background velocities from being updated. To successfully recover background velocities, previous authors have resorted to nonlinear, global search inversion techniques. We propose a two-step inversion procedure using local descent methods in which we perform alternate inversions for the reflectors and the background velocities. For our reflector inversion we exploit the efficiency of the back-propagation method when inverting for a large parameter set. For our background velocity inversion we use Newton inverse methods. During the background velocity inversions it is crucial to adaptively depth-stretch the model to preserve the vertical traveltimes. This reduces nonlinearity by largely decoupling the effects of the background velocities and reflectors on the data. Nonlinearity is further reduced by choosing to invert for slownesses and by inverting for a sparse parameter set which is partially defined using geological reflector picks. Applying our approach to shallow seismic data from the North Sea collected over a gas-sand deposit, we demonstrate that the proposed method is able to estimate both the geometry and internal velocity of a significant velocity structure not present in the initial model. Over successive iterations, the use of adaptive depth stretching corrects the pull-down of the base of the gas sand. Vertical background velocity gradients are also resolved. For an insignificant extra cost the acoustic attenuation parameter Q is included in the inversion scheme. The final attenuation tomogram contains realistic values of Q for the expected lithologies and for the effect of partial fluid saturation associated with a shallow bright spot. The attenuation image may also indicate the presence of fracturing. } +} + + + +@Article{HS94, + author = {B. Hofmann and O. Scherzer}, + title = {Factors influencing the ill-posedness of nonlinear problems}, + journal = {Inverse Problems}, + year = 1994, + volume = 10, + pages = {1277--1297} +} + +@Article{HTGS03, + author = {J. P Houston and A. B. Thompson and M. Gurfinkel and E. M. Sevick-Muraca}, + title = {Sensitivity and depth penetration of continuous wave versus + frequency-domain photon migration near-infrared fluorescence + contrast-enhanced diagnostic imaging}, + journal = {Photochem. and Photobiol.}, + year = 2003, + volume = 77, + pages = {420--431} +} + + +@Article{HV99, + author = {M. Heinkenschloss and L. Vicente}, + title = {An interface between optimization and application for the + numerical solution of optimal control problems}, + journal = {ACM Trans. Math. Softw.}, + year = 1999, + volume = 25, + pages = {157--190} +} + +@Article{HW05, + author = {M. Hu and L. V. Wang}, + title = {Universal back-projection algorithm for photoacoustic + computed tomography}, + journal = {Phys. Rev. E}, + year = 2005, + volume = 71, + pages = {016706/1--016706/7} +} + +@Article{Hab05, + author = {E. Haber}, + title = {Quasi-{N}ewton methods for large-scale electromagnetic inverse problems}, + journal = {Inverse Problems}, + year = 2005, + volume = 21, + pages = {305--323} +} + +@Article{Han97, + author = {M. Hanke}, + title = {Regularizing properties of a truncated {N}ewton-{CG} algorithm for + nonlinear inverse problems}, + journal = {Numer. Funct. Anal. Optimization}, + year = 1997, + volume = 18, + pages = {971--993} +} + +@PhdThesis{Hei91, + author = {M. Heinkenschloss}, + title = {{G}auss-{N}ewton Methods for Infinite Dimensional + Least Squares Problems with Norm Constraints}, + school = {University of Trier, Germany}, + year = 1991 +} + + +@Article{Hoh00, + author = {T. Hohage}, + title = {Regularization of exponentially ill-posed problems}, + journal = {Numer. Funct. Anal. Optim.}, + year = 2000, + volume = 21, + pages = {439--464} +} + + +@Article{Hoh01, + author = {T. Hohage}, + title = {On the numerical solution of a three-dimensional inverse + medium scattering problem}, + journal = {Inverse Problems}, + year = 2001, + volume = 17, + pages = {1643--1663} +} + +@Article{Hoo00, + author = {A. T. de Hoop}, + title = {Areas for exploration in electromagnetic modelling + and inversion}, + journal = {Inverse Problems}, + year = 2000, + volume = 16, + pages = {1083--1096} +} + + +@Article{IK00, + author = {K. Ito and K. Kunisch}, + title = {Optimal control of elliptic variational inequalities}, + journal = {Appl. Math. Optim.}, + year = 2000, + volume = 41, + pages = {343--364} +} + +@Article{IK90, + author = {K. Ito and K. Kunisch}, + title = {The augmented {L}agrangian method for parameter estimation in + elliptic systems}, + journal = {SIAM J. Contr. Optim.}, + year = 1990, + volume = 28, + pages = {113--136} +} + + +@Article{IK92a, + author = {K. Ito and K. Kunisch}, + title = {On the choice of the regularization parameter in nonlinear inverse problems}, + journal = {SIAM J. Optimization}, + year = 1992, + volume = 2, + pages = {376--404} +} + +@Article{IK92b, + author = {K. Ito and K. Kunisch}, + title = {Sensitivity analysis of solutions to optimization problems in {H}ilbert + spaces with applications to optimal control and estimation}, + journal = {J. Diff. Eq.}, + year = 1992, + volume = 99, + pages = {1--40} +} + +@Article{IK94, + author = {K. Ito and K. Kunisch}, + title = {On the injectivity and linearization of the coefficient-to-solution + mapping for elliptic boundary value problems}, + journal = {J. Math. Anal. Appl.}, + year = 1994, + volume = 188, + pages = {1040--1066} +} + +@Article{IK96, + author = {K. Ito and K. Kunisch}, + title = {Augmented {L}agrangian-{S}{Q}{P}-methods in {H}ilbert spaces and + application to control in the coefficients problems}, + journal = {SIAM J. Optimization}, + year = 1996, + volume = 6, + pages = {96--125} +} + + +@Article{IK97, + author = {K. Ito and K. Kunisch}, + title = {Estimation of the convection coefficient in elliptic equations}, + journal = {Inverse Problems}, + year = 1997, + volume = 13, + pages = {995--1013} +} + + + +@Article{IK99, + author = {K. Ito and K. Kunisch}, + title = {An active set strategy based on the augmented {L}agrangian + formulation for image reconstruction}, + journal = {M2AN}, + year = 1999, + volume = 33, + pages = {1--21} +} + +@Article{IKK91, + author = {K. Ito and M. Kroller and K. Kunisch}, + title = {A numerical study of an augmented {L}agrangian method for the estimation of + parameters in elliptic systems}, + journal = {SIAM J. Sci. Stat. Comput.}, + year = 1991, + volume = 12, + pages = {884--910} +} + +@Article{IR99, + author = {K. Ito and F. Reitich}, + title = {A high-order perturbation approach to profile + reconstruction: I. Perfectly conducting gratings}, + journal = {Inverse Problems}, + year = 1999, + volume = 15, + pages = {1067--1085} +} + +@Article{IY01, + author = {O. Yu. Imanuvilov and M. Yamamoto}, + title = {Global {L}ipschitz stability in an inverse hyperbolic problem + by interior observations}, + journal = {Inverse Problems}, + year = 2001, + volume = 17, + pages = {717--728} +} + + +@Article{Ike01, + author = {M. Ikehata}, + title = {On reconstruction from a partial knowledge of the + {N}eumann-to-{D}irichlet operator}, + journal = {Inverse Problems}, + year = 2001, + volume = 17, + pages = {45--51} +} + + +@Article{Isa88, + author = {V. Isakov}, + title = {On uniqueness of recovery of a discontinuous conductivity + coefficient}, + journal = {Commun. Pure Appl. Math.}, + year = 1988, + volume = 41, + pages = {865--877} +} + + +@Article{JRL00, + author = {S. L. Jacques and J. R. Roman and K. Lee}, + title = {Imaging superficial tissues with polarized light}, + journal = {Lasers in Surgical Medicine}, + year = 2000, + volume = 26, + pages = {119--129} +} + +@Article{JSS04, + author = {C. Jackson and M. K. Sen and P. L. Stoffa}, + title = {An efficient stochastic {B}ayesian approach to optimal + parameter and uncertainty estimation for climate model + predictions}, + journal = {J. Climate}, + year = 2004, + volume = 17, + pages = {2828--2841} +} + +@Article{Joh97, + author = {C. R. Johnson}, + title = {Computational and Numerical Methods for Bioelectric Field + Problems}, + journal = {Critical Reviews in BioMedical Engineering}, + year = 1997, + volume = 25, + pages = {1--81} +} + + + +@Article{Jon99, + author = {E. Jonsson}, + title = {Electrical conductivity reconstruction using nonlocal boundary conditions}, + journal = {SIAM J. Appl. Math.}, + year = 1999, + volume = 59, + pages = {1582--1598} +} + + +@article {katz:etal:2003, + author = {Katz, Richard F. and Spiegelman, Marc and Langmuir, Charles H.}, + title = {A new parameterization of hydrous mantle melting}, + journal = {Geochemistry, Geophysics, Geosystems}, + volume = {4}, + number = {9}, + doi = {10.1029/2002GC000433}, + pages = {n/a--n/a}, + year = {2003} +} + + +@Article{KCHCB03, + author = {M. A. Kupinski and E. Clarkson and J. W. Hoppin and L. Chen and H. H. Barrett}, + title = {Experimental determination of object statistics from noisy images}, + journal = {J. Opt. Soc. Amer. A}, + year = 2003, + volume = 20, + pages = {421--429} +} + + +@Article{KH09, + author = {H. K. Kim and A. H. Hielscher}, + title = {A {PDE}-constrained {SQP} algorithm for optical tomography based + on the frequency-domain equation of radiative transfer}, + journal = {Inverse Problems}, + year = 2009, + volume = 25, + pages = {015010/1--20}} + +@Article{KH03, + author = {A. D. Klose and A. H. Hielscher}, + title = {Quasi-{N}ewton methods in optical tomographic image reconstruction}, + journal = {Inverse Problems}, + year = 2003, + volume = 19, + pages = {387--409} +} + +@Article{KKBS04, + author = {S. K{\"o}rkel and E. Kostina and H. G. Bock and + J. B. Schl{\"o}der}, + title = {Numerical methods for optimal control problems in design of + robust optimal experiments for nonlinear dynamic processes}, + journal = {Opt. Meth. Softw.}, + year = 2004, + volume = 19, + pages = {327--338} +} + +@Article{KKSV00, + author = {J. P. Kaipio and V. Kohlemainen and E. Somersalo and M. Vauhkonen}, + title = {Statistical inversion and {M}onte {C}arlo sampling methods in + electrical impedance tomography}, + journal = {Inverse Problems}, + year = 2000, + volume = 16, + pages = {1487--1522} +} + +@Article{KLF97, + author = {M. V. Klibanov and T. R. Lucas and R. M. Frank}, + title = {A fast and accurate imaging algorithms in optical/diffusion tomography}, + journal = {Inverse Problems}, + year = 1997, + volume = 13, + pages = {1341--1361} +} + +@Article{KL99, + author = {M. V. Klibanov and T. R. Lucas}, + title = {Numerical solution of a parabolic inverse problem in + optical tomography using experimental data}, + journal = {SIAM J. Appl. Math.}, + year = 1999, + volume = 59, + pages = {1763--1789}} + +@InProceedings{KLR02, + author = {V. Kretz and M. Le Ravalec-Dupin and F. Roggero}, + title = {Integrating production history with 4d-seismic for + reservoir characterization}, + booktitle = {ECMOR VIII: 8th European Conference on the Mathematics + of Oil Recovery, Freiberg, Germany}, + pages = {E-60}, + year = 2002, + organization = {European Association of Geoscientists and + Engineers (EAGE)} +} + +@Article{KLSGLNPMLD03, + author = {S. Kim and Y. T. Lim and E. G. Soltesz and A. M. D. Grand and J. Lee and A. Nakayama and J. A. Parker and T. Mihaljevic and R. G. Laurence and D. M. Dor}, + title = {Near-infrared fluorescent type {II} quantum dots for sentinel lymph node mapping}, + journal = {Nat. Biotechnol.}, + year = 2003, + volume = 22, + pages = {93--97} +} + + + +@InProceedings{KLY02, + author = {K. Kunisch and W. Liu and N. Yan}, + title = {A posteriori error estimators for a model parameter + estimation problem}, + booktitle = {Proceedings of the ENUMATH 2001 conference}, + year = 2002 +} + + +@Article{KLZG97, + author = {M. Kempe and M. Larionov and D. Zaslavsky and A. Z. Genack}, + title = {Acousto-optic tomography with multiply scattered light}, + journal = {J. Opt. Soc. Am. A}, + year = 1997, + volume = 14, + pages = {1151--1158} +} + + + +@Article{KN01, + author = {S. Kindermann and A. Neubauer}, + title = {Estimation of discontinuous parameters of elliptic partial + differential equations by regularization for surface representations}, + journal = {Inverse Problems}, + year = 2001, + volume = 17, + pages = {789--903} +} + +@Article{KNH05, + author = {A. D. Klose and V. Ntziachristos and A. Hielscher}, + title = {The inverse source problem based on the radiative + transfer equation in optical molecular imaging}, + journal = {J. Comp. Phys.}, + year = 2005, + volume = 202, + pages = {323--345} +} + +@Article{KP91, + author = {K. Kunisch and G. Peichl}, + title = {Estimation of a temporally and spatially varying diffusion coefficient + in a parabolic system by an augmented {L}agrangian technique}, + journal = {Numer. Math.}, + year = 1991, + volume = 59, + pages = {473--509} +} + +@Article{KQEW86, + author = {M. W. Kissin and G. Querci della Rovere and D. Easton and G. Westbury}, + title = {Risk of lymphoedema following the treatment of breast cancer}, + journal = {Br. J. Surg.}, + year = 1986, + volume = 73, + pages = {580--584} +} + + + +@InProceedings{KQRS05, + author = {S. K{\"o}rkel and H. Qu and G. R{\"u}cker and S. Sager}, + title = {Derivative Based vs. Derivative Free Optimization Methods + for Nonlinear Optimum Experimental Design}, + booktitle = {Current Trends in High Performance Computing and Its + Applications. Proceedings of the International Conference on + High Performance Computing and Applications, August 2004, + Shanghai, China}, + pages = {339--344}, + year = 2005, + editor = {W. Zhang and W. Tong and Z. Chen and R. Glowinski}, + publisher = {Springer, Berlin Heidelberg}} + +@Article{KR01, + author = {R. Kress and W. Rundell}, + title = {Inverse scattering for shape and impedance}, + journal = {Inverse Problems}, + year = 2001, + volume = 17, + pages = {1075--1085} +} + + +@TechReport{KS01, + author = {B. Kaltenbacher and J. Sch{\"o}berl}, + title = {A Saddle Point Variational Formulation for Projection-Regularized + Parameter Identification}, + institution = {SFB F013, University of Linz}, + year = 2000, + number = {00-13} +} + +@Article{KS06, + author = {M. E. Kilmer and E. de Sturler}, + title = {Recycling Subspace Information for Diffuse + Optical Tomography}, + journal = {SIAM J. Sc. Comput.}, + year = 2006, + volume = 27, + pages = {2140--2166} +} + +@Book{KS05, + author = {J. Kaipio and E. Somersalo}, + title = {Statistical and Computational Inverse Problems}, + publisher = {Springer}, + year = 2006 +} + +@Article{KS85, + author = {C. Kravaris and J. H. Seinfeld}, + title = {Identification of parameters in distributed parameter systems + by regularization}, + journal = {SIAM J. Control Optim.}, + year = 1985, + volume = 23, + pages = {217--241} +} + +@Article{kunisch:sachs:1992, + author = {K. Kunisch and E. W. 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Kaltenbacher}, + title = {A projection-regularized {N}ewton method for nonlinear + ill-posed problems and its application to parameter + identification problems with finite element discretization}, + journal = {SIAM J. Numer. Anal.}, + year = 2000, + volume = 37, + pages = {1885--1908} +} + +@TechReport{Kal00tr03, + author = {B. Kaltenbacher}, + title = {A multi-grid method with a priori and a posteriori level choice for + the regularization of nonlinear ill-posed problems}, + institution = {SFB013, University of Linz}, + year = 2000, + number = {00-3} +} + +@Article{Kal01, + author = {B. Kaltenbacher}, + title = {On the regularization properties of a full multigrid method for + ill-posed problems}, + journal = {Inverse Problems}, + year = 2001, + volume = 17, + pages = {767--788} +} + + +@Article{Kli98, + author = {M. V. Klibanov}, + title = {Global Convexity in a Three-Dimensional Inverse Acoustic Problem}, + journal = {SIAM J. Numer. Anal.}, + year = 1998, + volume = 28, + pages = {1371--1388} +} + + + +@Article{Klo02, + author = {A. D. Klose}, + title = {Optical Tomography Using the Time-Independent Equation of +Radiative Transfer -- {P}art 2: Inverse Model}, + journal = {J. Quantitive Spectroscopy and Radiative +Transfer}, + year = 2002, + volume = 72, + pages = 715 +} + + +@Article{Kun06, + author = {L. A. Kunyansky}, + title = {Explicit inversion formulas for the spherical mean {R}adon + transform}, + doi = {10.1088/0266-5611/23/1/021}, + url = {https://doi.org/10.1088%2F0266-5611%2F23%2F1%2F021}, + year = 2007, + month = jan, + publisher = {{IOP} Publishing}, + volume = {23}, + number = {1}, + pages = {373--383}, + journal = {Inverse Problems}, + abstract = {We derive explicit formulae for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulae are important for problems of thermo- and photo-acoustic tomography. A closed-form inversion formula of a filtration-backprojection type is found for the case when the centres of the integration spheres lie on a sphere in surrounding the support of the unknown function.} +} + +@Article{LBLS99, + author = {S. L{\'e}v{\^ e}que and A. C. Boccara and M. Lebec and + H. Saint-Jalmes}, + title = {Ultrasonic tagging of photon paths in scattering media: + parallel speckle modulation processing}, + journal = {Optics Letters}, + year = 1999, + volume = 24, + pages = {181--183} +} + + + +@Article{LCU98, + author = {M. Lassas and M. Cheney and G. Uhlmann}, + title = {Uniqueness for a wave propagation inverse problem in a half space}, + journal = {Inverse Problems}, + year = 1998, + volume = 14, + pages = {679--684} +} + +@Article{LF99, + author = {D. Li and M. Fukushima}, + title = {A globally and superlinearly convergent + {G}auss-{N}ewton-based {B}{F}{G}{S} method for + symmetric nonlinear equations}, + journal = {SIAM J. Numer. 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Control Optim.}, + year = 2001, + volume = 40, + number = 1, + pages = {1--38} +} + +@Article{leveque-fort:2001, + author = {S. L{\'e}v{\^ e}que-Fort}, + title = {Three-dimensional acousto-optic imaging in + biological tissues with parallel signal processing}, + journal = {Applied Optics}, + year = 2001, + volume = 40, + pages = {1029--1036} +} + +@PhdThesis{Liu97, + author = {L. Liu}, + title = {Stability estimates for the two-dimensional inverse + conductivity problem}, + school = {Department of Mathematics, University of Rochester, New York}, + year = 1997 +} + + + + +@ARTICLE{MBCD02, + author={M. Molinari and B. H. Blott and S. J. Cox and G. J. Daniell}, + title={Optimal Imaging with Adaptive Mesh Refinement in Electrical Impedence Tomography}, + journal={Physiological Measurement}, + volume={23}, + year={2002}, + pages={121--128}, +} + +@Article{MBQL01, + author = {R. Marklein and K. Balasubramanian and + A. Qing and K. J. Langenberg}, + title = {Linear and nonlinear iterative scalar inversion of + multi-frequency multi-bistatic experimental + electromagnetic scattering data}, + journal = {Inverse Problems}, + year = 2001, + volume = 17, + pages = {1623--1634} +} + +@article{Martinec2018, + author={Martinec, Z. and Klemann, V. and van der Wal, W. and Riva, R. E. M. and Spada, G. and Sun, Y. and Melini, D. and Kachuck, S. B. and Barletta, V. and Simon, K. and A, G. and James, T. S.}, + title={A benchmark study of numerical implementations of the sea level equation in GIA modelling}, + journal=gji, + volume={215}, + number={1}, + year={2018}, + pages={389-414} +} + +@InProceedings{MC02, + author = {J. L. Maryak and D. C. Chin}, + title = {Global optimization via {SPSA}}, + booktitle = {Proceedings of the 2002 PerMIS Workshop}, + year = 2002, + editor = {E. R. Messina and A. M. Meystel}, + series = {NIST Special Publications 990} +} + +@ARTICLE{MCBD01, + author={M. Molinari and S. J. Cox and B. H. Blott and G. J. Daniell}, + title={Adaptive Mesh Refinement techniques for Electrical Impedence Tomography}, + journal={Physiological Measurement}, + volume={22}, + year={2001}, + pages={91--96}, +} + +@Article{morency:doin:2004, + title={Numerical simulations of the mantle lithosphere delamination}, + author={C. Morency and M.-P. Doin}, + journal={Journal of Geophysical Research: Solid Earth (1978--2012)}, + volume={109}, + number={B3}, + year={2004}, + publisher={Wiley Online Library} +} + + +@Article{METU98, + author = {G. D. Mahan and W. E. Engler and + J. J. Tiemann and E. Uzgiris}, + title = {Ultrasonic tagging of light: {T}heory}, + journal = {Proc. Natl. Acad. Sc.}, + year = 1998, + volume = 95, + pages = {14015-14019} +} + + + +@Article{MJ93, + author = {S. McCormick and J. 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Atlan and A. C. Boccara + and M. Gross and P. Delaye and G. Roosen}, + title = {Photorefractive detection of tagges photons in ultrasound + modulated optical tomography of thick biological tissues}, + journal = {Optics Express}, + year = 2004, + volume = 12, + pages = {5469--5474} +} + +@Article{ritsema:vanheijst:2000, + author = {J. Ritsema and H. J. van Heijst}, + title = {Seismic imaging of structural heterogeneity in Earth's mantle: Evidence for large-scale mantle flow}, + journal = {Sci. Progr.}, + year = 2000, + volume = 83, + pages = {243--259}} + +@Article{ritsema:etal:2011, + author = {J. Ritsema and A. Deuss and H. J. van Heijst and J. H. Woodhouse}, + title = {S40RTS: a degree-40 shear-velocity model for the mantle from new Rayleigh wave dispersion, teleseismic traveltime and normal-mode splitting function measurements}, + journal = {Geophysical Journal International}, + year = 2011, + volume = 184, + pages = {1223--1236}} + + +@Article{ROO05, + author = {P. S. Routh and G. A. Oldenburger and D. W. Oldenburg}, + title = {Optimal survey design using the point spread function + measure of resolution}, + journal = {Proceedings of the SEG, Houston 2005 Annual Meeting}, + year = 2005, + pages = {1033--1037}} + + +@Article{RGS03, + author = {R. Roy and A. Godavarty and E. M. Sevick-Muraca}, + title = {Fluorescence-enhanced optical tomography using referenced + measurements of heterogeneous media}, + journal = {IEEE Trans. Med. Imag.}, + year = 2003, + volume = 22, + pages = {824--836} +} + +@Article{RS99a, + author = {R. Roy and E. M. Sevick-Muraca}, + title = {Truncated {N}ewton's optimization scheme for absorption + and fluorescence optical tomography: {P}art {I} {T}heory + and formulation}, + journal = {Optics Express}, + year = 1999, + volume = 4, + pages = {353--371} +} + + +@Article{RS99b, + author = {R. Roy and E. M. Sevick-Muraca}, + title = {Truncated {N}ewton's optimization scheme for absorption + and fluorescence optical tomography: {P}art {II} + {R}econstruction from synthetic measurements}, + journal = {Optics Express}, + year = 1999, + volume = 4, + pages = {372--382} +} + + + +@Article{RTGS03, + author = {R. Roy and A. B. Thompson and A. Godavarty and E. M. Sevick-Muraca}, + title = {Penalty stroke modified barrier function method for diagnstic imaging + using area and point illumination geometries in fluorescence-enhanced + optical tomography}, + journal = {IEEE Transactions in Medical Imaging}, + year = 2003 +} + +@Article{RTGS04, + author = {R. Roy and A. B. Thompson and A. Godavarty and + E. M. Sevick-Muraca}, + title = {Tomographic fluorescence imaging in tissue phantoms: a novel + reconstruction algorithm and imaging geometry}, + journal = {IEEE Trans. Med. Imaging}, + year={2005}, + volume={24}, + number={2}, + pages={137-154} +} + + +@Article{RTMTWCSS99, + author = {J. S. Reynolds and T. L. Troy and R. H. Mayer and A. B. Thompson and D. J. Waters and K. K. Cornell and P. W. Snyder and E. M. Sevick-Muraca}, + title = {Imaging of spontaneous canine mammary tumors using fluorescent contrast agents}, + journal = {Photochem. and Photobiol.}, + year = 1999, + volume = 70, + pages = {87--94} +} + + +@Article{Rin00, + author = {W. Ring}, + title = {Structural properties of solutions to total variation + regularization problems}, + journal = {ESAIM: M2AN}, + year = 2000, + volume = 34, + pages = {799--810} +} + + +@Article{Roc93, + author = {R. T. Rockafellar}, + title = {Lagrange multipliers and optimality}, + journal = {SIAM Review}, + year = 1993, + volume = 35, + pages = {183--238} +} + + +@Article{SCSD07, + author = {M. Secanell and B. Carnes and A. Suleman and N. Djilali}, + title = {Numerical optimization of proton exchange membrane fuel + cell cathodes}, + journal = {Electrochimica Acta}, + year = 2007, + volume = 52, + pages = {2668--2682} +} + +@Article{SDS07, + author = {M. Shahram and D. L. Donoho and J. L. Stark}, + title = {Multiscale representation for data on the sphere and + applications to geopotential data}, + journal = {Proc. SPIE Ann. Meeting}, + year = 2007, + pages = {670101a1--67010a11} +} + +@Article{SDSLP95, + author = {M. K. Sen and A. Datta-Gupta and P. L. Stoffa and L. W. Lake + and G. A. Pope}, + title = {Stochastic reservoir modeling using simulated annealing and + genetic algorithms}, + journal = {SPE Formation Evaluation}, + year = 1995, + pages = {49--55}, + month = mar +} + +@Article{SEK93, + author = {O. Scherzer and H. W. Engl and K. Kunisch}, + title = {Optimal a-posteriori parameter choice for {T}ikhonov regularization + for solving nonlinear ill-posed problems}, + journal = {SIAM J. Numer. Anal.}, + year = 1993, + volume = 30, + pages = {1796--1838} +} + +@InProceedings{SERSVTPS04, + author = {R. B. Schulz and G. Echner and H. Ruehle and W. Stroh and + J. Vierling and T. Vogt and J. Peter and W. Semmler}, + title = {Development of a fully rotational non-contact fluorescence + tomographer for small animals}, + booktitle = {Proc. IEEE Micro-Imaging Conf., Puerto Rico, 2005}, + year = 2005 +} + + +@Article{SGA03, + author = {M. Schweiger and A. Gibson and S. R. Arridge}, + title = {Computational aspects of diffuse optical tomography}, + journal = {Comp. Sc. Engrg.}, + year = 2003, + volume = 5, + number = 6, + pages = {33--41} +} + + +@inproceedings{SGX04, + AUTHOR = {Son, I. Y. and Guven, M. and B. Yazici and X. Intes}, + TITLE = {A 2-level domain decomposition algorithm for inverse diffuse optical +tomography}, + BOOKTITLE = {Proceedings of the International Conference on Image Processing 2004}, + YEAR = 2004, + PAGES = {V: 3315-3318} +} + + + +@InProceedings{SJM09, + author = {D. Sale and J. Jonkman and W. Musial}, + title = {A hydrodynamic optimization method and design code for + stall-regulated hydrokinetic turbine rotors}, + booktitle = {Proceedings of the ASME 28th International Conference + on Ocean, Offshore and Arctic Engineering (OMAE2009), + May 31 -- June 5, 2009, Honolulu, Hawaii}, + pages = {OMAE2009-79513/1--6}, + year = 2009} + +@InBook{SKGHR03, + author = {Sevick-Muraca, E. M. and Kuwana, E. and Godavarty, A. and Houston, + J. P. and Thompson, A. B. and R. Roy}, + editor = {J. Vo-Dinh}, + title = {Near infrared fluorescence imaging and spectroscopy in + random media and tissues}, + chapter = 33, + publisher = {CRC Press}, + year = 2003, + series = {Biomedical Photonics Handbook} +} + + + +@Article{SLTRH97, + author = {E. M. Sevick-Muraca and G. Lopez and T. L. Troy and J. S. Reynolds and C. L. Hutchinson}, + title = {Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques}, + journal = {Photochem. and Photobiol.}, + year = 1997, + volume = 66, + pages = {55-64} +} + + + +@Article{SM82, + author = {R. Sanchez and N. J. McCormick}, + title = {Numerical evaluation of optical single-scattering properties using + multiple-scattering inverse transport methods}, + journal = {J. Quant. Spectrosc. Rad. Transfer}, + year = 1982, + volume = 28, + pages = {169--184} +} + + + +@Article{SM82b, + author = {R. Sanchez and N. J. McCormick}, + title = {A Review of Neutron Transport +Approximations}, + journal = {Nucl. Sci. Eng.}, + year = 1982, + volume = 80, + pages = 481 +} + + +@Article{SMSCZ88, + author = {Sanchez, R. and Mondot, J. and Stankovski, Z. and Cossic, A. and + Zmijarevic, I.}, + title = {{APOLLO II: A} user-oriented, portable, modular code for multigroup transport assembly calculations}, + journal = {Nucl. Sci. Eng.}, + year = 1988, + volume = 100, + pages = {352--362} +} + + +@Article{SRJS05, + author = {A. K. Sahu and R. Roy and A. Joshi and E. M. Sevick-Muraca}, + title = {Evaluation of anatomical structure and non-uniform + distribution of imaging agent in near-infrared + fluorescence-enahnced optical tomography}, + journal = {Optics Express}, + year = 2005, + volume = 13, + pages = {10182--10199} +} + +@Article{SRN03, + author = {R. B. Schulz and J. Ripoll and V. Ntziachristos}, + title = {Noncontact optical tomography of turbid media}, + journal = {Optics letters}, + year = 2003, + volume = 28, + pages = {1701--1703} +} + + +@Article{SS03, + author = {C. S. Stolk and W. W. Symes}, + title = {Smooth objective functionals for seismic velocity inversion}, + journal = {Inverse Problems}, + year = 2003, + volume = 19, + pages = {73--89} +} + +@Article{SS91, + author = {M. K. Sen and P. L. Stoffa}, + title = {Nonlinear one-dimensional seismic waveform inversion + using simulated annealing}, + journal = {Geophysics}, + year = 1991, + volume = 56, + pages = {1624--1638} +} + + + +@Article{SSKB97, + author = {P. Serra and A. F. Stanton and S. Kais and R. E. Bleil}, + title = {Comparison study of pivot methods for global optimization}, + journal = {J. Chem. Phys.}, + year = 1997, + volume = 106, + pages = {7170--7177} +} + +@Article{SST85, + author = {H. Schwetlick and W. Schellong and V. Tiller}, + title = {{G}auss-{N}ewton-like methods for nonlinear least squares with equality + constraints. {L}ocal convergence and applications to parameter estimation + in implicit models}, + journal = {Statistics}, + year = 1985, + volume = 16, + pages = {167--178} +} + + +@Article{SU03, + author = {P. Stefanov and G. Uhlmann}, + title = {Optical tomography in two dimensions}, + journal = {Meth. Appl. Anal.}, + year = 2003, + volume = 10, + pages = {1--9} +} + + +@Article{SU87, + author = {J. Sylvester and G. Uhlmann}, + title = {A global uniqueness theorem for an inverse boundary value problem}, + journal = {Ann. of Math.}, + year = 1987, + volume = 125, + pages = {153--169} +} + + + +@InProceedings{SYK06, + author = {A. Serdaroglu and B. Yazici and K. Kwon}, + title = {Optimum source design for detection of heterogeneities in + diffuse optical imaging}, + booktitle = {Optical methods for tumor treatment and detection: + {M}echanisms and techniques in photodynamic therapy {XV}}, + pages = {61391A/1--11}, + year = 2006, + editor = {D. Kessel}, + volume = 6139, + series = {Proc. of SPIE}} + +@Article{SW04, + author = {S. Sakad{\v z}i{\'c} and L. V. Wang}, + title = {High-resolution ultrasound-modulated optical tomography + in biological tissues}, + journal = {Optics Letters}, + year = 2004, + volume = 29, + pages = {2770--2772} +} + + +@Article{SWP95, + author = {Z.-M. Song and P. R. Williamson and R. Gerhard Pratt}, + title = {Frequency-domain acoustic-wave modelling and inversion of + crosshole data: {II}---{I}nversion method, synthetic + experiments adn real-data results}, + journal = {Geophysics}, + year = 1995, + volume = 60, + pages = {796--809} +} + +@Article{Sab01, + author = {P. Sabatier}, + title = {Should we study sophisticated inverse problems?}, + journal = {Inverse Problems}, + year = 2001, + volume = 17, + pages = {1219--1223} +} + +@Article{Sch92, + author = {O. Scherzer}, + title = {The use of {T}ikhonov regularization in the identification of electrical + conductivities from overdetermined boundary data}, + journal = {Result. Math.}, + year = 1992, + volume = 22, + pages = {598--618} +} + +@InCollection{schmeling:2000, + title={Partial melting and melt segregation in a convecting mantle}, + author={Schmeling, Harro}, + booktitle={Physics and Chemistry of Partially Molten Rocks}, + pages={141--178}, + year={2000}, + publisher={Springer} +} + +@Article{Spa00, + author = {J. C. Spall}, + title = {Adaptive stochastic approximation by the simulateous + perturbation method}, + journal = {IEEE Trans. Autom. Contr.}, + year = 2000, + volume = 45, + pages = {1839--1853} +} + + +@Article{Spa98, + author = {J. C. Spall}, + title = {An overview of the simultaneous perturbation method for + efficient optimization}, + journal = {Johns Hopkins APL Tech. Dig.}, + year = 1998, + volume = 19, + pages = {482--492} +} + +@article{simpson:spiegelman:2011, + title={Solitary wave benchmarks in magma dynamics}, + author={Simpson, Gideon and Spiegelman, Marc}, + journal={Journal of Scientific Computing}, + volume={49}, + number={3}, + pages={268--290}, + year={2011}, + publisher={Springer} +} + +@Article{Sym94, + author = {W. Symes}, + title = {The plane wave detection problem}, + journal = {Inverse Problems}, + year = 1994, + volume = 10, + pages = {1361--1391} +} + + + +@TechReport{Sym99, + author = {W. W. Symes}, + title = {All stationary points of differential semblance are + asymptotic global minimizers: {L}ayered acoustics}, + institution = {Stanford Exploration Project}, + year = 1999, + number = 100, + note = {pages 71--92} +} + +@Book{TA77, + author = {A. Tikhonov and V. Arsenin}, + title = {Methods for Solving Ill-posed Problems}, + publisher = {Wiley}, + year = 1977 +} + +@Article{TJ03, + author = {U. Tautenhahn and Q. Jin}, + title = {Tikhonov regularization and a posteriori rules for + solving nonlinear ill posed problems}, + journal = {Inverse Problems}, + year = 2003, + volume = 19, + pages = {1--21} +} + +@Article{tamburrino:rubinacci:2002, + author = {A. Tamburrino and G. Rubinacci}, + title = {A new non-iterative inversion method for electrical + resistance tomography}, + journal = {Inverse Problems}, + year = 2002, + volume = 18, + pages = {1809--1829} +} + +@Article{TS03, + author = {A. B. Thompson and E. M. Sevick-Muraca}, + title = {{NIR} fluorescence contrast enhanced imaging with {ICCD} homodyne detection measurement precision and accuracy}, + journal = {J. Biomed. Opt.}, + year = 2003, + volume = 8, + pages = {111-120} +} + +@Book{Tar04, + author = {A. Tarantola}, + title = {Inverse Problem Theory and Methods for Model Parameter Estimation}, + publisher = {SIAM}, + year = 2004 +} + +@Book{Tar87, + author = {A. Tarantola}, + title = {Inverse Problem Theory}, + publisher = {Elsevier, Amsterdam, New York}, + year = 1987 +} + +@Article{Tau94, + author = {U. Tautenhahn}, + title = {Error estimates for regularized solutions of non-linear ill-posed problems}, + journal = {Inverse Problems}, + year = 1994, + volume = 10, + pages = {485--500} +} + +@Article{Ten01, + author = {L. Tenorio}, + title = {Statistical regularization of inverse problems}, + journal = {SIAM Review}, + year = 2001, + volume = 43, + pages = {347--366} +} + + +@InProceedings{Tur03, + author = {A. Tura}, + title = {Time-lapse seismic: {A}re we there yet?}, + booktitle = {Proceedings of the SEG International Exposition and + Seventy-Third Annual Meeting, October 2003, Dallas, Texas}, + year = 2003 +} + +@Article{UGBHU02, + author = {A. M. Urmanov and A. V. Gribok and H. Bozdogan and + J. W. Hines and R. E. Uhrig}, + title = {Information complexity-based regularization parameter + selection for solution of ill conditioned inverse problems}, + journal = {Inverse Problems}, + year = 2002, + volume = 18, + pages = {L1--L9} +} + +@Book{Uci04, + author = {D. Uci{\'n}ski}, + title = {Optimal Measurement Methods for Distributed Parameter System Identification}, + publisher = {CRC Press}, + PAGES= 392, + isbn = 9780367393984, + year = 2004} + +@Article{UU07, + author = {M. Ulbrich and S. Ulbrich}, + title = {Primal-dual interior-point methods for PDE-constrained optimization}, + journal = {Math. Prog.}, + year = {2007}, +} + + +@Article{UUH99, + author = {M. Ulbrich and S. Ulbrich and M. Heinkenschloss}, + title = {Global Convergence of Trust-Region Interior-Point + Algorithms for Infinite-Dimensional Nonconvex + Minimization Subject to Pointwise Bounds}, + journal = {SIAM J. Contr. Optim.}, + year = 1999, + volume = 37, + pages = {731--764} +} + +@Article{Uhl01, + author = {G. Uhlmann}, + title = {A time-dependent approach to the inverse backscattering problem}, + journal = {Inverse Problems}, + year = 2001, + volume = 17, + pages = {703--716} +} + +@Article{VPTZ01, + author = {L. Vel{\'a}zques and G. N. Philips and R. A. Tapia + and Y. Zhang}, + title = {Selective search for global optimization of zero or + small residual least-squares problems: {A} numerical study}, + journal = {Comp. Opt. Appl.}, + year = 2001, + volume = 20, + pages = {299--315} +} + +@InProceedings{VSS96, + author = {C. L. Varela and P. L. Stoffa and M. K. Sen}, + title = {Automatic background velocity estimation in 2{D} media}, + booktitle = {58th Meeting of the European Association of Exploration + Geophysics, Extended abstracts, Session X009}, + year = 1996 +} + +@Article{VW08, + author = {B. Vexler and W. Wollner}, + title = {Adaptive finite elements for elliptic optimization problems with + control constraints}, + journal = {SIAM J. Control Optim.}, + year = 2008, + volume = 47, + pages = {509--534}} + +@Article{VM07, + author = {I. M. Vellekoop and A. P. Mosk}, + title = {Focusing coherent light through opaque strongly scattering media}, + journal = {Optics Letters}, + year = 2007, + volume = 32, + pages = {2309--2311}} + +@Book{Vog02, + author = {C. R. Vogel}, + title = {Computational Methods for Inverse Problems}, + publisher = {SIAM}, + year = 2002 +} + + +@Article{Vog03, + author = {M. V{\"o}geler}, + title = {Reconstruction of the three-dimensional refractive index + in electromagnetic scattering by using a + propagation-backpropagation method}, + journal = {Inverse Problems}, + year = 2003, + volume = 19, + pages = {739--753} +} + +@Article{Vog99, + author = {C. R. Vogel}, + title = {Sparse matrix computations arising in distributed parameter + identification}, + journal = {SIAM J. Matrix Anal. Appl.}, + year = 1999, + volume = 20, + pages = {1027--1037} +} + + +@TechReport{WD01, + author = {M. Weiser and P. Deuflhard}, + title = {The central path towards the numerical solution of + optimal control problems}, + institution = {Konrad-Zuse-Zentrum f\"u{}r Informationstechnik Berlin}, + year = 2001, + number = {01-12}, + month = Jul +} + + +@TechReport{WEFUR01, + author = {S. F. Wojtkiewicz and M. S. Eldred and R. V. Field and + A. Urbina and J. R. Red-Horse}, + title = {Uncertainty quantification in large computational + engineering models}, + institution = {Sandia National Laboratories}, + year = 2001, + number = {AIAA-2001-1455} +} + + + +@Article{WLB09, + author = {D. Wang and X. Liu and J. Bai}, + journal = {Opt. Express}, + keywords = {Spectroscopy, fluorescence and luminescence; Tomography; Turbid media; Diffuse optical tomography; Image quality; Imaging systems; Numerical simulation; Optical imaging; Real time imaging}, + number = {24}, + pages = {21376--21395}, + publisher = {OSA}, + title = {Analysis of fast full angle fluorescence diffuse optical tomography with beam-forming illumination}, + volume = {17}, + month = nov, + year = {2009}, + url = {http://www.opticsexpress.org/abstract.cfm?URI=oe-17-24-21376}, + doi = {10.1364/OE.17.021376}, + abstract = {Challenges remain in imaging fast biological activities through whole body using fluorescence diffuse optical tomography (FDOT). We propose and analyze three full angle FDOT systems with different beam-forming illuminations (BF-FDOT), including line illumination (L-FDOT), area illumination (A-FDOT), and multiple-points illumination (MP-FDOT). Singular value analysis and experimental validation are used to optimize the experimental parameters in terms of hardware design, data collection and utilization. Comparisons are made on the system performance between L-FDOT and the conventional point illumination based full angle FDOT system (P-FDOT) with both numerical simulation and phantom experiment. We demonstrate that at least three cycles of projections are needed for P-FDOT to achieve comparable whole body image quality with L-FDOT. We also compare these three BF-FDOT systems and further discuss how these optimized parameters can be employed to improve spatial and temporal performances within current computational capacities, and guide the design of the BF-FDOT systems.}, +} + + +@Article{WZ05, + author = {J. Wang and N. Zabaras}, + title = {Hierarchical {B}ayesian models for inverse problems in + heat conduction}, + journal = {Inverse Problems}, + year = 2005, + volume = 21, + pages = {183--206} +} + + +@Article{WZ97, + author = {L. V. Wang and X. Zhao}, + title = {Ultrasound-modulated optical tomography of absorbing objects + buried in dense tissue-simulating turbid media}, + journal = {Applied Optics}, + year = 1997, + volume = 36, + pages = {7277--7282} +} + + +@Article{Wan01, + author = {L. V. Wang}, + title = {Mechanisms of ultrasonic modulation of multiply scattered + coherent light: an analytic model}, + journal = {Phys. Rev. Lett.}, + year = 2001, + volume = 87, + pages = {43903/1-4} +} + +@Article{Wan03, + author = {L. V. Wang}, + title = {Ultrasound-mediated biophotonic imaging: {A} review + of acousto-optical tomography and photo-acoustic + tomography}, + journal = {Disease Markers}, + year = {2004}, + volume = 19, + doi = {10.1155/2004/478079}, + pages = {123--138} +} + +@Article{Wei05, + author = {M. Weiser}, + title = {Interior point methods in function space}, + journal = {SIAM J. Control Optim.}, + year = 2005, + volume = 44, + pages = {1766--1786}} + +@Article{Wei06, + author = {R. Weissleder}, + title = {Molecular imaging in cancer}, + journal = {Science}, + year = 2006, + volume = 312, + pages = {1168--1171} +} + + +@Article{XWAK04, + author = {Y. Xu and L. V. Wang and G. Ambartsoumian and P. Kuchment}, + title = {Reconstructions in limited-view thermoacoustic tomography}, + journal = {Med. Phys.}, + year = 2004, + volume = 31, + pages = {724--733} +} + +@Article{XYJSS04, + author = {Y. Xia and Z.-L. Yang and C. Jackson and P. L. Stoffa and + M. K. Sen}, + title = {Impacts of data length on optimal parameter and uncertainty + estimation of a land surface model}, + journal = {J. Geoph. Res.}, + year = 2004, + volume = {109, D07101} +} + +@Article{YB96, + author = {W. K. Yeung and K. P. Bube}, + title = {A priori estimates and convergence for the discrete forward and + inverse problems of reflection seismology}, + journal = {SIAM J. Numer. Anal.}, + year = 1996, + volume = 33, + pages = {247--279} +} + +@Article{YBDA04, + author = {B. Yeten and D. R. Brouwer and L. J. Durlofsky and K. Aziz}, + title = {Decision analysis under uncertainty for smart well deployment}, + journal = {J. Petrol. Sc. Engrg.}, + volume = {44}, + number = {1}, + pages = {175 - 191}, + year = {2004}, + note = {Risk Analysis Applied to Petroleum Exploration and Production}, + issn = {0920-4105}, + doi = {10.1016/j.petrol.2004.09.002}, + url = {http://www.sciencedirect.com/science/article/pii/S0920410504001299}, + keywords = {Optimization, Smart wells, Nonconventional wells, Control, Uncertainty, Reliability}, + abstract = {Downhole inflow control devices allow for the flexible operation of nonconventional wells. In this paper, a method for determining the optimal performance of smart wells, i.e., wells containing downhole inflow control devices, is presented. The method entails the use of a gradient-based optimization technique in conjunction with a reservoir simulator. The optimization accounts for uncertain geology as well as the risk of failure of the control devices. A decision analysis approach is presented to determine whether or not to deploy smart completions in light of these uncertainties. The overall optimization technique is applied to several example problems involving geological models with multiple geostatistical realizations and with different reliability scenarios for the control devices. It is shown that there is significant variation in the level of improvement attainable using inflow control devices and that this improvement varies with both the valve reliability and the particular geological realization. Decision-making techniques are used to quantify the benefits obtained using optimized smart wells under different risk attitudes.} +} + +@Article{YPNM03, + author = {P. Yu and L. Peng and D. D. Nolte and M. R. Melloch}, + title = {Ultrasound detection through turbid media}, + journal = {Optics Letters}, + year = 2003, + volume = 28, + pages = {819--821} +} + +@Article{YW00, + author = {G. Yao and L. V. Wang}, + title = {Theoretical and experimental studies of ultrasound-modulated + optical tomography in biological tissue}, + journal = {Applied Optics}, + year = 2000, + volume = 39, + pages = {659--664} +} + +@Article{Yu96, + author = {W. H. Yu}, + title = {Necessary conditions for optimality in the identification + of elliptic systems with parameter constraints}, + journal = {J. Optimization Theory Appl.}, + year = 1996, + volume = 88, + pages = {725--742} +} + +@Article{ZBJVK06, + author = {M. J. Zandvliet and O. H. Bosgra and J. D. Jansen and + P. M. J. {Van den Hof} and J. F. B. M. Kraaijevanger}, + title = {Bang-bang control and singular arcs in reservoir flooding}, + journal = {J. Petrol. Sc. Engrg., submitted}, + volume = {58}, + number = {1}, + pages = {186 - 200}, + year = {2007}, + issn = {0920-4105}, + doi = {10.1016/j.petrol.2006.12.008}, + url = {http://www.sciencedirect.com/science/article/pii/S0920410507000101}, + keywords = {Optimal control, Bang-bang control, Singular arcs, Reservoir flooding}, + abstract = {Over the past few years, dynamic optimization of reservoir flooding using optimal control theory has received significant attention. Various studies have shown that dynamic (time-varying) injection and production settings can yield a higher Net Present Value (NPV) than conventional reactive settings. In these studies, the optimization procedure itself is always gradient-based, where the gradients are obtained with an adjoint formulation. However, the shape of the optimal injection and production settings is generally not known beforehand. The main contribution of this paper is to investigate why and under what conditions reservoir flooding problems can be expected to have bang-bang (on-off) optimal solutions. A major practical advantage of bang-bang controls is that they can be implemented with simple on-off valves. Furthermore, there are sufficient optimality conditions that are tailor-made for bang-bang solutions, meaning we can actually check whether a solution is locally optimal or not. These results are illustrated by a water flooding example of a 3-dimensional reservoir in a fluvial depositional environment, modeled with 18.553 grid blocks. The valve settings of 8 injection and 4 production wells are optimized over the life of the reservoir, with the objective to maximize NPV. It turns out that optimal settings are sometimes bang-bang, and sometimes bang-bang in combination with so-called singular arcs. For the latter situations, however, bang-bang solutions are found that are only slightly suboptimal.} +} + + +@Article{Zar09, + author = {C. A. Zarzer}, + title = {On {T}ikhonov regularization with non-convex sparsity + constraints}, + journal = {Inverse Problems}, + year = 2009, + volume = 25, + pages = {025006/1--13}} + +@Article{RBSHBRN09, + author = {R. Ziegler and B. Brendel and A. Schipper and R. Harbes + and M. van Beek and H. Rinneberg and T. Nielsen}, + title = {Investigation of detection limits for diffuse optical + tomography: {I}. {T}heory and experiment}, + journal = {Phys. Med. Biol.}, + year = 2009, + volume = 54, + pages = {399--412}} + +@Article{RBRN09, + author = {R. Ziegler and B. Brendel and H. Rinneberg and T. Nielsen}, + title = {Investigation of detection limits for diffuse optical + tomography: {II}. {A}nalysis of slab and cup geometry + for breast imaging}, + journal = {Phys. Med. Biol.}, + year = 2009, + volume = 54, + pages = {413--431}} + +@InProceedings{ZR02, + author = {F. Zhang and A. C. Reynolds}, + title = {Optimization algorithms for automatic history + matching of production data}, + booktitle = {ECMOR VIII: 8th European Conference on the Mathematics + of Oil Recovery, Freiberg, Germany}, + pages = {E-48}, + year = 2002, + organization = {European Association of Geoscientists and + Engineers (EAGE)} +} + +@Article{ZW04, + author = {H. Zhang and L. V. Wang}, + title = {Acousto-electric tomography}, + journal = {Proc. SPIE}, + year = 2004, + volume = 5320, + pages = {145--149} +} + + +@Article{asadzadeh-eriksson:94, + author = {Mohammad Asadzadeh and Kenneth Eriksson}, + title = {On adaptive finite element methods for Fredholm + integral equations of the second kind}, + journal = {SIAM J. Numer. Anal.}, + year = 1994, + volume = 31, + number = 3, + pages = {831--855} +} + +@Article{asadzadeh-kumlin-larsson:92, + author = {Mohammad Asadzadeh and Peter Kumlin and Stig Larsson}, + title = {The discrete ordinates method for the neutron + transport equation in an infinite cylindrical domain}, + journal = {Math. Models Methods Appl. Sci.}, + year = 1992, + volume = 2, + number = 3, + pages = {317--338} +} + +@Article{asadzadeh:2d:86, + author = {Mohammad Asadzadeh}, + title = {Analysis of a fully discrete scheme for neutron + transport in two-dimensional geometry}, + journal = {SIAM J. Numer. Anal.}, + year = 1986, + volume = 23, + pages = {543--561} +} + +@Article{asadzadeh:88, + author = {Mohammad Asadzadeh}, + title = {$L^2$-error estimates for the discrete ordinates + method for three-dimensional neutron transport}, + journal = {Transp. Theory Stat. Phys.}, + year = 1988, + volume = 17, + pages = {1--24} +} + +@PhdThesis{asadzadeh:dis:86, + author = {Mohammad Asadzadeh}, + title = {Convergence Analysis of some Numerical Methods for + Neutron Transport and Vlasov Equations}, + school = {Chalmers Tekniska H\"ogskola, G\"oteborg}, + year = 1986 +} + +@Article{auer-paletou:94, + author = {L. H. Auer and F. Paletou}, + title = {Two--dimensional radiative transfer with partial redistribution}, + journal = {A\&A}, + year = 1994, + volume = 284, + pages = {675--686} +} + +@Article{baschek-adam-plate-stoerzer-wehrse:88, + author = {B. Baschek and J. Adam and R. Plate and H. St\"orzer + and R. Wehrse}, + title = {Line Radiation from Accretion Discs: Spatially + Resolved Distribution}, + journal = {Adv. Space Res.}, + year = {1988}, + OPTkey = {}, + volume = {8}, + number = {2}, + OPTmonth = {}, + pages = {315--319}, + OPTnote = {}, + OPTannote = {} +} + +@Article{borysiewicz-mika-spiga:81, + author = {M. Borysiewicz and J. Mika and G. Spiga}, + title = {Asymptotic Analysis of the Linear Boltzmann Equation}, + journal = {Math. Meth. Appl. Sci.}, + year = 1981, + volume = 3, + pages = {405--423} +} + +@Article{borysiewicz-stankiewicz:second-order:79, + author = {M. Borysiewicz and R. Stankiewicz}, + title = {Variational Formulation and Projectional Methods for + the Second Order Transport Equation}, + journal = {J. Math. Anal. Appl.}, + year = 1979, + volume = 71, + pages = {210--231} +} + +@Article{borysiewicz-stankiewicz:weak-solution:79, + author = {M. Borysiewicz and R. Stankiewicz}, + title = {Weak Solution and Approximate Methods for the + Transport Equation}, + journal = {J. Math. Anal. Appl.}, + year = 1979, + volume = 68, + pages = {191--210} +} + +@Book{chandrasekhar:1960, + author = {Chandrasekhar, Subrahmanyan}, + title = {Radiative Transfer}, + publisher = {Oxford University Press}, + year = 1960 +} + +@PhdThesis{dittmann:95, + author = {Olaf J. Dittmann}, + title = {Transport polarisierter {S}trahlung in {M}edien + beliebiger {G}eometrie}, + school = {Universit{\"a}t Heidelberg}, + year = 1995, + type = {Dissertation} +} + +@Misc{eriksson-hansbo-johnson:neutron, + author = {Kenneth Eriksson and Peter Hansbo and Claes Johnson}, + title = {Parallelization of numerical methods for the neutron + transport equation}, + howpublished = {unpublished}, + year = 1994 +} + +@Book{goethe:10, + author = {von Goethe, Johann Wolfgang}, + title = {Zur Farbenlehre}, + publisher = {Cotta}, + year = 1810, + address = {Hamburg} +} + +@Article{golse-perthame:86, + author = {F. Golse and B. Perthame}, + title = {Generalized Solutions of the Radiative Transfer + Equations in a Singular Case}, + journal = {Commun. Math. Phys.}, + year = 1986, + volume = 106, + pages = {211--239}, + annote = {nonlinear local energy balance} +} + +@Article{johnson-pitkaeranta:83, + author = {Claes Johnson and Juhani Pitk{\"a}ranta}, + title = {Convergence of a Fully Discrete Scheme for + Two--Dimensional Neutron Transport}, + journal = {SIAM J. Numer. Anal.}, + year = 1983, + volume = 20, + number = 5, + month = oct, + pages = {951--966} +} + +@Article{kalkofen-wehrse:82, + author = {W. Kalkofen and R. Wehrse}, + title = {Radiative Transfer: Comparison of Finite Difference + Equations}, + journal = {Aston. Astrophys.}, + year = 1982, + volume = 110, + pages = {18--22} +} + +@Article{larsen-morel-miller:87, + author = {Edward W. Larsen and J. E. Morel and Warren + F. {Miller Jr.}}, + title = {Asymptotic Solutions of Numerical Transport Problems + in Optically Thick, Diffusive Regions}, + journal = {Comp. Phys.}, + year = 1987, + volume = 69, + pages = {283--324} +} + +@Book{mikhalas-mikhalas:84, + author = {Mikhalas, Dimitri and Weibel Mikhalas, Barbara}, + title = {Foundations of Radiation Hydrodynamics}, + publisher = {Oxford University Press}, + year = 1984 +} + +@Article{olson-auer-buchler:86, + author = {G. L. Olson and L. H. Auer and J. R. Buchler}, + title = {A Rapidly Convergent Iterative Solution of the + non--LTE Line Radiation Transfer Problem}, + journal = {JQSRT}, + year = 1986, + volume = 35, + pages = {431--442}, + keywords = {short characteristics} +} + +@Book{oxenius:86, + author = {Oxenius, Joachim}, + title = {Kinetic Theory of Particles and Photons + Theoretical Foundations of non-LTE + Plasma Spectroscopy}, + publisher = {Springer}, + year = 1986 +} + +@Article{pitkaeranta:79, + author = {Juhani Pitk{\"a}ranta}, + title = {On the Differential Properties of Solutions to + Fredholm Equations with Weakly Singular Kernels}, + journal = {J. Inst. Math. Appl.}, + year = 1979, + volume = 24, + pages = {109--119} +} + +@Article{pitkaeranta:80, + author = {Juhani Pitk{\"a}ranta}, + title = {Estimates for the Derivatives of Solutions to Weakly + Singular Fredholm Integral Equations}, + journal = {SIAM J. Math. Anal.}, + year = 1980, + volume = 11, + number = 6, + month = nov, + pages = {952--968}, + annote = {radiative transfer, regularity} +} + +@PhdThesis{ressel:94, + author = {Klaus J\"urgen Ressel}, + title = {Least--Squares Finite--Element Solution of the + Neutron Transport Equation in Diffusive Regimes}, + school = {University of Colorado}, + year = {1994}, + address = {Denver}, + OPTtype = {} +} + +@Article{stenholm-stoerzer-wehrse:91, + author = {L. G. Stenholm and H. St\"orzer and R. Wehrse}, + title = {An Efficient Method for the Solution of 3-D + Radiative Transfer Problems}, + journal = {J. Quant. Spectrosc. Radiat. Transfer}, + year = 1991, + volume = 45, + number = 1, + pages = {47--56} +} + +@Book{unsoeld-baschek:88, + author = {Albrecht Uns\"old and Bodo Baschek}, + title = {Der neue Kosmos}, + publisher = {Springer}, + year = 1988, + address = {Berlin, Heidelberg, \ldots}, + edition = 4 +} + +@Article{vaeth:94, + author = {H. M. V{\"a}th}, + title = {Three--dimensional radiative transfer on a massively + parallel computer}, + journal = {A\&A}, + year = 1994, + volume = 284, + pages = {319--331} +} + +@Misc{ACE, + author = {Douglas C. Schmidt et al.}, + title = {{W}{W}{W} homepage of the {A}daptive {C}ommunications {E}nvironment {A}{C}{E}, + {http://www.cs.wustl.edu/\~{}schmidt/ACE.html}} +} + +@InCollection{BL97, + author = {Are Magnus Bruaset and Hans Petter Langtangen}, + title = {A Comprehensive Set of Tools for Solving Partial + Differential Equations; {D}iff{P}ack}, + booktitle = {Numerical Methods and Software Tools in Industrial + Mathematics}, + publisher = {Birkh{\"a}user, Boston}, + year = {1997}, + editor = {M. D{\ae}hlen and A. Tveito}, + pages = {61--90} +} + +@Book{Cus93, + author = {H. Custer}, + title = {Inside Windows NT}, + publisher = {Microsoft Press, Redmont, Washington}, + year = 1993 +} + + + + +@Misc{DEAL1, + author = {Roland Becker and Guido Kanschat and Franz-Theo Suttmeier}, + title = {{DEAL} --- Dif\-fe\-ren\-tial Equa\-tions Ana\-ly\-sis Library}, + howpublished = {Available via {http://gaia.iwr.uni-heidelberg.de/DEAL.html}}, + year = 1995 +} + + + + + + +@Misc{FEMLists, + note = {Lists of available finite element software can, for example, + be found on ``The Object-Oriented Numerics Page'' + ({http://www.oonumerics.org/oon}), or the + ``Numerical Analysis \& Associated Fields Resource Guide'' + ({http://www.mathcom.com/nafaq/index.html})}, +} + +@Book{LL98, + author = {Stanley B. Lippmann and Jos{\'e}e Lajoie}, + title = {{C++} Primer}, + publisher = {Addison-Wesley}, + year = 1998, + edition = 3 +} + +@Article{castillo:etal:2005, + author = {P. Castillo and R. Rieben and D. White}, + title = {{FEMSTER:} {A}n object-oriented class library of + higher-order discrete differential forms}, + journal = {ACM Trans. Math. Software}, + year = 2005, + volume = 31, + pages = {425--457} +} + +@TechReport{PosixThreads96, + author = {IEEE}, + title = {Threads Extensions for Portable Operating Systems}, + institution = {IEEE}, + year = 1995 +} + +@TechReport{schmidt:wang:1995, + author = {Douglas C. Schmidt and Nanbor Wang}, + title = {An {O}{O} Encapsulation of Lightweight {O}{S} Concurrency + Mechanisms in the {A}{C}{E} Toolkit}, + institution = {Washington University, St. Louis}, + year = 1995, + number = {WUCS-95-31} +} + +@InProceedings{Sch94, + author = {Douglas C. Schmidt}, + title = {{A}{C}{E}: an Object-Oriented Framework for Developing + Distributed Applications}, + booktitle = {Proceedings of the Sixth USENIX C++ Technical Conference, + Cambridge, Massachusetts}, + year = 1994, + month = apr, + organization = {USENIX Association} +} + + +@InProceedings{SolarisThreads92, + author = {J. Eykholt and S. Kleinman and S. Barton and R. Faulkner and + A. Shivalingiah and M. Smith and D. Stein and J. Voll and + M. Weeks and D. Williams}, + title = {Beyon Multiprocessing... {M}ultithreading the {S}un{O}{S} Kernel}, + booktitle = {Proceedings of the Summer USENIX C++ Technical Conference, + San Antonio, Texas}, + year = 1992, + month = jun +} + + +@Book{Str97, + author = {Bjarne Stroustrup}, + title = {The {C++} Programming Language}, + publisher = {Addison-Wesley}, + year = 1997, + edition = 3 +} + + +@Article{Dav04, + author = {T. A. Davis}, + title = {Algorithm 832: {UMFPACK V4.3}---{A}n unsymmetric-pattern + multifrontal method}, + journal = {ACM Trans. Math. Software}, + year = 2004, + volume = 30, + pages = {196--199} +} + +@InProceedings{TTTPAR05, +author = {Thomas, Nathan and Tanase, Gabriel and Tkachyshyn, Olga and Perdue, Jack and Amato, Nancy M. and Rauchwerger, Lawrence}, +title = {A Framework for Adaptive Algorithm Selection in STAPL}, +year = {2005}, +isbn = {1595930809}, +publisher = {Association for Computing Machinery}, +address = {New York, NY, USA}, +url = {https://doi.org/10.1145/1065944.1065981}, +doi = {10.1145/1065944.1065981}, +booktitle = {Proceedings of the Tenth ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming}, +pages = {277-288}, +numpages = {12}, +keywords = {adaptive algorithms, machine learning, matrix multiplication, parallel algorithms, sorting}, +location = {Chicago, IL, USA}, +series = {PPoPP '05} +} + + +@Article{Li05, + author = {X. S. Li}, + title = {An overview of {SuperLU}: {A}lgorithms, implementation, + and user interface}, + journal = {ACM Trans. Math. Software}, + year = 2005, + volume = 31, + pages = {302--325} +} + + + +@Article{Log09, + author = {A. Logg}, + title={Efficient representation of computational meshes}, + volume={4}, + ISSN={1742-7193}, + url={http://dx.doi.org/10.1504/IJCSE.2009.029164}, + DOI={10.1504/ijcse.2009.029164}, + number={4}, + journal={International Journal of Computational Science and Engineering}, + publisher={Inderscience Publishers}, + year={2009}, + pages={283} +} + +@Article{Mu05, + author = {M. Mu}, + title = {{PDE.Mart}: {A} network-based problem-solving environment + for {PDE}s}, + journal = {ACM Trans. Math. Softw.}, + year = 2005, + volume = 31, + pages = {508--531} +} + + +@Article{PB01, + author = {B. Patz{\'a}k and Z. Bittnar}, + title = {Design of object oriented finite element code}, + journal = {Adv. Engrg. Softw.}, + year = 2001, + volume = 32, + pages = {759--767} +} + +@Article{rheinboldt:mesztenyi:1980, + author = {Rheinboldt, W. C. and Mesztenyi, C. K.}, + title = {On a Data Structure for Adaptive Finite Element Mesh Refinements}, + journal = {ACM Trans. Math. Softw.}, + pages = {166-187}, + volume = {6}, + year = {1980} +} + +@Article{KPSC07, + author = {B.~Kirk and J.~W.~Peterson and R.~H.~Stogner and G.~F.~Carey}, + title = {{{libMesh}: A C++ Library for Parallel Adaptive Mesh + Refinement/Coarsening Simulations}}, + journal = {Engineering with Computers}, + volume = {22}, + number = {3--4}, + pages = {237--254}, + year = {2006} +} + + +@Article{BA07, +author = {Berube, Paul and Amaral, Jos{\'e}}, +year = {2007}, +month = {01}, +pages = {}, +title = {Benchmark Design for Robust Profile-Directed Optimization}, +journal = {2007 SPEC Benchmark Workshop} +} + +@Article{PBSABV07, + author = {L. Pesch and A. Bell and H. Sollie and V. R. Ambati and + O. Bokhove and J. W. van der Vegt}, + title = {{hpGEM}~--~{A} software framework for discontinuous + {G}alerkin finite element methods}, + journal = {ACM Trans. Math. Softw.}, + year = 2007, + volume = 33, + number = 4, + pages = {23/1--23/25} +} + +@Article{SCD07, + author = {P. {\v S}ol{\'i}n and J. {\v C}erven{\'y} and I. Dole{\v z}el}, + title = {Arbitrary-Level Hanging Nodes and Automatic Adaptivity in + the hp-{FEM}}, + journal = {Math. Comput. Sim.}, + year = {2008}, + volume = 77, + pages = {117--132} +} + +@Article{FL02, + author = {P. Frauenfelder and C. Lage}, + title = {Concepts -- {A}n object-oriented software package for partial + differential equations}, + journal = {M2AN}, + year = 2002, + volume = 36, + pages = {937--951} +} + + +@Article{LCWCDZK06, + author = {O. S. Lawlor and S. Chakravorty and T. L. Wilmarth and + N. Choudhury and I. Dooley and G. Zheng and L. V. Kal{\'e}}, + title = {{ParFUM}: a parallel framework for unstructured meshes + for scalable dynamic physics applications}, + journal = {Eng. Comp.}, + year = 2006, + volume = 22, + pages = {215--235} +} + +@InProceedings{SSP07, + author = {J. Singler and P. Sanders and F. Putze}, + title = {{MCSTL}: The multi-core standard template library}, + booktitle = {Proceedings of the Euro-Par 2007 Parallel Processing + Conference}, + pages = {682--694}, + year = 2007, + editor = {Kermarrec, A.-M. and Boug{\'e}, L. and Priol T.}, + volume = 4641, + series = {Lecture Notes in Computer Science}, + publisher = {Springer} +} + +@Misc{NSF_software, + key = {NSF software strategy}, + author = {US National Science Foundation}, + title = {Grant general conditions (GC-1) \#38---Sharing of findings, + data, and other research products}, + howpublished = {\url{http://www.nsf.gov/pubs/policydocs/gc1_607.pdf}}, + month = jun, + year = 2007} + +@Book{Rei07, + author = {J. Reinders}, + title = {Intel Threading Building Blocks}, + publisher = {O'Reilly}, + year = 2007} + + +@TechReport{DVWC09, + author = {D. Das and M. Valluri and M. Wong and C. Cambly}, + title = {Speeding up {STL} set/map usage in {C}++ applications}, + institution = {IBM}, + year = 2009} + + +@Article{ABEI99, + author = {M. Aza{\"i}ez and F. {Ben Belgacem} and H. {El Fekih} + and M. Ismail}, + title = {Numerical simulation of the wave equation with + discontinuous coefficients by nonconforming finite elements}, + journal = {Numer. Methods Partial Differential Eq.}, + year = 1999, + volume = 15, + pages = {637--656} +} + + + +@Article{AGH00, + author = {Bradley Alpert and Leslie Greengard and Thomas Hagstrom}, + title = {Rapid evaluation of nonreflecting boundary kernels + for time-domain wave propagation}, + journal = {SIAM J. Numer. Anal.}, + year = 2000, + volume = 37, + number = 4, + pages = {1138--1164} +} + + +@InCollection{ALT98, + author = {D. Aubry and D. Lucas and B. Tie}, + title = {Adaptive strategy for transient/coupled problems. {A}pplications to + thermoelasticity and elastodynamics}, + booktitle = {Advances in Adaptive Computational Methods in Mechanics}, + pages = {325--332}, + publisher = {Elsevier Science}, + year = 1998, + editor = {P. Ladev{\`e}ze and J. T. Oden}, + series = {Studies in Applied Mechanics 47} +} + +@Article{AM89, + author = {A. K. Aziz and P. Monk}, + title = {Continuous finite elements in space and time for the heat equation}, + journal = {Math. Comp.}, + year = 1989, + volume = 52, + pages = {255--274} +} + +@Article{AP92, + author = {Najib A. Abboud and Peter M. Pinksky}, + title = {Finite element dispersion analysis for the + three-dimensional second-order scalar wave equation}, + journal = {Int. J. Numer. Meth. Eng.}, + year = 1992, + volume = 35, + pages = {1183--1218} +} + +@Article{BD80, + author = {G. A. Baker and V. A. Dougalis}, + title = {On the $L^\infty$-convergence of {G}alerkin approximations + for second-order hyperbolic equations}, + journal = {Math. Comput.}, + year = 1980, + volume = 34, + pages = {401--424} +} + + +@TechReport{BIK01, + author = {J. Behrens and A. Iske and M. K{\"a}ser}, + title = {Adaptive meshfree method of backward characteristics for + nonlinear transport equations}, + institution = {Technical University Munich, Faculty of Mathematics}, + year = 2001, + number = {TUM-M0110}, + month = nov +} + +@TechReport{BJT98, + author = {Eliane B\'ecache and Patrick Joly and Chrysoula Tsogka}, + title = {Some new mixed finite elements in view of the numerical solution + of time dependent wave propagation problems}, + institution = {INRIA}, + year = 1998, + type = {Rapport de recherche}, + number = 3445 +} + +@Article{BL94, + author = {L. Bales and I. Lasiecka}, + title = {Continuous finite elements in space and time for the nonhomogeneous wave equation}, + journal = {Computers Math. Applic.}, + year = 1994, + volume = 27, + number = 3, + pages = {91--102} +} + +@Article{BL95, + author = {L. Bales and I. Lasiecka}, + title = {Negative norm estimates for fully discrete finite element approximations + to the wave equation with nonhomogeneous ${L}_2$ {D}irichlet boundary data}, + journal = {Math. Comp.}, + year = 1995, + volume = 64, + pages = {89--115} +} + + +@Article{BNSI99, + author = {Ruperto P. Bonet and Norberto Nigro and Mario A. Storti + and Sergio R. Idelsohn}, + title = {Discrete non-local absorbing boundary conditions for + exterior problems governed by {H}elmholtz equation}, + journal = {Int. J. Numer. Methods Fluids}, + year = 1999, + volume = 29, + pages = {605--621} +} + +@Article{BR98scat, + author = {Bruno, Oscar P. and Reitich, Fernando}, + title = {Boundary-variation solutions for bounded-obstacle + scattering problems in three dimensions}, + journal = {J. Acoust. Soc. Am.}, + year = 1998, + volume = 104, + number = 5, + pages = {2579--2583} +} + +@Article{BS97, + author = {Ivo M. Babu{\v s}ka and Stefan A. Sauter}, + title = {Is the pollution effect of the {F}{E}{M} avoidable + for the {H}elmholtz equation considering high wave numbers?}, + journal = {SIAM J. Numer. Anal.}, + year = 1997, + volume = 34, + pages = {2392--2423} +} + +@Article{BT80, + author = {A. Bayliss and E. Turkel}, + title = {Radiation boundary conditions for wave-like equations}, + journal = {Commun. Pure Appl. Math.}, + year = 1980, + volume = 33, + pages = {707--725} +} + +@Article{BT93, + author = {T. Belytschko and M. Tabbara}, + title = {H-adaptive finite element methods for dynamic problems, with emphasis on localization}, + journal = {Int. J. Numer. Methods Engrg.}, + year = 1993, + volume = 36, + pages = {4245--4265} +} + +@Article{Baj87, + author = {C. I. Bajer}, + title = {Notes on the stability of non-rectangular space-time finite elements}, + journal = {Internat. J. Numer. Methods Engrg.}, + year = 1987, + volume = 24, + pages = {1721--1739} +} + +@Article{Baz78, + author = {Z. P. Ba{\v z}ant}, + title = {Spurious reflection of elastic waves in nonuniform finite element grids}, + journal = {Comput. Methods Appl. Mech. Engrg.}, + year = {1978}, + volume = {16}, + pages = {91--100} +} + +@Article{Ber94, + author = {Berenger, Jean-Pierre}, + title = {A Perfectly Matched Layer for the Absorption of Electromagnetic Waves}, + journal = {Comp. Phys.}, + year = 1994, + volume = 114, + pages = {185--200} +} + +@Article{Ber96, + author = {Berenger, Jean-Pierre}, + title = {Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic Waves}, + journal = {Comp. Phys.}, + year = 1996, + volume = 127, + pages = {363--379} +} + +@Book{But82, + author = {Anatoliy G. Butkovski}, + title = {Green's Functions and Transfer Functions Handbook}, + publisher = {Ellis Horwood Ltd., New York, Brisbane, Chichester, Toronto}, + year = {1982}, + series = {Series in Mathematics and its Applications} +} + +@Article{CC01, + author = {Carlos Castro and Steven J. Cox}, + title = {Achieving arbitrarily large decay in the damped wave equation}, + journal = {SIAM J. Control Optim.}, + year = 2001, + volume = 39, + number = 6, + pages = {1748--1755} +} + +@Article{CE77, + author = {R. Clayton and B. Engquist}, + title = {Absorbing boundary conditions for acoustic and elastic + wave equations}, + journal = {Bull. Seism. Soc. Am.}, + year = {1977}, + volume = {67}, + pages = {1529--1540} +} + +@Article{CKKR85, + author = {C. Cerjan and D. Kosloff and R. Kosloff and M. Reshef}, + title = {A nonreflecting boundary condition for discrete acoustic and + elastic wave equations}, + journal = {Geophysics}, + year = {1985}, + volume = {50}, + pages = {705--708} +} + +@Article{Chr99, + author = {Mark A. Christon}, + title = {The influence of the mass matrix on the dispersive nature of the semi-discrete, + second-order wave equation}, + journal = {Comput. Methods Appl. Mech. Engrg.}, + year = 1999, + volume = 173, + pages = {147--166} +} + +@Article{DHT81, + author = {M. Delfour and W. Hager and F. Trochu}, + title = {Dicontinuous {G}alerkin methods for ordinary differential equations}, + journal = {Math. Comp.}, + year = 1981, + volume = 36, + pages = {455--473} +} + + + +@Article{DKT06, + author = {M. Dumbser and M. K{\"a}ser and E. F. Toro}, + title = {An arbitrary high order discontinuous {G}alerkin method for + elastic waves on unstructured meshes {V}: {L}ocal time + stepping and $p$-adaptivity}, + journal = {Geophysical Journal International}, + volume = {171}, + number = {2}, + pages = {695-717}, + keywords = {ADER approach, Discontinuous Galerkin schemes, elastic waves, local time stepping, p-adaptivity, tetrahedral meshes}, + doi = {10.1111/j.1365-246X.2007.03427.x}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1365-246X.2007.03427.x}, + eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1365-246X.2007.03427.x}, + abstract = {SUMMARY This article describes the extension of the arbitrary high-order Discontinuous Galerkin (ADER-DG) method to treat locally varying polynomial degress of the basis functions, so-called p-adaptivity, as well as locally varying time steps that may be different from one element to another. The p-adaptive version of the scheme is useful in complex 3-D models with small-scale features which have to be meshed with reasonably small elements to capture the necessary geometrical details of interest. Using a constant high polynomial degree of the basis functions in the whole computational domain can lead to an unreasonably high CPU effort since good spatial resolution at the surface may be already obtained by the fine mesh. Therefore, it can be more adequate in some cases to use a lower order method in the small elements to reduce the CPU effort without loosing much accuracy. To further increase computational efficiency, we present a new local time stepping (LTS) algorithm. For usual explicit time stepping schemes the element with the smallest time step resulting from the stability criterion of the method will dictate its time step to all the other elements of the computational domain. In contrast, by using local time stepping, each element can use its optimal time step given by the local stability condition. Our proposed LTS algorithm for ADER-DG is very general and does not need any temporal synchronization between the elements. Due to the ADER approach, accurate time interpolation is automatically provided at the element interfaces such that the computational overhead is very small and such that the method maintains the uniform high order of accuracy in space and time as in the usual ADER-DG schemes with a globally constant time step. However, the LTS ADER-DG method is computationally much more efficient for problems with strongly varying element size or material parameters since it allows to reduce the total number of element updates considerably. This holds especially for unstructured tetrahedral meshes that contain strongly degenerate elements, so-called slivers. We show numerical convergence results and CPU times for LTS ADER-DG schemes up to sixth order in space and time on irregular tetrahedral meshes containing elements of very different size and also on tetrahedral meshes containing slivers. Further validation of the algorithm is provided by results obtained for the layer over half-space (LOH.1) benchmark problem proposed by the Pacific Earthquake Engineering Research Center. Finally, we present a realistic application on earthquake modelling and ground motion prediction for the alpine valley of Grenoble.}, + year = {2007} +} + +@Article{ELV92, + author = {R. E. Ewing and R. D. Lazarov and A. T. Vassilev}, + title = {Adaptive techniques for time-dependent problems}, + journal = {Comput. Methods Appl. Mech. Engrg.}, + year = 1992, + volume = 101, + pages = {113--126} +} + +@Article{EM77, + author = {Bjorn Engquist and Andrew Majda}, + title = {Absorbing Boundary Conditions for the Numerical Simulation of Waves}, + journal = {Math. 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Comp.}, + year = 1999, + volume = 68, + number = 225, + pages = {145--168} +} + + +@Article{Fre79, + author = {I. Freid}, + title = {Accuracy of string element mass matrix}, + journal = {Comput. Methods Appl. Mech. Engrg.}, + year = {1979}, + volume = {20}, + pages = {317--321} +} + +@Article{Fre93, + author = {Donald A. French}, + title = {A space-time finite element method for the wave equation}, + journal = {Comput. Methods Appl. Mech. Engrg.}, + year = 1993, + volume = 107, + pages = {145--157} +} + +@Article{GK00siam, + author = {M. J. Grote and J. B. Keller}, + title = {Exact nonreflecting boundary condition for elastic waves}, + journal = {SIAM J. Appl. Math.}, + year = 2000, + volume = 60, + pages = {803--819} +} + +@Article{GK95, + author = {M. J. Grote and J. B. Keller}, + title = {Exact nonreflecting boundary condition for the + time dependent wave equation}, + journal = {SIAM J. Appl. 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Phys.}, + year = 2000, + volume = 161, + pages = {331--353} +} + +@InCollection{Gro01, + author = {Marcus Grote}, + title = {Nonreflecting boundary conditions for time dependent + wave propagation}, + booktitle = {Artificial Boundary Conditions, with Applications to + Computational Fluid Dynamics}, + publisher = {Nova Science Publisher, New York}, + year = {2001}, + editor = {L. Tourette} +} + + +@TechReport{Gro98, + author = {M. J. Grote}, + title = {Nonreflecting boundary conditions for electromagnetic scattering}, + institution = {Seminar f"ur Angewandte Mathematik, Eidgen"ossische + Technische Hochschule, Z"urich}, + year = {1998}, + type = {Research Report}, + number = {98-09}, + month = sep +} + + +@Article{HBG97, + author = {Isaac Harari and Paul E. Barbone amd Joshua M. Montgomery}, + title = {Finite element formulation for exterior problems: + {A}pplication to hybrid methods, non-reflecting boundary + conditions, and infinite elements}, + journal = {Int. J. Numer. Methods Engrg.}, + year = 1007, + volume = 40, + pages = {2791--2805} +} + + + +@Article{HH88, + author = {T. J. R. Hughes and G. M. Hulbert}, + title = {Space-time FEM for elastodynamics and error estimates}, + journal = {Comp. Meth. Appl. Mech. Engrg.}, + year = 1988, + volume = 66, + pages = {339--363} +} + +@Article{HH90, + author = {Gregory M. Hulbert and Thomas J. R. Hughes}, + title = {Space-time finite element methods for second-order hyperbolic equations}, + journal = {Comput. Methods Appl. Mech. Engrg.}, + year = 1990, + volume = 84, + pages = {327--348} +} + +@Article{HT00, + author = {Runnong Huan and Lonny L. Thompson}, + title = {Accurate Radiation Boundary Conditions for the + Time-Dependent Wave Equation in Unbounded Domains}, + journal = {Inter. J. Numer. Methods Engrg.}, + year = 2000, + volume = 47, + pages = {1569--1603} +} + + + +@Article{HW09, + author = {T. Hagstrom and T. Warburton}, + title = {Complete radiation boundary conditions: {M}inimizing + the long term error growth of local methods}, + journal = {SIAM Journal on Numerical Analysis}, + volume = {47}, + number = {5}, + pages = {3678-3704}, + year = {2009}, + doi = {10.1137/090745477}, + URL = {https://doi.org/10.1137/090745477}, + eprint = {https://doi.org/10.1137/090745477} +} + +@InCollection{Hag99, + author = {Thomas Hagstrom}, + title = {Radiation Boundary Conditions for the Numerical + Simulation of Waves}, + booktitle = {Acta Numerica 1999}, + pages = {47--106}, + publisher = {Cambridge University Press}, + year = 1999, + editor = {A. Iserles}, + volume = 8 +} + +@Article{Har97, + author = {Isaac Harari}, + title = {Reducing spurious dispersion, anisotropy and reflection in + finite element analysis of time-harmonic acoustics}, + journal = {Comput. Methods Appl. Mech. Engrg.}, + year = {1997}, + volume = {140}, + pages = {39--58} +} + +@Article{Hig92, + author = {R. L. 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Engrg.}, + year = 1993, + volume = 103, + pages = {187--230} +} + +@Article{song:williamson:1995, + author = {Z.-M. Song and P. R. Williamson}, + title = {Frequency-domain acoustic-wave modelling and inversion of + crosshole data: {I}---2.5-d modelling method}, + journal = {Geophysics}, + year = 1995, + volume = 60, + pages = {784--795} +} + +@TechReport{SW96, + author = {Endre S"uli and Catherine Wilkins}, + title = {Adaptive Finite Element Methods for the Damped Wave Equation}, + institution = {Oxford University Computing Laboratory}, + year = {1996}, + type = {Report no. 96/23} +} + + + + + +@Article{BS05, + author = {C. Bernardi and E. S{\"u}li}, + title = {Time and space adaptivity for the second-order wave equation}, + journal = {Math. Models Methods Appl. Sci.}, + year = 2005, + volume = 15, + pages = {199--225} +} + + +@Article{SY97, + author = {Frank Schmidt and David Yevick}, + title = {Discrete absorbing boundary conditions for + {S}chr{\"o}dinger-type equations}, + journal = {J. Comput. Phys.}, + year = 1997, + volume = 134, + pages = {96--107} +} + + +@InProceedings{Sch00, + author = {Frank Schmidt}, + title = {Discrete nonreflecting boundary conditions for the {H}elmholtz equation}, + booktitle = {Proceedings of the Fifth International Conference on Mathematical + and Numerical Aspects of Wave Propagation (Waves2000), Santiago + de Compostela, Spain, 2000}, + pages = {921--925}, + year = 2000, + editor = {Alfredo Berm\'udez and Dolores G\'omez and Christophe Hazard and + Patrick Joly and Jean E. Roberts}, + publisher = {SIAM} +} + + + +@MastersThesis{Sch95, + author = {Martin Schemann}, + title = {Eine adaptive {Rothe}-{M}ethode f"ur die + zweidimensionale {W}ellengleichung}, + school = {Freie Universit{"a}t Berlin, Institut f"ur Mathematik I}, + year = {1995}, + type = {Diplomarbeit}, + month = nov +} + + +@article{Sch97a, +author = {Schmidt, Frank}, +year = {2001}, +month = {09}, +pages = {}, +title = {Construction of discrete transparent boundary conditions for + {S}chr{\"o}dinger-type equations}, +volume = {9}, +journal = {Surv. Math. Ind.} +} + + +@TechReport{Sch97b, + author = {Frank Schmidt}, + title = {Computation of discrete transparent boundary conditions + for the 2{D} {H}elmholtz equation}, + institution = {Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin}, + year = 1998, + volume = 30, + pages = {427--4641}, +} + +@Article{TH00, + author = {Lonny L. 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Pinsky}, + title = {A space-time finite element method for the exterior structural + acoustics problem: {T}ime-dependent radiation boundary conditions + in two space dimensions}, + journal = {Int. J. Numer. Methods Eng.}, + year = 1996, + volume = 39, + pages = {1635--1657} +} + +@Article{TP96b, + author = {Lonny L. Thompson and Peter M. Pinsky}, + title = {A space-time finite element method for structural acoustics in infinite + domains. {P}art 1: {F}ormulation, stability and convergence}, + journal = {Comput. Methods Appl. Mech. Eng.}, + year = 1996, + volume = 132, + pages = {195--227} +} + +@Article{TP96c, + author = {Lonny L. Thompson and Peter M. Pinsky}, + title = {A space-time finite element method for structural acoustics in infinite + domains. {P}art 2: {E}xact time-dependent non-reflecting boundary conditions}, + journal = {Comput. Methods Appl. Mech. Eng.}, + year = 1996, + volume = 132, + pages = {229--258} +} + +@PhdThesis{Tho94, + author = {Lonny L. Thompson}, + title = {Design and Analysis of Space-Time and {G}alerkin/Least-Squares Finite + Element Methods for Fluid-Structure Interaction in Exterior Domains}, + school = {Stanford University}, + year = 1994, + month = apr +} + +@Article{Vir86, + author = {J. Virieux}, + title = {P-{S}{V} wave propagation in heterogeneous media: + velocity-stress finite-difference method}, + journal = {Geophysics}, + year = {1986}, + volume = {51}, + pages = {889--901} +} + +@Article{WL94, + author = {N.-E. Wiberg and X. D. Li}, + title = {A postprocessed error estimate and an adaptive procedure for the semidiscrete + finite element method in dynamic analysis}, + journal = {Int. J. Numer. Methods Engrg.}, + year = 1994, + volume = 37, + pages = {3585--3603} +} + +@Article{WL98, + author = {N.-E. Wiberg and X. D. Li}, + title = {Adaptive discontinuous {G}alerkin procedures for linear and + nonlinear structural dynamics}, + journal = {International Journal for Numerical Methods in Engineering}, + volume = {46}, + number = {10}, + pages = {1781-1802}, + keywords = {discontinuous Galerkin, space-time finite elements, structural dynamics, error estimation, h-adaptivity}, + doi = {10.1002/(SICI)1097-0207(19991210)46:10<1781::AID-NME724>3.0.CO;2-7}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291097-0207%2819991210%2946%3A10%3C1781%3A%3AAID-NME724%3E3.0.CO%3B2-7}, + eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/%28SICI%291097-0207%2819991210%2946%3A10%3C1781%3A%3AAID-NME724%3E3.0.CO%3B2-7}, + year = {1999} +} + + +@Article{WZL92, + author = {N.-E. Wiberg and L. F. Zeng and X. D. Li}, + title = {Error estimation and adaptivity in elastodynamics}, + journal = {Comput. Methods Appl. Mech. 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Burtscher and O. Ghattas and G. Stadler and T. Tu and L. C. Wilcox}, + title={{ALPS}: {A} framework for parallel adaptive {PDE} solution}, + journal={J. Physics: Conf. Series}, + volume={180}, + pages={012009}, + year={2009} +} + + +@Article{heroux:etal:2005, + author = {M. A. Heroux and R. A. Bartlett and V. E. Howle and R. J. Hoekstra and J. J. Hu + and T. G. Kolda and R. B. Lehoucq and K. R. Long and R. P. Pawlowski and + E. T. Phipps and A. G. Salinger and H. K. Thornquist and R. S. Tuminaro and + J. M. Willenbring and A. Williams and K. S. Stanley}, + title = {An overview of the {T}rilinos project}, + journal = {ACM Trans. Math. Softw.}, + year = 2005, + volume = 31, + pages = {397--423}} + +@Misc{trilinos-web-page, + Author = {M. A. Heroux and others}, + Title = {{Trilinos} web page}, + Note = {http://trilinos.sandia.gov}, + Year = {2011} + } + + + + + + + + +@Article{KRH90, + author = {S. D. King and A. Raefsky and B. H. Hager}, + title = {Conman: {V}ectorizing a finite element code for incompressible two-dimensional convection in the Earth's mantle}, + journal = {Phys. Earth Planet. Inter.}, + year = 1990, + volume = 59, + pages = {195--207}} + +@Article{MZG96, + author = {L. Moresi and S. J. Zhong and M. Gurnis}, + title = {The accuracy of finite element solutions of {S}tokes' flow with strongly varying viscosity}, + journal = {Phys. Erath Planet. Inter.}, + year = 1996, + volume = 97, + pages = {83--94}} + +@Article{Alb00, + author = {M. Albers}, + title = {A Local Mesh Refinement Multigrid Method for 3-{D} Convection Problems with Strongly Variable Viscosity}, + journal = {J. Comp. Phys.}, + year = 2000, + volume = 160, + pages = {126--150}} + + +@Article{DDHMN07, + author = {D. R. Davies and J. H. Davies and O. Hassan and K. Morgan and P. Nithiarasu}, + title = {Investigations into the applicability of adaptive finite element methods to two-dimensional infinite {P}randtl number thermal and thermochemical convection}, + journal = {Geoch. Geophs. Geosystems}, + year = 2007, + volume = 8, + pages = {Q05010/1--25}} + +@Article{DDHMN07a, + author = {D. R. Davies and J. H. Davies and O. Hassan and K. Morgan and P. Nithiarasu}, + title = {Adaptive finite element methods in geodynamics: {C}onvection dominated mid-ocean ridge and subduction zone simulations}, + journal = {Int. J. Numer. Meth. Heat Fluid Flow}, + year = 2007, + volume = 18, + pages = {1015--1035}} + +@BOOK{Girault1986, + title = {Finite Element Methods for the {N}avier--{S}tokes Equations}, + publisher = {Springer--Verlag}, + year = {1986}, + author = {V. Girault and P.--A. Raviart}, + address = {New York}, + owner = {heister}, + timestamp = {2010.02.16} +} + + + + +@Misc{dealiistep31, + author = {M. Kronbichler and W. Bangerth}, + title = {deal.{II} tutorial program step-31, \url{http://www.dealii.org/developer/doxygen/deal.II/step_31.html}}, + year = 2011 +} + +@Misc{dealiistep32, + author = {M. Kronbichler and T. Heister and W. Bangerth}, + title = {deal.{II} tutorial program step-32, \url{http://www.dealii.org/developer/doxygen/deal.II/step_32.html}}, + year = 2011 +} + + + + + + +@article{Sheldon59, +title = {One-dimensional, incompressible, non-capillary, two-phase fluid flow in a porous medium}, +journal = {Trans. SPE AIME}, +volume = {216}, +pages = {290--296}, +year = {1959}, +author = {J. W. Sheldon and B. Zondek and W. T. Cardwell} +} + +@article{Stone61, +title = {Analysis of gas-cap or dissolved-gas reservoirs}, +journal = {Trans. SPE AIME}, +volume = {222}, +pages = {92--104}, +year = {1961}, +author = {H. L. Stone and A. O. Garder} +} + +@Book{Chen_book06, + author = {Z. Chen}, + title = {Computational Methods for Multi-phase Flows in Porous Media}, + publisher = {SIAM}, + year = 2006 +} + + + + + + +@article{guermond:etal:2011, + author = {{Jean-Luc Guermond and Richard Pasquetti and Bojan Popov}}, + title = {Entropy viscosity method for nonlinear conservation laws}, + journal = {Journal of Computational Physics}, + year = {2011}, + volume = {230}, + pages = {4248--4267} +} + +@article{LundTownend07, + Author = {B. Lund and J. Townend}, + Title = {Calculating horizontal stress orientations with full or partial knowledge of the tectonic stress tensor}, + Journal = {Geophys. J. Int.}, + Volume = {170}, + Pages = {1328--1335}, + Year = {2007} +} + + + + + + +@article{becker:etal:2003, +author = {Becker, Thorsten W. and Kellogg, James B. and Ekstr{\"{o}}m, G{\"{o}}ran and O'Connell, Richard J.}, +doi = {10.1046/j.1365-246X.2003.02085.x}, +issn = {0956540X}, +journal = {Geophysical Journal International}, +month = nov, +number = {2}, +pages = {696--714}, +publisher = {Oxford University Press}, +title = {{Comparison of azimuthal seismic anisotropy from surface waves and finite strain from global mantle-circulation models}}, +url = {http://doi.wiley.com/10.1046/j.1365-246X.2003.02085.x}, +volume = {155}, +year = {2003} +} + +@article{mckenzie:jackson:1983, +author = {McKenzie, Dan and Jackson, James}, +doi = {10.1016/0012-821X(83)90198-X}, +issn = {0012821X}, +journal = {Earth and Planetary Science Letters}, +number = {1}, +pages = {182--202}, +publisher = {Elsevier}, +title = {{The relationship between strain rates, crustal thickening, palaeomagnetism, finite strain and fault movements within a deforming zone}}, +volume = {65}, +year = {1983} +} + +@book{dahlen:tromp:1998, + title={Theoretical global seismology}, + author={Dahlen, FA and Tromp, Jeroen}, + year={1998}, + publisher={Princeton University Press} +} + +@article{ribe:1992, +author = {Ribe, Neil M.}, +doi = {10.1029/92JB00551}, +issn = {0148-0227}, +journal = {Journal of Geophysical Research}, +number = {B6}, +pages = {8737}, +title = {{On the relation between seismic anisotropy and finite strain}}, +url = {http://doi.wiley.com/10.1029/92JB00551}, +volume = {97}, +year = {1992} +} + +@article{buiter2008dissipation, + title={Dissipation analysis as a guide to mode selection during crustal extension and implications for the styles of sedimentary basins}, + author={Buiter, S. J. H. and Huismans, R. S. and Beaumont, C.}, + journal={Journal of Geophysical Research: Solid Earth}, + volume={113}, + number={B6}, + year={2008}, + publisher={Wiley Online Library} +} + +@Article{rose_freesurface, + Title = {Stability and accuracy of free surface time integration in viscous flows}, + Author = {Ian Rose and Bruce Buffett and Timo Heister}, + Journal = {Physics of the Earth and Planetary Interiors}, + Year = {2017}, + Pages = {90 - 100}, + Volume = {262}, + Doi = {10.1016/j.pepi.2016.11.007}, + ISSN = {0031-9201}, + Url = {http://dx.doi.org/10.1016/j.pepi.2016.11.007} +} + +@article{heister:etal:2017, + title = {High Accuracy Mantle Convection Simulation through Modern Numerical Methods. + {II}: {R}ealistic Models and Problems}, + author = {Heister, Timo and Dannberg, Juliane and + Gassm{\"o}ller, Rene and Bangerth, Wolfgang}, + journal = {Geophysical Journal International}, + year = {2017}, + number = {2}, + pages = {833-851}, + volume = {210}, + DOI = {10.1093/gji/ggx195}, + URL = {https://doi.org/10.1093/gji/ggx195} +} + +@misc{aspect-doi-v1.5.0, + title = {{ASPECT} v1.5.0 [software]}, + author = {Wolfgang Bangerth and + Juliane Dannberg and + Rene Gassmoeller and + Timo Heister and + others}, + month = mar, + year = {2017}, + doi = {10.5281/zenodo.344623}, + note = {doi:10.5281/zenodo.344623}, + url = {https://doi.org/10.5281/zenodo.344623}, + organization = {Computational Infrastructure for Geodynamics}, + address = {Davis, CA}, +} + +@misc{aspect-doi-v2.0.0, + title = {{ASPECT} v2.0.0 [software]}, + author = {Wolfgang Bangerth and + Juliane Dannberg and + Rene Gassmoeller and + Timo Heister and + others}, + month = may, + year = 2018, + DOI = {10.5281/zenodo.1244587}, + URL = {https://doi.org/10.5281/zenodo.1244587}, + organization = {Computational Infrastructure for Geodynamics}, + address = {Davis, CA}, +} + +@misc{aspect-doi-v2.0.1, + title = {{ASPECT} v2.0.1 [software]}, + author = {Wolfgang Bangerth and + Juliane Dannberg and + Rene Gassmoeller and + Timo Heister and + others}, + month = jun, + year = 2018, + DOI = {10.5281/zenodo.1297145}, + URL = {https://doi.org/10.5281/zenodo.1297145}, + organization = {Computational Infrastructure for Geodynamics}, + address = {Davis, CA}, +} + +@misc{aspect-doi-v2.1.0, + title = {{ASPECT} v2.1.0 [software]}, + author = {Wolfgang Bangerth and + Juliane Dannberg and + Rene Gassmoeller and + Timo Heister and + others}, + month = apr, + year = 2019, + DOI = {10.5281/zenodo.2653531}, + URL = {https://doi.org/10.5281/zenodo.2653531}, + organization = {Computational Infrastructure for Geodynamics}, + address = {Davis, CA}, +} + +@software{aspect-doi-v2.2.0, + author = {Wolfgang Bangerth and + Juliane Dannberg and + Rene Gassmoeller and + Timo Heister}, + title = {ASPECT v2.2.0}, + month = jun, + year = 2020, + publisher = {Zenodo}, + version = {v2.2.0}, + doi = {10.5281/zenodo.3924604}, + url = {https://doi.org/10.5281/zenodo.3924604} +} + + +@software{aspect-doi-v2.3.0, + author = {Wolfgang Bangerth and + Juliane Dannberg and + Menno Fraters and + Rene Gassmoeller and + Anne Glerum and + Timo Heister and + John Naliboff}, + title = {ASPECT v2.3.0}, + month = jul, + year = 2021, + publisher = {Zenodo}, + version = {v2.3.0}, + doi = {10.5281/zenodo.5131909}, + url = {https://doi.org/10.5281/zenodo.5131909} +} + +@software{aspect-doi-v2.4.0, + author = {Wolfgang Bangerth and + Juliane Dannberg and + Menno Fraters and + Rene Gassmoeller and + Anne Glerum and + Timo Heister and + Robert Myhill and + John Naliboff}, + title = {ASPECT v2.4.0}, + month = jul, + year = 2022, + publisher = {Zenodo}, + version = {v2.4.0}, + doi = {10.5281/zenodo.6903424}, + url = {https://doi.org/10.5281/zenodo.6903424} +} + +@software{aspect-doi-v2.5.0, + author = {Wolfgang Bangerth and + Juliane Dannberg and + Menno Fraters and + Rene Gassmoeller and + Anne Glerum and + Timo Heister and + Robert Myhill and + John Naliboff}, + title = {ASPECT v2.5.0}, + month = jul, + year = 2023, + publisher = {Zenodo}, + version = {v2.5.0}, + doi = {10.5281/zenodo.8200213}, + url = {https://doi.org/10.5281/zenodo.8200213} +} + +@misc{aspectmanual, + title = {{{ASPECT}: Advanced Solver for Problems in Earth's ConvecTion, User Manual}}, + author = {Bangerth, Wolfgang and Dannberg, Juliane and Fraters, Menno and Gassmoeller, Rene and Glerum, Anne and Heister, Timo and Myhill, Robert and Naliboff, John}, + year = {2023}, + month = jul, + DOI = {10.6084/m9.figshare.4865333}, + note = {doi:10.6084/m9.figshare.4865333}, + URL = {https://doi.org/10.6084/m9.figshare.4865333} +} + +@article{gassmoller:etal:2018, + title={Flexible and Scalable Particle-in-Cell Methods With Adaptive Mesh Refinement for Geodynamic Computations}, + author={Gassm{\"o}ller, Rene and Lokavarapu, Harsha and Heien, Eric and Puckett, Elbridge Gerry and Bangerth, Wolfgang}, + journal={Geochemistry, Geophysics, Geosystems}, + volume={19}, + number={9}, + pages={3596--3604}, + year={2018}, + url={https://doi.org/10.1029/2018GC007508}, + doi={10.1029/2018GC007508} +} + +@article{He_2017_DG, + Title = {A discontinuous {G}alerkin method with a bound preserving limiter for the advection of non-diffusive fields in solid Earth geodynamics }, + Author = {Ying He and Elbridge Gerry Puckett and Magali I. Billen}, + Journal = {Physics of the Earth and Planetary Interiors }, + Year = {2017}, + Pages = {23 - 37}, + Volume = {263}, + Doi = {10.1016/j.pepi.2016.12.001}, + ISSN = {0031-9201}, + Keywords = {Geodynamics}, + Url = {https://doi.org/10.1016/j.pepi.2016.12.001} +} + + +@Article{NPB+04, + author = {Nimmo, F. and Price, G.D. and Brodholt, J. and Gubbins, D. + }, + title = {The influence of potassium on core and geodynamo evolution}, + journal = {Geophysical Journal International}, + year = 2004, + volume = 156, + pages = {363-376} +} + +@Article{tosi:etal:2015, + author = {Tosi, N. and Stein, C. and Noack, L. and H\"uttig, C. and Maierova, P. and Samual, H. and Davies, D. R. and Wilson, C. R. and Kramer, S. C. and Thieulot, C. and Glerum, A. and Fraters, M. and Spakman, W. and Rozel, A. and Tackley, P. J.}, + title = {A community benchmark for viscoplastic thermal convection in a 2-D square box}, + journal = g3, + year = 2015, + volume = 16, + pages = {2175-2196} +} + +@Book{donea:huerta:2003, + author = {Donea, J. and Huerta, A.}, + title = {Finite Element Methods for Flow Problems}, + publisher = {John Wiley \& Sons, Ltd}, + year = 2003 +} + +@article{yamauchi:takei:2016, + author = {Yamauchi, H. and Takei, Y.}, + title = {Polycrystal anelasticity at near-solidus temperatures}, + journal = {Journal of Geophysical Research: Solid Earth}, + year={2016}, + volume={121}, + number={11}, + pages={7790--7820} +} + +@article{mckenzie:etal:2005, + author = {McKenzie, Dan and Jackson, James and Priestley, Keith}, + title = {Thermal structure of oceanic and continental lithosphere}, + journal = {Earth \& Planetary Science Letters}, + year = {2005}, + volume = {233}, + number = {3-4}, + pages = {337--349}, + +} + +@article{priestley:etal:2012, + author = {Priestley, Keith and McKenzie, Dan and Barron, Jamie and Tatar, Mohammad and Debayle, Eric}, + title = {The Zagros core: Deformation of the continental lithospheric mantle}, + journal = {Geochemistry, Geophysics, Geosystems}, + volume = {13}, + number = {11}, + pages = {Q11014}, + year = {2012} +} + +@article{hirschmann:2000, +author = {Hirschmann, Marc M.}, +journal = {Geochemistry, Geophysics, Geosystems}, +title = {Mantle solidus: Experimental constraints and the effects of peridotite composition}, +number = {10}, +volume = {1}, +year = {2000} +} + +@article{rudi2017weighted, + title={Weighted BFBT Preconditioner for Stokes Flow Problems with Highly Heterogeneous Viscosity}, + author={Rudi, Johann and Stadler, Georg and Ghattas, Omar}, + journal={SIAM Journal on Scientific Computing}, + volume={39}, + number={5}, + pages={S272--S297}, + year={2017}, + publisher={SIAM} +} + + +@article{DohrmannBochev2004, + doi = {10.1002/fld.752}, + url = {https://doi.org/10.1002/fld.752}, + year = {2004}, + month = aug, + publisher = {Wiley}, + volume = {46}, + number = {2}, + pages = {183--201}, + author = {Clark R. Dohrmann and Pavel B. Bochev}, + title = {A stabilized finite element method for the Stokes problem based on polynomial pressure projections}, + journal = {International Journal for Numerical Methods in Fluids} +} + + +@Article{fraters:etal:2019, + author = {M. R. T. Fraters and W. Bangerth and C. Thieulot and A. C. Glerum and W. Spakman}, + title = {Efficient and practical {N}ewton solvers for nonlinear {S}tokes systems in geodynamics problems}, + journal = {Geophysics Journal International}, + volume = {218}, + number = {2}, + pages = {873-894}, + year = {2019}, + month = {04}, + issn = {0956-540X}, + doi = {10.1093/gji/ggz183}, + url = {https://doi.org/10.1093/gji/ggz183}, + eprint = {http://oup.prod.sis.lan/gji/article-pdf/218/2/873/28693654/ggz183.pdf}, +} + +@article{fraters_billen_2021_cpo, +author = {Fraters, M. R. T. and Billen, M. I.}, +title = {On the Implementation and Usability of Crystal Preferred Orientation Evolution in Geodynamic Modeling}, +journal = {Geochemistry, Geophysics, Geosystems}, +volume = {22}, +number = {10}, +pages = {e2021GC009846}, +keywords = {crystal preferred orientation, CPO, LPO, D-Rex, ASPECT}, +doi = {10.1029/2021GC009846}, +url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2021GC009846}, +eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2021GC009846}, +note = {e2021GC009846 2021GC009846}, +abstract = {Abstract Flow in the Earth's mantle causes the preferred orientation of crystals called lattice/crystal preferred orientation (LPO or CPO). This preferred orientation is one of the main reasons why seismic anisotropy is observed. Seismic anisotropy observations could therefore be used to constrain the mantle flow in geodynamic models through tracking CPO evolution, and computing the resulting elastic tensor and the anisotropy predicted at the surface. Even though there are many types of CPO models, only a few studies include CPO calculations due to the complexity and computational cost. Here, we implemented an extended version of the CPO model D-Rex into the open-source community geodynamics code ASPECT. We show that the implementation is correct, how to use it, and that it is feasible and important to use in large 3D models. We also show that it is important to calculate CPO, especially for models focusing on plate boundary of smaller scale flow because the resulting fast axis directions can greatly deviate from the flow direction. The added infrastructure will also allow for future enhancement, testing, and even replacement of the CPO model.}, +year = {2021} +} + + +@article{weinberg:schmeling:1992, + title={{Polydiapirs: multiwavelength gravity structures}}, + author={R.F. Weinberg and H. Schmeling}, + journal={Journal of Structural Geology}, + volume={14}, + number={4}, + pages={425--436}, + year={1992} +} + + +@book{ramberg:1981, +Author = {H. Ramberg}, +Publisher = {Academic Press, London, 214pp.}, +Title = {Gravity, Deformation, and the Earth's Crust: In Theory, Experiments and Geological Application}, +Year = {1981} +} + +@book{jackson:hudec:2017, +Author = {M. Jackson and M. Hudec}, +Publisher={Cambridge: Cambridge University Press}, +title={Salt Tectonics: Principles and Practice}, +doi={10.1017/9781139003988}, +year={2017} +} + +@article{schmalholz:2011, + title={{A simple analytical solution for slab detachment}}, + author={S. M. Schmalholz}, + journal=epsl, + volume={304}, + number={}, + pages={45--54}, + year={2011} +} + +@Article{hillebrand:etal:2014, +AUTHOR = {Hillebrand, B. and Thieulot, C. and Geenen, T. and van den Berg, A. P. and Spakman, W.}, +TITLE = {Using the level set method in geodynamical modeling of multi-material flows and {E}arth's free surface}, +JOURNAL = {Solid Earth}, +VOLUME = {5}, +YEAR = {2014}, +NUMBER = {2}, +PAGES = {1087--1098}, +URL = {https://www.solid-earth.net/5/1087/2014/}, +DOI = {10.5194/se-5-1087-2014} +} + + +@article{glerum:etal:2018, +TITLE = {Nonlinear viscoplasticity in {ASPECT}: benchmarking and applications to subduction}, + author={A. Glerum and C. Thieulot and M. Fraters and C. Blom and W. Spakman}, + journal={Solid Earth}, + volume={9}, +NUMBER = {2}, + pages={267--294}, +DOI = {10.5194/se-9-267-2018}, + year={2018} +} + +@article{vanhunen:allen:2011, + title={{Continental collision and slab break-off: A comparison of 3-D numerical models with observations}}, + author={J. {van Hunen} and M.B. Allen}, + journal=epsl, + volume={302}, + pages={27-37}, + year={2011} +} + +@article{wortel:spakman:2000, + title={{Subduction and slab detachment in the Mediterranean-Carpathian region}}, + author={M.J.R. Wortel and W. Spakman}, + journal={Science}, + volume={290}, + number={}, + pages={1910-1917}, + year={2000} +} + +@article{garzanti:etal:2018, +title = {Slab breakoff: A critical appraisal of a geological theory as applied in space and time}, +author = {E. Garzanti and G. Radeff and M.G. Malus{\`a}}, +journal = {Earth-Science Reviews}, +volume = {177}, +pages = {303--319}, +year = {2018}, +doi = {10.1016/j.earscirev.2017.11.012}, +} + +@Misc{thieulot:2019, + author = {C. Thieulot}, + title = {The Finite Element Method in Geodynamics}, + url = {https://github.com/cedrict/fieldstone/blob/master/manual.pdf}, + year = {2019} +} + +@incollection{john:knobloch:2006, + doi = {10.1007/978-3-540-34288-5_27}, + publisher = {Springer Berlin Heidelberg}, + pages = {336--344}, + year = {2006}, + author = {Volker John and Petr Knobloch}, + title = {On Discontinuity{\textemdash}Capturing Methods for Convection{\textemdash}Diffusion Equations}, + booktitle = {Numerical Mathematics and Advanced Applications} +} + +@Misc{clevenger:heister:2019, + author = {Thomas C. Clevenger and Timo Heister}, + title = {deal.{II} tutorial program step-63, \url{http://www.dealii.org/developer/doxygen/deal.II/step_63.html}}, + year = 2019 +} + +@article{chri92, + title={{An Eulerian technique for thermomechanical modeling of lithospheric extension}}, + author={R.R. Christensen}, + journal=jgr, + volume={97}, + number={B2}, + pages={2015--2036}, + year={1992} +} + +@article{cibi15, + title={{Geodynamics of trench advance: Insights from a Philippine-Sea-style geometry}}, + author={H. {\v C}{\'i}{\v z}kov{\'a} and C.R. Bina}, + journal=epsl, + volume={430}, + number={}, + pages={408--415}, + doi={10.1016/j.epsl.2015.07.004}, + year={2015} +} + +@article{cibi13, + title={{Effects of mantle and subduction-interface rheologies on slab stagnation and trench rollback}}, + author={H. {\v C}{\'i}{\v z}kov{\'a} and C.R. Bina}, + journal=epsl, + volume={379}, + number={}, + pages={95--103}, + doi={10.1016/j.epsl.2013.08.011}, + year={2013} +} + +@article{vavv02, + title={{On the role of subducting oceanic plateaus in the development of shallow flat subduction}}, + author={J. van Hunen and A.P. van den Berg and N.J. Vlaar}, + journal={Tectonophysics}, + volume={352}, + number={3-4}, + pages={317--333}, + doi={10.1016/S0040-1951(02)00263-9}, + year={2002} +} + +@article{buiter:etal:2016, + title={{Benchmarking numerical models of brittle thrust wedges}}, + author={S.J.H. Buiter and G. Schreurs and M. Albertz and T.V. Gerya and B. Kaus and W. Landry and L. le Pourhiet and Y. Mishin and D.L. Egholm and M. Cooke and B. Maillot and C. Thieulot and T. Crook and D. May and P. Souloumiac and C. Beaumont}, + journal={Journal of Structural Geology}, + volume={92}, + number={}, + pages={140--177}, + doi={10.1016/j.jsg.2016.03.003}, + year={2016} +} + +@article{ramberg:1968, +Author = {Hans Ramberg}, +Journal = {Phys. Earth Planet. Interiors}, +Pages = {427--447}, +Title = {Instability of layered systems in the field of gravity}, +Volume = {1}, +Year = {1968}} + + +@Article{clevenger:heister:2021, + Title = {Comparison Between Algebraic and Matrix-free Geometric Multigrid for a {S}tokes Problem on an Adaptive Mesh with Variable Viscosity}, + Author = {Thomas C. Clevenger and Timo Heister}, + Journal = {Numerical Linear Algebra with Applications}, + Year = {2021}, + Month = mar, + Doi = {10.1002/nla.2375}, + Publisher = {Wiley}, + Url = {https://arxiv.org/abs/1907.06696} +} + +@Article{clevenger:etal:2020, + Title = {A Flexible, Parallel, Adaptive Geometric Multigrid Method for FEM}, + Author = {Thomas C. Clevenger and Timo Heister and Guido Kanschat and Martin Kronbichler}, + Journal = {ACM Trans. Math. 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H. and Hill, T. R.}, + title = {Triangular mesh methods for the neutron transport equation}, + institution = {Los Alamos Scientific Laboratory}, + year = 1973, + type = {Tech. Report}, + number = {LA-UR-73-479} +} + +@Article{RS98, + author = {Rannacher, R. and Suttmeier, F. T.}, + title = {A posteriori error control in finite element methods via + duality techniques: application to perfect plasticity}, + journal = {Comp. Mech.}, + year = 1998, + volume = {21/2}, + pages = {123--133} +} + + +@InProceedings{RT77, + author = {Raviart, P. A. and Thomas, J. -M.}, + title = {A mixed finite element method for second order elliptic problems}, + booktitle = {Mathematical Aspects of the Finite Element Method}, + pages = {292--315}, + year = 1977, + editor = {Galligani, I. and Magenes, E.}, + address = {New York}, + publisher = {Springer} +} + + +@InCollection{RT91, + author = {Roberts, J. 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Robey}, + TITLE = {On the Design, Implementation, and Use of a Volume-of-Fluid Interface + Tracking Algorithm For Modeling Convection and other Processes in the + {E}arth's Mantle}, + YEAR = {2019}, + note = {Ph.D. Thesis}, + type = {Applied Mathematics}, + month = sep, + school = {University of California, Davis}, + language = {English}, + isbn = {9781392640074} +} + + + +@ARTICLE{robey:puckett:2019, + TITLE = {Implementation of a Volume-of-Fluid method in a finite element code with + applications to thermochemical convection in a density stratified fluid in the {E}arth's + mantle}, + AUTHOR = {Jonathan M. Robey and Elbridge Gerry Puckett}, + JOURNAL = {Computers \& Fluids}, + YEAR = {2019}, + volume = {190}, + number = {2}, + pages = {217--253}, + note = {Special Issue on Modeling Fluid Interfaces}, + issn = {0045-7930}, + doi = {10.1016/j.compfluid.2019.05.015}, +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% SSSS +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +@Article{SGBWAG10, + author = {G. Stadler and M. Gurnis and C. Burstedde and L. C. Wilcox and L. Alisic and O. Ghattas}, + title = {The Dynamics of Plate Tectonics and Mantle Flow: {F}rom Local to Global Scales}, + journal = {Science}, + year = 2010, + volume = 329, + pages = {1033--1038}} + + + + +@Article{schmid:podladchikov:2003, + title={Analytical solutions for deformable elliptical inclusions in general shear}, + author={Schmid, D. W. and Podladchikov, Y. 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Worthen}, + title = {Inverse Problems in Mantle Convection: Models, Algorithms, and Applications}, + school = {University of Texas at Austin, in preparation}, + year = {2012}} + + + +@article{willett:1999, +Author = {S. D. Willett}, +Journal = {Tectonophysics}, +Pages = {419-435}, +Title = {Rheological dependence of extension in wedge models of convergent orogens}, +Volume = {305}, +Year = {1999}} + + +@Article{WY00, + author = {Wheeler, M. F. and Yotov, I.}, + title = {Multigrid on the interface for mortar mixed finite element methods + for elliptic problems}, + journal = {Comput. Methods Appl. Mech. Engrg.}, + year = 2000, + volume = 184, + pages = {287--302} +} + + +@Article{WY04, + author = {Wheeler, M. 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