## Gander, Martin Jakob

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 Author ID: gander.martin-j Published as: Gander, Martin J.; Gander, M. J.; Gander, Martin; Gander, M. more...less Homepage: http://www.unige.ch/~gander/ External Links: MGP · ORCID · Wikidata · Google Scholar · dblp · GND · IdRef · theses.fr
 Documents Indexed: 191 Publications since 1996, including 3 Books 8 Contributions as Editor · 1 Further Contribution Co-Authors: 133 Co-Authors with 188 Joint Publications 3,140 Co-Co-Authors
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### Co-Authors

 11 single-authored 33 Halpern, Laurence 20 Dolean, Victorita 14 Kwok, Felix 10 Santugini-Repiquet, Kévin 8 Nataf, Frédéric 8 Xu, Yingxiang 8 Zhang, Hui 7 Ciaramella, Gabriele 7 Lanteri, Stéphane 6 Chaouqui, Faycal 6 Vanzan, Tommaso 5 Cocquet, Pierre-Henri 5 El Bouajaji, Mohamed 5 Japhet, Caroline 5 Loisel, Sébastien 5 Ruehli, Albert E. 5 Wanner, Gerhard 4 Hubert, Florence 4 Krell, Stella 4 Mandal, Bankim C. 4 Martin, Véronique 4 Veneros, Erwin 3 Al-Khaleel, Mohammad D. 3 Bai, Zhongzhi 3 Côté, Jean-François 3 Dubois, Olivier 3 Gutknecht, Martin H. 3 Hajian, Soheil 3 Kumbhar, Pratik M. 3 Laayouni, Lahcen 3 Magoulès, Frédéric 3 Meurant, Gérard A. 3 Michaud, Jérôme 3 Perrussel, Ronan 3 Petcu, Madalina 3 Redivo-Zaglia, Michela 3 Rodriguez, Giuseppe 3 Song, Bo 3 St-Cyr, Amik 3 Szyld, Daniel B. 2 Beck, Mélanie 2 Bennequin, Daniel 2 Berninger, Heiko 2 Caetano, Filipa 2 Claeys, Xavier 2 Daoud, Daoud S. 2 Ernst, Oliver G. 2 Frénod, Emmanuel 2 Gouarin, Loïc 2 Graham, Ivan G. 2 Güttel, Stefan 2 Hairer, Ernst 2 Jiang, Yaolin 2 Lee, Jin-Fa 2 Liebendörfer, Matthias 2 Liu, Yongxiang 2 Loneland, Atle 2 Masson, Roland 2 Peng, Zhen 2 Qaddouri, Abdessamad 2 Rohde, Christian 2 Salomon, Julien 2 Spence, Euan A. 2 Szeftel, Jérémie 2 Vandewalle, Stefan G. 2 Widlund, Olof B. 2 Wu, Shulin 2 Xiang, Xueshuang 1 Ayala, Alan 1 Barucq, Hélène 1 Benzi, Michele 1 Bercovier, Michel 1 Betcke, Timo 1 Bjørstad, Petter Erling 1 Bourlioux, Anne 1 Brenner, Susanne Cecelia 1 Brezinski, Claude 1 Butcher, John C. 1 Cai, Xiao-Chuan 1 Chang, Xiaowen 1 Chen, Zhiming 1 Courvoisier, Yves 1 Descombes, Stéphane 1 Dickopf, Thomas 1 Drexler, Michael 1 Efstathiou, Evridiki 1 Erhel, Jocelyne 1 Gander, Walter 1 Gautschi, Walter 1 Gerardo-Giorda, Luca 1 Golub, Gene Howard 1 Gong, Shihua 1 Haynes, Ronald D. 1 Hennicker, Julian 1 Karaa, Samir 1 Kheriji, Walid 1 Klawonn, Axel 1 Kornhuber, Ralf 1 Krause, Rolf H. 1 Kulchytska-Ruchka, Iryna ...and 39 more Co-Authors
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### Serials

 27 SIAM Journal on Scientific Computing 12 SIAM Journal on Numerical Analysis 7 BIT 7 Numerical Algorithms 7 ETNA. Electronic Transactions on Numerical Analysis 5 SIAM Review 4 Mathematics of Computation 4 Numerische Mathematik 4 Numerical Linear Algebra with Applications 3 Applied Numerical Mathematics 3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 3 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 3 Lecture Notes in Computational Science and Engineering 2 Journal of Computational and Applied Mathematics 2 Journal of Scientific Computing 2 Vietnam Journal of Mathematics 2 Journal of Computational Acoustics 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Boletín de la Sociedad Española de Matemática Aplicada. S$$\vec{\text{e}}$$MA 2 IEEE Transactions on Circuits and Systems I: Regular Papers 2 Fundamentals of Algorithms 1 International Journal for Numerical Methods in Fluids 1 Journal of Computational Physics 1 Journal of Mathematical Biology 1 ACM Transactions on Mathematical Software 1 SIAM Journal on Matrix Analysis and Applications 1 Elemente der Mathematik 1 SIAM Journal on Mathematical Analysis 1 The Canadian Applied Mathematics Quarterly 1 International Journal of Applied Mathematics and Computer Science 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 AMRX. Applied Mathematics Research eXpress 1 NATO Science Series II: Mathematics, Physics and Chemistry 1 Texts in Computational Science and Engineering 1 Networks and Heterogeneous Media 1 S$$\vec{\text{e}}$$MA Journal 1 Contemporary Mathematicians 1 SMAI Journal of Computational Mathematics
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### Fields

 185 Numerical analysis (65-XX) 105 Partial differential equations (35-XX) 18 Optics, electromagnetic theory (78-XX) 10 Fluid mechanics (76-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 8 Ordinary differential equations (34-XX) 7 General and overarching topics; collections (00-XX) 6 Information and communication theory, circuits (94-XX) 5 History and biography (01-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Mechanics of particles and systems (70-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Computer science (68-XX) 2 Real functions (26-XX) 2 Mechanics of deformable solids (74-XX) 2 Astronomy and astrophysics (85-XX) 2 Biology and other natural sciences (92-XX) 2 Systems theory; control (93-XX) 1 Number theory (11-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

### Citations contained in zbMATH Open

171 Publications have been cited 2,506 times in 969 Documents Cited by Year
Optimized Schwarz methods. Zbl 1117.65165
Gander, Martin J.
2006
Optimized Schwarz methods without overlap for the Helmholtz equation. Zbl 1021.65061
Gander, Martin J.; Magoulès, Frédéric; Nataf, Frédéric
2002
Analysis of the parareal time-parallel time-integration method. Zbl 1141.65064
Gander, Martin J.; Vandewalle, Stefan
2007
Why it is difficult to solve Helmholtz problems with classical iterative methods. Zbl 1248.65128
Ernst, O. G.; Gander, M. J.
2012
50 years of time parallel time integration. Zbl 1337.65127
Gander, Martin J.
2015
Optimized Schwarz waveform relaxation methods for advection reaction diffusion problems. Zbl 1140.65063
Gander, M. J.; Halpern, L.
2007
Schwarz methods over the course of time. Zbl 1171.65020
Gander, Martin J.
2008
Optimal Schwarz waveform relaxation for the one dimensional wave equation. Zbl 1085.65077
Gander, Martin J.; Halpern, Laurence; Nataf, Frédéric
2003
Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems. Zbl 1052.65015
Benzi, Michele; Gander, Martin J.; Golub, Gene H.
2003
Space-time continuous analysis of waveform relaxation for the heat equation. Zbl 0911.65082
Gander, Martin J.; Stuart, Andrew M.
1998
Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: What is the largest shift for which wavenumber-independent convergence is guaranteed? Zbl 1328.65238
Gander, M. J.; Graham, I. G.; Spence, E. A.
2015
A class of iterative solvers for the Helmholtz equation: factorizations, sweeping preconditioners, source transfer, single layer potentials, polarized traces, and optimized Schwarz methods. Zbl 1417.65216
Gander, Martin J.; Zhang, Hui
2019
Optimized Schwarz methods for Maxwell’s equations. Zbl 1192.78044
Dolean, V.; Gander, M. J.; Gerardo-Giorda, L.
2009
Nonlinear convergence analysis for the parareal algorithm. Zbl 1140.65336
Gander, Martin J.; Hairer, Ernst
2008
A homographic best approximation problem with application to optimized Schwarz waveform relaxation. Zbl 1198.65179
Bennequin, D.; Gander, M. J.; Halpern, L.
2009
An optimized Schwarz method with two-sided Robin transmission conditions for the Helmholtz equation. Zbl 1125.65114
Gander, M. J.; Halpern, L.; Magoulès, F.
2007
Analysis of a new space-time parallel multigrid algorithm for parabolic problems. Zbl 1342.65225
Gander, Martin J.; Neumüller, Martin
2016
St-Cyr, A.; Gander, M. J.; Thomas, S. J.
2007
Efstathiou, Evridiki; Gander, Martin J.
2003
PARAEXP: a parallel integrator for linear initial-value problems. Zbl 1266.65123
Gander, Martin J.; Güttel, Stefan
2013
A waveform relaxation algorithm with overlapping splitting for reaction diffusion equations. Zbl 0983.65107
Gander, Martin J.
1999
Absorbing boundary conditions for the wave equation and parallel computing. Zbl 1074.65114
Gander, Martin J.; Halpern, Laurence
2005
Analysis of a Krylov subspace enhanced parareal algorithm for linear problems. Zbl 1156.65322
Gander, M.; Petcu, M.
2008
Optimized Schwarz methods for the time-harmonic Maxwell equations with damping. Zbl 1259.78047
El Bouajaji, M.; Dolean, V.; Gander, M. J.; Lanteri, S.
2012
Overlapping Schwarz waveform relaxation for the heat equation in $$n$$ dimensions. Zbl 1022.65112
Gander, Martin J.; Zhao, Hongkai
2002
How large a shift is needed in the shifted Helmholtz preconditioner for its effective inversion by multigrid? Zbl 1365.65269
Cocquet, Pierre-Henri; Gander, Martin J.
2017
The optimized Schwarz method with a coarse grid correction. Zbl 1248.65127
Dubois, Olivier; Gander, Martin J.; Loisel, Sébastien; St-Cyr, Amik; Szyld, Daniel B.
2012
Analysis for parareal algorithms applied to Hamiltonian differential equations. Zbl 1291.65209
Gander, Martin J.; Hairer, Ernst
2014
An incomplete Lu preconditioner for problems in acoustics. Zbl 1189.76362
Gander, Martin J.; Nataf, Frédéric
2005
Optimized Schwarz methods for a diffusion problem with discontinuous coefficient. Zbl 1314.65155
Gander, Martin J.; Dubois, Olivier
2015
Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms for parabolic problems. Zbl 1355.65128
Gander, Martin J.; Kwok, Felix; Mandal, Bankim C.
2016
Best Robin parameters for optimized Schwarz methods at cross points. Zbl 1254.65126
Gander, Martin J.; Kwok, Felix
2012
Optimized Schwarz methods for circular domain decompositions with overlap. Zbl 1304.65261
Gander, Martin J.; Xu, Yingxiang
2014
Overlapping Schwarz waveform relaxation for convection-dominated nonlinear conservation laws. Zbl 1105.65098
Gander, Martin J.; Rohde, Christian
2005
Nonlinear preconditioning: how to use a nonlinear Schwarz method to precondition Newton’s method. Zbl 1352.65326
Dolean, V.; Gander, M. J.; Kheriji, W.; Kwok, F.; Masson, R.
2016
Effective transmission conditions for domain decomposition methods applied to the time-harmonic curl-curl Maxwell’s equations. Zbl 1349.78064
Dolean, Victorita; Gander, Martin J.; Lanteri, Stephane; Lee, Jin-Fa; Peng, Zhen
2015
Optimized Schwarz waveform relaxation for advection reaction diffusion equations in two dimensions. Zbl 1356.65225
Bennequin, Daniel; Gander, Martin J.; Gouarin, Loic; Halpern, Laurence
2016
Optimized Schwarz methods with nonoverlapping circular domain decomposition. Zbl 1355.65167
Gander, Martin J.; Xu, Yingxiang
2017
Optimized Schwarz methods with an overset grid for the shallow-water equations: Preliminary results. Zbl 1133.76037
2008
Analysis of two parareal algorithms for time-periodic problems. Zbl 1283.65077
Gander, Martin J.; Jiang, Yao-Lin; Song, Bo; Zhang, Hui
2013
Scientific computing. An introduction using Maple and MATLAB. Zbl 1296.65001
Gander, Walter; Gander, Martin J.; Kwok, Felix
2014
Cross-points in domain decomposition methods with a finite element discretization. Zbl 1347.65187
Gander, Martin J.; Santugini, Kévin
2016
Algorithm 932: PANG: software for nonmatching grid projections in 2D and 3D with linear complexity. Zbl 1295.65120
Gander, Martin J.; Japhet, Caroline
2013
Schwarz waveform relaxation algorithms for semilinear reaction-diffusion equations. Zbl 1262.35009
Caetano, Filipa; Gander, Martin J.; Halpern, Laurence; Szeftel, Jérémie
2010
SHEM: an optimal coarse space for RAS and its multiscale approximation. Zbl 1367.65183
Gander, Martin J.; Loneland, Atle
2017
Ailu for Helmholtz problems: a new preconditioner based on the analytic parabolic factorization. Zbl 1360.76181
Gander, Martin J.; Nataf, Frédéric
2001
Analysis of the parallel Schwarz method for growing chains of fixed-sized subdomains. I. Zbl 1366.65111
Ciaramella, G.; Gander, M. J.
2017
AILU: a preconditioner based on the analytic factorization of the elliptic operator. Zbl 1051.65054
Gander, Martin J.; Nataf, Frédéric
2000
Time parallelization for nonlinear problems based on diagonalization. Zbl 1367.65118
Gander, Martin J.; Halpern, Laurence
2017
A direct time parallel solver by diagonalization for the wave equation. Zbl 1407.65175
Gander, Martin J.; Halpern, Laurence; Rannou, Johann; Ryan, Juliette
2019
On the influence of geometry on optimized Schwarz methods. Zbl 1328.65261
Gander, Martin J.
2011
Analysis of the parallel Schwarz method for growing chains of fixed-sized subdomains. II. Zbl 1435.65223
Ciaramella, Gabriele; Gander, Martin J.
2018
A new cement to glue nonconforming grids with Robin interface conditions: the finite element case. Zbl 1067.65144
Gander, Martin J.; Japhet, Caroline; Maday, Yvon; Nataf, Frédéric
2005
Domain decomposition approaches for mesh generation via the equidistribution principle. Zbl 1253.65144
Gander, Martin J.; Haynes, Ronald D.
2012
A direct solver for time parallelization. Zbl 1339.65114
Gander, Martin J.; Halpern, Laurence; Ryan, Juliet; Thuy Thi Bich Tran
2016
A new coarse grid correction for RAS/AS. Zbl 1382.65438
Gander, Martin J.; Halpern, Laurence; Repiquet, Kévin Santugini
2014
Optimized waveform relaxation methods for $$RC$$ type circuits. Zbl 1374.94946
Gander, Martin J.; Ruehli, Albert E.
2004
From Euler, Ritz, and Galerkin to modern computing. Zbl 1263.01013
Gander, Martin J.; Wanner, Gerhard
2012
Analysis of the parareal algorithm applied to hyperbolic problems using characteristics. Zbl 1242.65212
Gander, Martin J.
2008
Optimization of transmission conditions in waveform relaxation techniques for RC circuits. Zbl 1300.94127
Al-Khaleel, Mohammad D.; Gander, Martin J.; Ruehli, Albert E.
2014
Chladni figures and the Tacoma Bridge: motivating PDE eigenvalue problems via vibrating plates. Zbl 1251.65155
Gander, Martin J.; Kwok, Felix
2012
Analysis of a new dimension-wise splitting iteration with selective relaxation for saddle point problems. Zbl 1342.76074
Gander, Martin J.; Niu, Qiang; Xu, Yingxiang
2016
Dirichlet-Neumann and Neumann-Neumann waveform relaxation for the wave equation. Zbl 1339.65165
Gander, Martin J.; Kwok, Felix; Mandal, Bankim C.
2016
Discontinuous coarse spaces for DD-methods with discontinuous iterates. Zbl 1382.65439
Gander, Martin J.; Halpern, Laurence; Repiquet, Kévin Santugini
2014
Optimized Schwarz methods with overlap for the Helmholtz equation. Zbl 1351.65094
Gander, Martin J.; Zhang, Hui
2016
A superlinear convergence estimate for the parareal Schwarz waveform relaxation algorithm. Zbl 1414.65018
Gander, Martin J.; Jiang, Yao-Lin; Song, Bo
2019
Méthodes de relaxation d’ondes (SWR) pour l’équation de la chaleur en dimension 1. (Optimized Schwarz waveform relaxation (SWR) for the one-dimensional heat equation). Zbl 1028.65100
Gander, Martin J.; Halpern, Laurence
2003
Optimal interface conditions for an arbitrary decomposition into subdomains. Zbl 1217.65223
Gander, Martin J.; Kwok, Felix
2011
Optimized Schwarz methods for model problems with continuously variable coefficients. Zbl 1348.65138
Gander, Martin J.; Xu, Yingxiang
2016
Analysis of Schwarz methods for a hybridizable discontinuous Galerkin discretization. Zbl 1312.65190
Gander, Martin J.; Hajian, Soheil
2015
Multigrid methods for Helmholtz problems: a convergent scheme in 1D using standard components. Zbl 1287.65133
Ernst, Oliver G.; Gander, Martin J.
2013
On the scalability of classical one-level domain-decomposition methods. Zbl 1406.65128
Chaouqui, F.; Ciaramella, G.; Gander, M. J.; Vanzan, T.
2018
Analysis of a modified parareal algorithm for second-order ordinary differential equations. Zbl 1152.65336
Gander, M.; Petcu, M.
2007
Schwarz methods for the time-parallel solution of parabolic control problems. Zbl 1369.65080
Gander, Martin J.; Kwok, Felix
2016
An optimal block iterative method and preconditioner for banded matrices with applications to PDEs on irregular domains. Zbl 1252.65068
Gander, Martin J.; Loisel, Sébastien; Szyld, Daniel B.
2012
Analysis of the parallel Schwarz method for growing chains of fixed-sized subdomains. III. Zbl 1404.65301
Ciaramella, Gabriele; Gander, Martin J.
2018
Convergence analysis of a periodic-like waveform relaxation method for initial-value problems via the diagonalization technique. Zbl 1472.65083
Gander, Martin J.; Wu, Shu-Lin
2019
Stochastic gene expression in switching environments. Zbl 1125.92044
Gander, Martin J.; Mazza, Christian; Rummler, Hansklaus
2007
Heterogeneous optimized Schwarz methods for second order elliptic PDEs. Zbl 1428.65105
Gander, Martin J.; Vanzan, Tommaso
2019
An algorithm for non-matching grid projections with linear complexity. Zbl 1183.65161
Gander, Martin J.; Japhet, Caroline
2009
Optimized Schwarz method with two-sided transmission conditions in an unsymmetric domain decomposition. Zbl 1339.65234
Gander, Martin J.; Xu, Yingxiang
2016
On the minimal shift in the shifted Laplacian preconditioner for multigrid to work. Zbl 1339.65231
Cocquet, Pierre-Henri; Gander, Martin J.
2016
On the relation between optimized Schwarz methods and source transfer. Zbl 1339.65230
Chen, Zhiming; Gander, Martin J.; Zhang, Hui
2016
On the positivity of Poisson integrators for the Lotka-Volterra equations. Zbl 1321.65184
Beck, Mélanie; Gander, Martin J.
2015
Viscous problems with inviscid approximations in subregions: a new approach based on operator factorization. Zbl 1419.76498
Gander, Martin J.; Halpern, Laurence; Japhet, Caroline; Martin, Veronique
2009
Optimized Schwarz methods with overlap for the Helmholtz equation. Zbl 1382.65442
Gander, Martin J.; Zhang, Hui
2014
Comparison of the Dirichlet-Neumann and optimal Schwarz method on the sphere. Zbl 1066.65142
Côté, J.; Gander, M. J.; Laayouni, L.; Loisel, S.
2005
Optimized overlapping Schwarz methods for parabolic PDEs with time-delay. Zbl 1066.65099
Vandewalle, Stefan; Gander, Martin J.
2005
A new algorithm based on factorization for heterogeneous domain decomposition. Zbl 1350.65108
Gander, Martin J.; Halpern, Laurence; Martin, Véronique
2016
On nilpotent subdomain iterations. Zbl 1367.65148
Chaouqui, Faycal; Gander, Martin J.; Santugini-Repiquet, Kévin
2017
On the definition of Dirichlet and Neumann conditions for the biharmonic equation and its impact on associated Schwarz methods. Zbl 1367.65182
Gander, Martin J.; Liu, Yongxiang
2017
Optimization of Schwarz waveform relaxation over short time windows. Zbl 1273.65135
Courvoisier, Yves; Gander, Martin J.
2013
A finite difference method with optimized dispersion correction for the Helmholtz equation. Zbl 1443.65280
Cocquet, Pierre-Henri; Gander, Martin J.; Xiang, Xueshuang
2018
A new parareal algorithm for problems with discontinuous sources. Zbl 1439.65075
Gander, Martin J.; Kulchytska-Ruchka, Iryna; Niyonzima, Innocent; Schöps, Sebastian
2019
Optimal Schwarz waveform relaxation for the one-dimensional wave equation. (Méthodes de décomposition de domaines pour l’équation des ondes en dimension 1.) Zbl 0986.65088
Gander, Martin J.; Halpern, Laurence
2001
Overlapping Schwarz waveform relaxation for convection reaction diffusion problems. Zbl 1026.65082
Daoud, D. S.; Gander, M. J.
2002
Optimized domain decomposition methods for the spherical Laplacian. Zbl 1215.65186
Loisel, S.; Côté, J.; Gander, M. J.; Laayouni, L.; Qaddouri, A.
2010
Multitrace formulations and Dirichlet-Neumann algorithms. Zbl 1339.65227
Dolean, Victorita; Gander, Martin J.
2016
Block Jacobi for discontinuous Galerkin discretizations: no ordinary Schwarz methods. Zbl 1382.65394
Gander, Martin J.; Hajian, Soheil
2014
Methods of reflections: relations with Schwarz methods and classical stationary iterations, scalability and preconditioning. Zbl 1435.65224
Ciaramella, Gabriele; Gander, Martin J.; Halpern, Laurence; Salomon, Julien
2019
Iterative methods and preconditioners for systems of linear equations. Zbl 07515819
Ciaramella, Gabriele; Gander, Martin J.
2022
Modeling and analysis of the coupling in discrete fracture matrix models. Zbl 1473.65338
Gander, Martin J.; Hennicker, Julian; Masson, Roland
2021
Dirichlet-Neumann waveform relaxation methods for parabolic and hyperbolic problems in multiple subdomains. Zbl 1466.65111
Gander, Martin J.; Kwok, Felix; Mandal, Bankim C.
2021
Closed form dispersion corrections including a real shifted wavenumber for finite difference discretizations of 2D constant coefficient Helmholtz problems. Zbl 1464.35064
Cocquet, Pierre-Henri; Gander, Martin J.; Xiang, Xueshuang
2021
Discrete optimization of Robin transmission conditions for anisotropic diffusion with discrete duality finite volume methods. Zbl 1482.65224
Gander, Martin J.; Halpern, Laurence; Hubert, Florence; Krell, Stella
2021
PARAOPT: a parareal algorithm for optimality systems. Zbl 1451.49034
Gander, Martin J.; Kwok, Felix; Salomon, Julien
2020
Multilevel optimized Schwarz methods. Zbl 1475.65212
Gander, Martin J.; Vanzan, Tommaso
2020
A continuous analysis of Neumann-Neumann methods: scalability and new coarse spaces. Zbl 1456.65175
Chaouqui, Faycal; Gander, Martin J.; Santugini-Repiquet, Kévin
2020
Exact BDF stability angles with Maple. Zbl 1451.65093
Gander, Martin J.; Wanner, Gerhard
2020
Optimized overlapping DDFV Schwarz algorithms. Zbl 1454.65180
Gander, Martin J.; Halpern, Laurence; Hubert, Florence; Krell, Stella
2020
A diagonalization-based parareal algorithm for dissipative and wave propagation problems. Zbl 1475.65098
Gander, Martin J.; Wu, Shu-Lin
2020
A class of iterative solvers for the Helmholtz equation: factorizations, sweeping preconditioners, source transfer, single layer potentials, polarized traces, and optimized Schwarz methods. Zbl 1417.65216
Gander, Martin J.; Zhang, Hui
2019
A direct time parallel solver by diagonalization for the wave equation. Zbl 1407.65175
Gander, Martin J.; Halpern, Laurence; Rannou, Johann; Ryan, Juliette
2019
A superlinear convergence estimate for the parareal Schwarz waveform relaxation algorithm. Zbl 1414.65018
Gander, Martin J.; Jiang, Yao-Lin; Song, Bo
2019
Convergence analysis of a periodic-like waveform relaxation method for initial-value problems via the diagonalization technique. Zbl 1472.65083
Gander, Martin J.; Wu, Shu-Lin
2019
Heterogeneous optimized Schwarz methods for second order elliptic PDEs. Zbl 1428.65105
Gander, Martin J.; Vanzan, Tommaso
2019
A new parareal algorithm for problems with discontinuous sources. Zbl 1439.65075
Gander, Martin J.; Kulchytska-Ruchka, Iryna; Niyonzima, Innocent; Schöps, Sebastian
2019
Methods of reflections: relations with Schwarz methods and classical stationary iterations, scalability and preconditioning. Zbl 1435.65224
Ciaramella, Gabriele; Gander, Martin J.; Halpern, Laurence; Salomon, Julien
2019
An introduction to multi-trace formulations and associated domain decomposition solvers. Zbl 1404.65302
Claeys, X.; Dolean, V.; Gander, M. J.
2019
Analysis of the parallel Schwarz method for growing chains of fixed-sized subdomains. II. Zbl 1435.65223
Ciaramella, Gabriele; Gander, Martin J.
2018
On the scalability of classical one-level domain-decomposition methods. Zbl 1406.65128
Chaouqui, F.; Ciaramella, G.; Gander, M. J.; Vanzan, T.
2018
Analysis of the parallel Schwarz method for growing chains of fixed-sized subdomains. III. Zbl 1404.65301
Ciaramella, Gabriele; Gander, Martin J.
2018
A finite difference method with optimized dispersion correction for the Helmholtz equation. Zbl 1443.65280
Cocquet, Pierre-Henri; Gander, Martin J.; Xiang, Xueshuang
2018
Complete, optimal and optimized coarse spaces for additive Schwarz. Zbl 1450.65157
Gander, Martin J.; Song, Bo
2018
Does SHEM for additive Schwarz work better than predicted by its condition number estimate? Zbl 1443.65415
Bjørstad, Petter E.; Gander, Martin J.; Loneland, Atle; Rahman, Talal
2018
A nonlinear ParaExp algorithm. Zbl 1443.65094
Gander, Martin J.; Güttel, Stefan; Petcu, Madalina
2018
Heterogeneous optimized Schwarz methods for coupling Helmholtz and Laplace equations. Zbl 1450.65158
Gander, Martin J.; Vanzan, Tommaso
2018
Analysis of Schwarz methods for a hybridizable discontinuous Galerkin discretization: the many-subdomain case. Zbl 1402.65144
Gander, Martin J.; Hajian, Soheil
2018
A coarse space to remove the logarithmic dependency in Neumann-Neumann methods. Zbl 1443.65418
Chaouqui, Faycal; Gander, Martin J.; Santugini-Repiquet, Kévin
2018
On optimal coarse spaces for domain decomposition and their approximation. Zbl 1443.65424
Gander, Martin J.; Halpern, Laurence; Santugini-Repiquet, Kévin
2018
Optimized Schwarz methods for advection diffusion equations in bounded domains. Zbl 1427.65403
Gander, Martin J.; Vanzan, Tommaso
2018
Optimal coarse spaces for FETI and their approximation. Zbl 1427.65400
Chaouqui, Faycal; Gander, Martin J.; Santugini-Repiquet, Kévin
2018
Multiscale analysis of heterogeneous domain decomposition methods for time-dependent advection-reaction-diffusion problems. Zbl 1394.65096
Gander, Martin J.; Halpern, Laurence; Martin, Véronique
2018
Asymptotic analysis of optimized Schwarz methods for Maxwell’s equations with discontinuous coefficients. Zbl 1417.65215
Dolean, Victorita; Gander, Martin J.; Veneros, Erwin
2018
Numerical analysis of partial differential equations using Maple and MATLAB. Zbl 1459.65001
Gander, Martin J.; Kwok, Felix
2018
Analysis of the shifted Helmholtz expansion preconditioner for the Helmholtz equation. Zbl 1443.65321
Cocquet, Pierre-Henri; Gander, Martin J.
2018
Convergence of substructuring methods for elliptic optimal control problems. Zbl 1443.65425
Gander, Martin J.; Kwok, Felix; Mandal, Bankim C.
2018
Restrictions on the use of sweeping type preconditioners for Helmholtz problems. Zbl 1450.65159
Gander, Martin J.; Zhang, Hui
2018
How large a shift is needed in the shifted Helmholtz preconditioner for its effective inversion by multigrid? Zbl 1365.65269
Cocquet, Pierre-Henri; Gander, Martin J.
2017
Optimized Schwarz methods with nonoverlapping circular domain decomposition. Zbl 1355.65167
Gander, Martin J.; Xu, Yingxiang
2017
SHEM: an optimal coarse space for RAS and its multiscale approximation. Zbl 1367.65183
Gander, Martin J.; Loneland, Atle
2017
Analysis of the parallel Schwarz method for growing chains of fixed-sized subdomains. I. Zbl 1366.65111
Ciaramella, G.; Gander, M. J.
2017
Time parallelization for nonlinear problems based on diagonalization. Zbl 1367.65118
Gander, Martin J.; Halpern, Laurence
2017
On nilpotent subdomain iterations. Zbl 1367.65148
Chaouqui, Faycal; Gander, Martin J.; Santugini-Repiquet, Kévin
2017
On the definition of Dirichlet and Neumann conditions for the biharmonic equation and its impact on associated Schwarz methods. Zbl 1367.65182
Gander, Martin J.; Liu, Yongxiang
2017
Optimized Schwarz methods for domain decompositions with parabolic interfaces. Zbl 1367.65184
Gander, Martin J.; Xu, Yingxiang
2017
On the origins of linear and non-linear preconditioning. Zbl 1367.65042
Gander, Martin J.
2017
Analysis of a new space-time parallel multigrid algorithm for parabolic problems. Zbl 1342.65225
Gander, Martin J.; Neumüller, Martin
2016
Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms for parabolic problems. Zbl 1355.65128
Gander, Martin J.; Kwok, Felix; Mandal, Bankim C.
2016
Nonlinear preconditioning: how to use a nonlinear Schwarz method to precondition Newton’s method. Zbl 1352.65326
Dolean, V.; Gander, M. J.; Kheriji, W.; Kwok, F.; Masson, R.
2016
Optimized Schwarz waveform relaxation for advection reaction diffusion equations in two dimensions. Zbl 1356.65225
Bennequin, Daniel; Gander, Martin J.; Gouarin, Loic; Halpern, Laurence
2016
Cross-points in domain decomposition methods with a finite element discretization. Zbl 1347.65187
Gander, Martin J.; Santugini, Kévin
2016
A direct solver for time parallelization. Zbl 1339.65114
Gander, Martin J.; Halpern, Laurence; Ryan, Juliet; Thuy Thi Bich Tran
2016
Analysis of a new dimension-wise splitting iteration with selective relaxation for saddle point problems. Zbl 1342.76074
Gander, Martin J.; Niu, Qiang; Xu, Yingxiang
2016
Dirichlet-Neumann and Neumann-Neumann waveform relaxation for the wave equation. Zbl 1339.65165
Gander, Martin J.; Kwok, Felix; Mandal, Bankim C.
2016
Optimized Schwarz methods with overlap for the Helmholtz equation. Zbl 1351.65094
Gander, Martin J.; Zhang, Hui
2016
Optimized Schwarz methods for model problems with continuously variable coefficients. Zbl 1348.65138
Gander, Martin J.; Xu, Yingxiang
2016
Schwarz methods for the time-parallel solution of parabolic control problems. Zbl 1369.65080
Gander, Martin J.; Kwok, Felix
2016
Optimized Schwarz method with two-sided transmission conditions in an unsymmetric domain decomposition. Zbl 1339.65234
Gander, Martin J.; Xu, Yingxiang
2016
On the minimal shift in the shifted Laplacian preconditioner for multigrid to work. Zbl 1339.65231
Cocquet, Pierre-Henri; Gander, Martin J.
2016
On the relation between optimized Schwarz methods and source transfer. Zbl 1339.65230
Chen, Zhiming; Gander, Martin J.; Zhang, Hui
2016
A new algorithm based on factorization for heterogeneous domain decomposition. Zbl 1350.65108
Gander, Martin J.; Halpern, Laurence; Martin, Véronique
2016
Multitrace formulations and Dirichlet-Neumann algorithms. Zbl 1339.65227
Dolean, Victorita; Gander, Martin J.
2016
Schwarz methods for second order Maxwell equations in 3D with coefficient jumps. Zbl 1342.78043
Dolean, Victorita; Gander, Martin J.; Veneros, Erwin
2016
DDFV ventcell Schwarz algorithms. Zbl 1339.65233
Gander, Martin J.; Halpern, Laurence; Hubert, Florence; Krell, Stella
2016
Domain decomposition methods in science and engineering XXII. Proceedings of the 22nd international conference on domain decomposition methods, Lugano, Switzerland, September 16–20, 2013. Zbl 1344.65005
2016
50 years of time parallel time integration. Zbl 1337.65127
Gander, Martin J.
2015
Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: What is the largest shift for which wavenumber-independent convergence is guaranteed? Zbl 1328.65238
Gander, M. J.; Graham, I. G.; Spence, E. A.
2015
Optimized Schwarz methods for a diffusion problem with discontinuous coefficient. Zbl 1314.65155
Gander, Martin J.; Dubois, Olivier
2015
Effective transmission conditions for domain decomposition methods applied to the time-harmonic curl-curl Maxwell’s equations. Zbl 1349.78064
Dolean, Victorita; Gander, Martin J.; Lanteri, Stephane; Lee, Jin-Fa; Peng, Zhen
2015
Analysis of Schwarz methods for a hybridizable discontinuous Galerkin discretization. Zbl 1312.65190
Gander, Martin J.; Hajian, Soheil
2015
On the positivity of Poisson integrators for the Lotka-Volterra equations. Zbl 1321.65184
Beck, Mélanie; Gander, Martin J.
2015
B-methods for the numerical solution of evolution problems with blow-up solutions. I: Variation of the constant. Zbl 1329.65303
Beck, Mélanie; Gander, Martin J.; Kwok, Felix
2015
Discontinuous Galerkin discretizations of optimized Schwarz methods for solving the time-harmonic Maxwell’s equations. Zbl 1330.65177
El Bouajaji, Mohamed; Dolean, Victorita; Gander, Martin J.; Lanteri, Stéphane; Perrussel, Ronan
2015
Continuous analysis of the additive Schwarz method: a stable decomposition in $$H^1$$ with explicit constants. Zbl 1320.65190
Gander, Martin J.; Halpern, Laurence; Santugini, Kévin
2015
Analysis for parareal algorithms applied to Hamiltonian differential equations. Zbl 1291.65209
Gander, Martin J.; Hairer, Ernst
2014
Optimized Schwarz methods for circular domain decompositions with overlap. Zbl 1304.65261
Gander, Martin J.; Xu, Yingxiang
2014
Scientific computing. An introduction using Maple and MATLAB. Zbl 1296.65001
Gander, Walter; Gander, Martin J.; Kwok, Felix
2014
A new coarse grid correction for RAS/AS. Zbl 1382.65438
Gander, Martin J.; Halpern, Laurence; Repiquet, Kévin Santugini
2014
Optimization of transmission conditions in waveform relaxation techniques for RC circuits. Zbl 1300.94127
Al-Khaleel, Mohammad D.; Gander, Martin J.; Ruehli, Albert E.
2014
Discontinuous coarse spaces for DD-methods with discontinuous iterates. Zbl 1382.65439
Gander, Martin J.; Halpern, Laurence; Repiquet, Kévin Santugini
2014
Optimized Schwarz methods with overlap for the Helmholtz equation. Zbl 1382.65442
Gander, Martin J.; Zhang, Hui
2014
Block Jacobi for discontinuous Galerkin discretizations: no ordinary Schwarz methods. Zbl 1382.65394
Gander, Martin J.; Hajian, Soheil
2014
Optimized Schwarz methods for Maxwell equations with discontinuous coefficients. Zbl 1383.78045
Dolean, Victorita; Gander, Martin J.; Veneros, Erwin
2014
A mathematical analysis of optimized waveform relaxation for a small RC circuit. Zbl 1290.65058
Al-Khaleel, Mohammad; Gander, Martin J.; Ruehli, Albert E.
2014
Constrained optimization: from Lagrangian mechanics to optimal control and PDE constraints. Zbl 1320.49003
Gander, Martin J.; Kwok, Felix; Wanner, Gerhard
2014
On the influence of curvature on transmission conditions. Zbl 1382.65433
Barucq, Hélène; Gander, Martin J.; Xu, Yingxiang
2014
Optimized Schwarz algorithms in the framework of DDFV schemes. Zbl 1382.65359
Gander, Martin J.; Hubert, Florence; Krell, Stella
2014
Block Jacobi relaxation for plane wave discontinuous Galerkin methods. Zbl 1382.65377
Betcke, T.; Gander, M. J.; Phillips, J.
2014
Optimized Schwarz methods for curl-curl time-harmonic Maxwell’s equations. Zbl 1383.78046
Dolean, Victorita; Gander, Martin J.; Lanteri, Stéphane; Lee, Jin-Fa; Peng, Zhen
2014
Domain decomposition methods in science and engineering XXI. Proceedings of the 21st international conference, Inria Rennes Center, France, June 25–29, 2012. Zbl 1381.65002
2014
Walter Gautschi, Volume 3. Selected works with commentaries. Edited by Claude Brezinski and Ahmed Sameh. Zbl 1292.01007
Gautschi, Walter
2014
DG discretization of optimized Schwarz methods for Maxwell’s equations. Zbl 1383.78038
El Bouajaji, Mohamed; Dolean, Victorita; Gander, Martin J.; Lanteri, Stéphane; Perrussel, Ronan
2014
Fuzzy domain decomposition: a new perspective on heterogeneous DD methods. Zbl 1382.65440
Gander, Martin J.; Michaud, Jérôme
2014
PARAEXP: a parallel integrator for linear initial-value problems. Zbl 1266.65123
Gander, Martin J.; Güttel, Stefan
2013
Analysis of two parareal algorithms for time-periodic problems. Zbl 1283.65077
Gander, Martin J.; Jiang, Yao-Lin; Song, Bo; Zhang, Hui
2013
Algorithm 932: PANG: software for nonmatching grid projections in 2D and 3D with linear complexity. Zbl 1295.65120
Gander, Martin J.; Japhet, Caroline
2013
Multigrid methods for Helmholtz problems: a convergent scheme in 1D using standard components. Zbl 1287.65133
Ernst, Oliver G.; Gander, Martin J.
2013
Optimization of Schwarz waveform relaxation over short time windows. Zbl 1273.65135
Courvoisier, Yves; Gander, Martin J.
2013
Derivation of the isotropic diffusion source approximation (IDSA) for supernova neutrino transport by asymptotic expansions. Zbl 1307.35181
Berninger, H.; Frénod, E.; Gander, M.; Liebendörfer, M.; Michaud, J.
2013
...and 71 more Documents
all top 5

### Cited by 1,419 Authors

 81 Gander, Martin Jakob 32 Wu, Shulin 26 Magoulès, Frédéric 21 Antoine, Xavier 21 Halpern, Laurence 19 Dolean, Victorita 19 Jiang, Yaolin 18 Spence, Euan A. 17 Geuzaine, Christophe A. 15 Xu, Yingxiang 14 Nataf, Frédéric 12 Kwok, Felix 11 Lorin, Emmanuel 11 Maday, Yvon 10 Ciaramella, Gabriele 10 Graham, Ivan G. 10 Tournier, Pierre-Henri 9 Haynes, Ronald D. 9 Jolivet, Pierre 9 Langer, Ulrich 9 Neumüller, Martin 8 Cao, Yang 8 Claeys, Xavier 8 Huang, Ting-Zhu 8 Japhet, Caroline 8 Krause, Rolf H. 8 Loisel, Sébastien 8 Schroder, Jacob B. 8 Vuik, Cornelis 8 Wu, Yujiang 8 Yang, Aili 7 Cai, Xiao-Chuan 7 Hoang, Thi-Thao-Phuong 7 Tran, Minh-Binh 7 Vanzan, Tommaso 7 Zhang, Hui 7 Zhou, Tao 6 Blayo, Eric 6 Boubendir, Yassine 6 Cocquet, Pierre-Henri 6 Falgout, Robert D. 6 Lanteri, Stéphane 6 Lee, Jin-Fa 6 Masson, Roland 6 Minion, Michael L. 6 Roux, François-Xavier 6 Santugini-Repiquet, Kévin 6 Song, Bo 6 Szyld, Daniel B. 5 Benzi, Michele 5 Bonazzoli, Marcella 5 Chaouqui, Faycal 5 Galkowski, Jeffrey 5 Ganesh, Mahadevan 5 Il’in, Valeriĭ Pavlovich 5 Ju, Lili 5 Karniadakis, George Em 5 Kern, Michel 5 Li, Liang 5 Rousseau, Antoine 5 Salomon, Julien 5 Southworth, Ben S. 5 Thierry, Bertrand 5 Vergara, Christian 5 Vohralík, Martin 4 Bai, Zhongzhi 4 Daoud, Daoud S. 4 Diele, Fasma 4 Dwarka, Vandana 4 Erlangga, Yogi A. 4 García Ramos, Luis 4 Gigante, Giacomo 4 Grigori, Laura 4 Guddati, Murthy N. 4 Guo, Xueping 4 He, Xiaoming 4 Keyes, David Elliot 4 Li, Junpu 4 Li, Shishun 4 Liu, Yongxiang 4 Mandal, Bankim C. 4 Marchand, Pierre 4 Miao, Zhen 4 Modave, Axel 4 Moiola, Andrea 4 Nabben, Reinhard 4 Ong, Benjamin W. 4 Peng, Zhen 4 Rodrigo, Carmen 4 Ruprecht, Daniel 4 Ryan, Juliette 4 Schöps, Sebastian 4 Series, Laurent 4 Stamm, Benjamin 4 Steinbach, Olaf 4 Toivanen, Jari 4 Wathen, Andrew John 4 Xiang, Xueshuang 4 Xu, Xuejun 4 Ying, Lexing ...and 1,319 more Authors
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### Cited in 141 Serials

 106 SIAM Journal on Scientific Computing 87 Journal of Computational Physics 58 Journal of Computational and Applied Mathematics 55 Computers & Mathematics with Applications 40 Computer Methods in Applied Mechanics and Engineering 38 Numerical Algorithms 35 Applied Numerical Mathematics 31 Journal of Scientific Computing 27 Numerische Mathematik 23 SIAM Journal on Numerical Analysis 22 Applied Mathematics and Computation 16 Mathematics of Computation 16 International Journal of Computer Mathematics 16 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 13 BIT 12 ETNA. Electronic Transactions on Numerical Analysis 10 Applied Mathematics Letters 9 International Journal for Numerical Methods in Engineering 9 SIAM Journal on Matrix Analysis and Applications 9 Applied Mathematical Modelling 9 SMAI Journal of Computational Mathematics 8 Computational Mechanics 8 Numerical Linear Algebra with Applications 8 Advances in Computational Mathematics 8 Computing and Visualization in Science 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 6 Computational Methods in Applied Mathematics 6 Discrete and Continuous Dynamical Systems. Series S 5 Linear Algebra and its Applications 5 Engineering Analysis with Boundary Elements 5 Communications in Computational Physics 4 Journal of Mathematical Analysis and Applications 4 Wave Motion 4 Computational and Applied Mathematics 4 Mathematical Problems in Engineering 4 Computational Geosciences 4 Multiscale Modeling & Simulation 4 Journal of Computational Acoustics 4 East Asian Journal on Applied Mathematics 3 Computers and Fluids 3 Calcolo 3 SIAM Journal on Mathematical Analysis 3 SIAM Review 3 Journal of Inequalities and Applications 3 Archives of Computational Methods in Engineering 3 Special Matrices 2 Computer Physics Communications 2 International Journal of Control 2 Journal of Engineering Mathematics 2 Journal of Mathematical Physics 2 Mathematical Biosciences 2 Mathematical Methods in the Applied Sciences 2 Journal of Differential Equations 2 Mathematics and Computers in Simulation 2 Quarterly of Applied Mathematics 2 SIAM Journal on Control and Optimization 2 Journal of Computational Mathematics 2 Numerical Methods for Partial Differential Equations 2 Japan Journal of Industrial and Applied Mathematics 2 SIAM Journal on Applied Mathematics 2 SIAM Journal on Optimization 2 Computational Optimization and Applications 2 Journal of Mathematical Sciences (New York) 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 2 Vietnam Journal of Mathematics 2 Abstract and Applied Analysis 2 Discrete and Continuous Dynamical Systems. Series B 2 Journal of Applied Mathematics 2 Journal of Numerical Mathematics 2 S$$\vec{\text{e}}$$MA Journal 1 Advances in Applied Probability 1 Applicable Analysis 1 Communications on Pure and Applied Mathematics 1 Inverse Problems 1 Journal of Mathematical Biology 1 ACM Transactions on Mathematical Software 1 Integral Equations and Operator Theory 1 Journal of Functional Analysis 1 Proceedings of the American Mathematical Society 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Applied Mathematics and Mechanics. (English Edition) 1 Parallel Computing 1 Mathematical and Computer Modelling 1 European Journal of Applied Mathematics 1 Annals of Operations Research 1 Journal of Global Optimization 1 Computational Mathematics and Mathematical Physics 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Opuscula Mathematica 1 Annals of Mathematics and Artificial Intelligence 1 Complexity 1 Journal of Vibration and Control 1 International Journal of Computational Fluid Dynamics 1 Differential Equations and Dynamical Systems 1 Optimization Methods & Software 1 Mathematical and Computer Modelling of Dynamical Systems ...and 41 more Serials
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### Cited in 46 Fields

 871 Numerical analysis (65-XX) 381 Partial differential equations (35-XX) 153 Fluid mechanics (76-XX) 71 Optics, electromagnetic theory (78-XX) 66 Mechanics of deformable solids (74-XX) 41 Calculus of variations and optimal control; optimization (49-XX) 38 Linear and multilinear algebra; matrix theory (15-XX) 31 Ordinary differential equations (34-XX) 21 Operations research, mathematical programming (90-XX) 20 Biology and other natural sciences (92-XX) 18 Computer science (68-XX) 17 Probability theory and stochastic processes (60-XX) 15 Geophysics (86-XX) 14 Systems theory; control (93-XX) 11 Classical thermodynamics, heat transfer (80-XX) 9 Operator theory (47-XX) 8 Dynamical systems and ergodic theory (37-XX) 8 Integral equations (45-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Statistical mechanics, structure of matter (82-XX) 7 Information and communication theory, circuits (94-XX) 6 Approximations and expansions (41-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 5 Real functions (26-XX) 5 Functions of a complex variable (30-XX) 5 Potential theory (31-XX) 5 Functional analysis (46-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Quantum theory (81-XX) 4 Special functions (33-XX) 4 Integral transforms, operational calculus (44-XX) 3 Difference and functional equations (39-XX) 3 Statistics (62-XX) 3 Mechanics of particles and systems (70-XX) 2 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Number theory (11-XX) 2 Differential geometry (53-XX) 2 Astronomy and astrophysics (85-XX) 2 Mathematics education (97-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Topological groups, Lie groups (22-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Relativity and gravitational theory (83-XX)

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