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## Le Bris, Claude

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 Author ID: le-bris.claude Published as: Le Bris, C.; Le Bris, Claude; LeBris, Claude; le Bris, C. External Links: MGP
 Documents Indexed: 136 Publications since 1992, including 9 Books
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#### Co-Authors

 13 single-authored 30 Blanc, Xavier 27 Legoll, Frédéric 27 Lions, Pierre-Louis 20 Cancès, Eric 19 Lelièvre, Tony 10 Gerbeau, Jean-Frédéric 8 Maday, Yvon 7 Catto, Isabelle 6 Jourdain, Benjamin 4 Costaouec, Ronan 4 Hager, William W. 3 Anantharaman, Arnaud 3 Barrault, Maxime 3 Bencteux, Guy 3 Defranceschi, Mireille 3 Madiot, François 3 Nguyen, Ngoc Cuong 3 Patera, Anthony T. 3 Thomines, Florian 3 Turinici, Gabriel 2 Auger, Anne 2 Bandrauk, André D. 2 Ben-Haj-Yedder, Adel 2 Benoit, David 2 Boyaval, Sébastien 2 Delfour, Michel Claude 2 Dobson, Matthew 2 Hauray, Maxime 2 He, Lingbing 2 Josien, Marc 2 Lozinski, Alexei 1 Atabek, O. 1 Bal, Guillaume 1 Bercovier, Michel 1 Cardaliaguet, Pierre 1 Castella, François 1 Chartier, Philippe 1 Dai, Xiaoying 1 Desjardins, Benoît 1 Dion, Claude M. 1 Engquist, Bjorn E. 1 Esteban, Maria J. 1 Faou, Erwan 1 Gati, Yousra 1 Gorynina, Olga Glebovna 1 Goubault, Eric 1 Hagedorn, George A. 1 Keller, Alexander 1 Kutzelnigg, Werner 1 Lasser, Caroline 1 Lemaire, Simon 1 Li, Kun 1 Luskin, Mitchell 1 Mennucci, Benedetta 1 Minvielle, William 1 Mirrahimi, Mazyar 1 Otto, Felix 1 Owhadi, Houman 1 Patz, Carsten 1 Pau, George Shu Heng 1 Perez, Danny 1 Pilot, Mathieu 1 Rabitz, Herschel A. 1 Schoenauer, Marc 1 Scuseria, Gustavo E. 1 Souganidis, Panagiotis E. 1 Tomasi, Jean-Christophe 1 Vanden-Eijnden, Eric
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#### Serials

 14 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 5 Multiscale Modeling & Simulation 5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 4 Differential and Integral Equations 4 Communications in Partial Differential Equations 4 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 3 Archive for Rational Mechanics and Analysis 3 Journal of Computational Physics 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Oberwolfach Reports 3 Networks and Heterogeneous Media 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Chinese Annals of Mathematics. Series B 2 Applied Mathematics Letters 2 Asymptotic Analysis 2 Advances in Differential Equations 2 Monte Carlo Methods and Applications 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 Discrete and Continuous Dynamical Systems. Series B 2 CRM Proceedings & Lecture Notes 2 Mathématiques & Applications (Berlin) 1 Computers and Fluids 1 Computer Methods in Applied Mechanics and Engineering 1 IMA Journal of Numerical Analysis 1 International Journal for Numerical Methods in Fluids 1 Nonlinearity 1 Bulletin des Sciences Mathématiques. Deuxième Série 1 Calcolo 1 Journal of Functional Analysis 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Numerische Mathematik 1 SIAM Journal on Numerical Analysis 1 Acta Mathematicae Applicatae Sinica. English Series 1 Constructive Approximation 1 Journal of Scientific Computing 1 Journal of Non-Newtonian Fluid Mechanics 1 Bulletin of the American Mathematical Society. New Series 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Notices of the American Mathematical Society 1 Journal of Nonlinear Science 1 SIAM Journal on Scientific Computing 1 Analele Universităţii din Craiova. Seria Matematică Informatică 1 Journal of Mathematical Chemistry 1 Markov Processes and Related Fields 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Archives of Computational Methods in Engineering 1 Milan Journal of Mathematics 1 Acta Numerica 1 Handbook of Numerical Analysis 1 Communications in Computational Physics 1 Kinetic and Related Models 1 Science China. Mathematics 1 Boletín de la Sociedad Española de Matemática Aplicada. S$$\vec{\text{e}}$$MA 1 Nonlinear Analysis. Theory, Methods & Applications 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 De Gruyter Series in Applied and Numerical Mathematics 1 Numerical Mathematics and Scientific Computation 1 Oxford Mathematical Monographs 1 Lecture Notes in Chemistry
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#### Fields

 75 Partial differential equations (35-XX) 43 Numerical analysis (65-XX) 35 Quantum theory (81-XX) 32 Statistical mechanics, structure of matter (82-XX) 28 Fluid mechanics (76-XX) 20 Mechanics of deformable solids (74-XX) 17 Probability theory and stochastic processes (60-XX) 8 General and overarching topics; collections (00-XX) 8 Dynamical systems and ergodic theory (37-XX) 8 Classical thermodynamics, heat transfer (80-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 Biology and other natural sciences (92-XX) 5 Ordinary differential equations (34-XX) 5 Mechanics of particles and systems (70-XX) 4 Systems theory; control (93-XX) 2 Operator theory (47-XX) 2 Computer science (68-XX) 2 Optics, electromagnetic theory (78-XX) 1 Nonassociative rings and algebras (17-XX) 1 Integral equations (45-XX) 1 Statistics (62-XX) 1 Relativity and gravitational theory (83-XX) 1 Operations research, mathematical programming (90-XX)

#### Citations contained in zbMATH Open

117 Publications have been cited 1,558 times in 962 Documents Cited by Year
Mathematical methods for the magnetohydrodynamics of liquid metals. Zbl 1107.76001
Gerbeau, Jean-Frédéric; Le Bris, Claude; Lelièvre, Tony
2006
From molecular models to continuum mechanics. Zbl 1028.74005
Blanc, X.; Le Bris, C.; Lions, P.-L.
2002
Existence and uniqueness of solutions to Fokker-Planck type equations with irregular coefficients. Zbl 1157.35301
Le Bris, C.; Lions, P.-L.
2008
Existence of solution for a density-dependent magnetohydrodynamic equation. Zbl 1023.35524
Gerbeau, J.-F.; Le Bris, C.
1997
Existence of solution for a micro-macro model of polymeric fluid: The FENE model. Zbl 1047.76004
Jourdain, Benjamin; Lelièvre, Tony; Le Bris, Claude
2004
From atoms to crystals: a mathematical journey. Zbl 1136.81371
Le Bris, Claude; Lions, Pierre-Louis
2005
Renormalized solutions of some transport equations with partially $$W^{1,1}$$ velocities and applications. Zbl 1170.35364
Le Bris, C.; Lions, P.-L.
2004
Reduced basis techniques for stochastic problems. Zbl 1269.65005
Boyaval, S.; Le Bris, C.; Lelièvre, T.; Maday, Y.; Nguyen, N. C.; Patera, A. T.
2010
Remarks on a nonhomogeneous model of magnetohydrodynamics. Zbl 1067.76097
Desjardins, B.; Le Bris, C.
1998
Computational quantum chemistry: a primer. Zbl 1070.81534
Cancès, Eric; Defranceschi, Mireille; Kutzelnigg, Werner; Le Bris, Claude; Maday, Yvon
2003
On the thermodynamic limit for Hartree-Fock type models. Zbl 0994.35115
Catto, I.; Le Bris, C.; Lions, P.-L.
2001
The mathematical theory of thermodynamic limits: Thomas-Fermi type models. Zbl 0938.81001
Catto, Isabelle; Le Bris, Claude; Lions, Pierre-Louis
1998
Long-time asymptotics of a multiscale model for polymeric fluid flows. Zbl 1089.76006
Jourdain, Benjamin; Le Bris, Claude; Lelièvre, Tony; Otto, Félix
2006
Results and questions on a nonlinear approximation approach for solving high-dimensional partial differential equations. Zbl 1191.65156
Le Bris, C.; Lelièvre, T.; Maday, Y.
2009
The energy of some microscopic stochastic lattices. Zbl 1173.82308
Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis
2007
Spurious velocities in the steady flow of an incompressible fluid subjected to external forces. Zbl 0893.76041
Gerbeau, J.-F.; Le Bris, C.; Bercovier, M.
1997
A reduced basis approach for variational problems with stochastic parameters: application to heat conduction with variable Robin coefficient. Zbl 1230.80013
Boyaval, Sébastien; Le Bris, Claude; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T.
2009
Stochastic homogenization and random lattices. Zbl 1129.60055
Blanc, X.; Le Bris, C.; Lions, P.-L.
2007
On some periodic Hartree-type models for crystals. Zbl 1005.81101
Catto, I.; Le Bris, C.; Lions, P.-L.
2002
Computational chemistry from the perspective of numerical analysis. Zbl 1119.65390
Le Bris, Claude
2005
Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics. Zbl 1330.74066
Blanc, Xavier; Le Bris, Claude; Legoll, Frédéric
2005
On the convergence of SCF algorithms for the Hartree-Fock equations. Zbl 1090.65548
Cancès, Eric; Le Bris, Claude
2000
An MsFEM type approach for perforated domains. Zbl 1316.35021
Le Bris, Claude; Legoll, Frédéric; Lozinski, Alexei
2014
Atomistic to continuum limits for computational materials science. Zbl 1144.82018
Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis
2007
On the time-dependent Hartree-Fock equations coupled with a classical nuclear dynamics. Zbl 1011.81087
Cancès, Eric; Le Bris, Claude
1999
Handbook of Numerical Analysis X. Special volume: Computational chemistry. Zbl 1052.81001
Le Bris, Claude (ed.)
2003
A definition of the ground state energy for systems composed of infinitely many particles. Zbl 1035.82004
Blanc, X.; Le Bris, C.; Lions, P. L.
2003
Symmetric parareal algorithms for Hamiltonian systems. Zbl 1269.65133
Dai, Xiaoying; Le Bris, Claude; Legoll, Frédéric; Maday, Yvon
2013
A variant of stochastic homogenization theory for elliptic operators. Zbl 1103.35014
Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis
2006
Numerical analysis of micro-macro simulations of polymeric fluid flows: A simple case. Zbl 1041.76003
Jourdain, Benjamin; Lelièvre, Tony; Le Bris, Claude
2002
Multiscale modelling of complex fluids: a mathematical initiation. Zbl 1157.76002
Le Bris, Claude; Lelièvre, Tony
2009
Simulations of MHD flows with moving interfaces. Zbl 1118.76359
Gerbeau, J.-F.; Lelièvre, T.; Le Bris, C.
2003
Bilinear optimal control of a Schrödinger equation. Zbl 0953.49005
Cancès, Eric; Le Bris, Claude; Pilot, Mathieu
2000
A numerical approach related to defect-type theories for some weakly random problems in homogenization. Zbl 1233.35014
Anantharaman, A.; Le Bris, C.
2011
A general approach for multiconfiguration methods in quantum molecular chemistry. Zbl 0837.35005
Le Bris, Claude
1994
MsFEM à la Crouzeix-Raviart for highly oscillatory elliptic problems. Zbl 1275.35021
Le Bris, Claude; Legoll, Frédéric; Lozinski, Alexei
2013
Elements of mathematical foundations for numerical approaches for weakly random homogenization problems. Zbl 1373.35027
Anantharaman, A.; Le Bris, C.
2012
A possible homogenization approach for the numerical simulation of periodic microstructures with defects. Zbl 1255.74051
Blanc, X.; Le Bris, C.; Lions, P.-L.
2012
A mathematical formalization of the parallel replica dynamics. Zbl 1243.82045
Le Bris, Claude; Lelièvre, Tony; Luskin, Mitchell; Perez, Danny
2012
On a variance reduction technique for micro–macro simulations of polymeric fluids. Zbl 1143.76333
Jourdain, Benjamin; Le Bris, Claude; Lelièvre, Tony
2004
A coupled system arising in magnetohydrodynamics. Zbl 0959.76092
Gerbeau, J.-F.; Le Bris, C.
1999
Mathematical modeling of point defects in materials science. Zbl 1282.35035
Cancès, Eric; Le Bris, Claude
2013
Some numerical approaches for weakly random homogenization. Zbl 1311.74101
Le Bris, Claude
2010
Variance reduction in stochastic homogenization using antithetic variables. Zbl 1260.35260
Blanc, X.; Costaouec, R.; Le Bris, C.; Legoll, F.
2012
Improving on computation of homogenized coefficients in the periodic and quasi-periodic settings. Zbl 1262.65115
Blanc, Xavier; Le Bris, Claude
2010
Periodicity of the infinite-volume ground state of a one-dimensional quantum model. Zbl 0992.82043
Blanc, X.; Le Bris, C.
2002
Convergence of molecular models to continuum mechanics models. Zbl 0986.74006
Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis
2001
Multiscale finite element approach for “weakly” random problems and related issues. Zbl 1300.65007
Le Bris, Claude; Legoll, Frédéric; Thomines, Florian
2014
Micro-macro models for viscoelastic fluids: modelling, mathematics and numerics. Zbl 1377.76006
Le Bris, Claude; Lelièvre, Tony
2012
Some results on the Thomas-Fermi-Dirac-von Weizsäcker model. Zbl 0828.49024
Le Bris, C.
1993
Local profiles for elliptic problems at different scales: defects in, and interfaces between periodic structures. Zbl 1333.35003
Blanc, X.; Le Bris, C.; Lions, P.-L.
2015
Variance reduction in stochastic homogenization: proof of concept, using antithetic variables. Zbl 1242.60039
Costaouec, Ronan; Le Bris, Claude; Legoll, Frédéric
2010
Finite-temperature coarse-graining of one-dimensional models: mathematical analysis and computational approaches. Zbl 1204.37081
Blanc, X.; Le Bris, C.; Legoll, F.; Patz, C.
2010
Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics: the convex case. Zbl 1177.65091
Blanc, Xavier; Le Bris, Claude; Legoll, Frédéric
2007
Feasibility and competitiveness of a reduced basis approach for rapid electronic structure calculations in quantum chemistry. Zbl 1330.81022
Cancès, Éric; Le Bris, Claude; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T.; Pau, George Shu Heng
2007
On the thermodynamic limit for Hartree and Hartree-Fock type models. Zbl 0919.35142
Catto, Isabelle; Le Bris, Claude; Lions, Pierre-Louis
1998
Thermodynamic limit for Thomas-Fermi type models. Zbl 0849.35114
Catto, Isabelle; Le Bris, Claude; Lions, Pierre-Louis
1996
Special quasirandom structures: a selection approach for stochastic homogenization. Zbl 1334.35450
Le Bris, Claude; Legoll, Frédéric; Minvielle, William
2016
Variance reduction in stochastic homogenization: the technique of antithetic variables. Zbl 1245.65050
Blanc, Xavier; Costaouec, Ronan; Le Bris, Claude; Legoll, Frédéric
2012
Homogenization of a weakly randomly perturbed periodic material. Zbl 1193.35008
Anantharaman, Arnaud; Le Bris, Claude
2010
Two remarks on generalized flows for ordinary differential equations. Zbl 1132.34043
Hauray, Maxime; Le Bris, Claude; Lions, Pierre-Louis
2007
Mathematical models and methods for ab initio quantum chemistry. Zbl 0979.00023
Defranceschi, M. (ed.); Le Bris, C. (ed.)
2000
A reduced basis approach for some weakly stochastic multiscale problems. Zbl 1269.35002
Le Bris, Claude; Thomines, Florian
2012
Mathematical study of a coupled system arising in magnetohydrodynamics. Zbl 0995.35049
Gerbeau, J.-F.; Le Bris, C.
2001
Examples of computational approaches for elliptic, possibly multiscale PDEs with random inputs. Zbl 1406.35496
Le Bris, Claude; Legoll, Frédéric
2017
Analysis of some discretization schemes for constrained stochastic differential equations. Zbl 1142.65308
Lelièvre, Tony; Le Bris, Claude; Vanden-Eijnden, Eric
2008
Multilevel domain decomposition for electronic structure calculations. Zbl 1147.81021
Barrault, M.; Cancès, E.; Hager, W. W.; Le Bris, C.
2007
Discrete to continuum limit for some models of stochastic lattices of atoms. Zbl 1095.74006
Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis
2006
Convergence to equilibrium of a multiscale model for suspensions. Zbl 1107.35022
Cancès, Eric; Le Bris, Claude
2006
Mathematical methods in quantum chemistry. An introduction. Zbl 1167.81001
Cancès, Eric; Le Bris, Claude; Maday, Yvon
2006
Comparison between two numerical methods for a magnetostatic problem. Zbl 0969.78003
Gerbeau, J.-F.; Le Bris, C.
2000
On correctors for linear elliptic homogenization in the presence of local defects. Zbl 1423.35092
Blanc, X.; Le Bris, C.; Lions, P.-L.
2018
Well-posedness of a multiscale model for concentrated suspensions. Zbl 1236.35118
Cancès, Eric; Catto, Isabelle; Gati, Yousra; Le Bris, Claude
2005
Long-time averaging for integrable Hamiltonian dynamics. Zbl 1084.65126
Cancès, Eric; Castella, François; Chartier, Philippe; Faou, Erwan; Le Bris, Claude; Legoll, Frédéric; Turinici, Gabriel
2005
A definition of interface energies using atomistic models. Zbl 1117.74006
Blanc, Xavier; Le Bris, Claude
2005
Optimal laser control of molecular systems: Methodology and results. Zbl 1017.92050
Auger, A.; Ben Haj Yedder, A.; Cances, E.; Le Bris, C.; Dion, C. M.; Keller, A.; Atabek, O.
2002
Thomas-Fermi type theories for polymers and thin films. Zbl 1223.35263
Blanc, X.; Le Bris, C.
2000
Geometry optimization for Thomas-Fermi type theories for solids. Zbl 0932.35004
Blanc, Xavier; Le Bris, Claude
1999
A numerical comparison of some multiscale finite element approaches for advection-dominated problems in heterogeneous media. Zbl 1373.65083
Le Bris, Claude; Legoll, Frédéric; Madiot, François
2017
Some variance reduction methods for numerical stochastic homogenization. Zbl 1353.82006
Blanc, X.; Le Bris, C.; Legoll, F.
2016
Local profiles and elliptic problems at different scales with defects. Zbl 1312.35054
Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis
2015
Coarse approximation of an elliptic problme with higly oscillatory coefficients. Zbl 1270.35064
Le Bris, Claude; Legoll, Frédéric; Li, Kun
2013
Symplectic schemes for highly oscillatory Hamiltonian systems: The homogenization approach beyond the constant frequency case. Zbl 1261.65131
Dobson, Matthew; Le Bris, Claude; Legoll, Frédéric
2013
A new proof of the uniqueness of the flow for ordinary differential equations with $$BV$$ vector fields. Zbl 1227.34013
Hauray, Maxime; Le Bris, Claude
2011
Integrators for highly oscillatory Hamiltonian systems: an homogenization approach. Zbl 1259.37051
Le Bris, Claude; Legoll, Frédéric
2010
Numerical approximation of a class of problems in stochastic homogenization. Zbl 1180.65166
Costaouec, Ronan; Le Bris, Claude; Legoll, Frédéric
2010
Molecular simulation and related topics: some open mathematical problems. Zbl 1158.35100
Cancès, Eric; Le Bris, C.; Lions, P.-L.
2008
Derivation of simplectic numerical schemes for highly oscillatory Hamiltonian systems. Zbl 1110.65117
Le Bris, Claude; Legoll, Frédéric
2007
Towards reduced basis approaches in ab initio electronic structure computations. Zbl 0998.81122
Cancès, Eric; LeBris, Claude; Maday, Yvon; Turinici, Gabriel
2002
On the long time behaviour of the solution to the two-fluids incompressible Navier-Stokes equations. Zbl 1022.35038
Gerbeau, J.-F.; Le Bris, C.
1999
On the perturbation methods for some nonlinear quantum chemistry models. Zbl 1007.81073
Cancès, Eric; Le Bris, Claude
1998
Computing a molecule: A mathematical viewpoint. Zbl 0890.92026
Defranceschi, M.; le Bris, C.
1997
On the spin polarized Thomas-Fermi model with the Fermi-Amaldi correction. Zbl 0914.35112
Le Bris, Claude
1995
Local precised approximation in multiscale problems with local defects. Zbl 1411.35024
Blanc, Xavier; Josien, Marc; Le Bris, Claude
2019
On the best constant matrix approximating an oscillatory matrix-valued coefficient in divergence-form operators. Zbl 1419.35020
Le Bris, Claude; Legoll, Frédéric; Lemaire, Simon
2018
Homogenization theory and multiscale numerical approaches for disordered media: some recent contributions. Zbl 1331.35035
Le Bris, Claude
2014
Periodic long-time behaviour for an approximate model of nematic polymers. Zbl 1250.35031
He, Lingbing; Le Bris, Claude; Lelièvre, Tony
2012
Beyond multiscale and multiphysics: multimaths for model coupling. Zbl 1264.82099
Blanc, Xavier; Le Bris, Claude; Legoll, Frédéric; Lelièvre, Tony
2010
Domain decomposition and electronic structure computations: a promising approach. Zbl 1147.81022
Bencteux, Guy; Barrault, Maxime; Cancès, Eric; Hager, William W.; Le Bris, Claude
2008
Hamiltonian identification for quantum systems: well-posedness and numerical approaches. Zbl 1123.93040
Le Bris, Claude; Mirrahimi, Mazyar; Rabitz, Herschel; Turinici, Gabriel
2007
Precised approximations in elliptic homogenization beyond the periodic setting. Zbl 1442.35091
Blanc, X.; Josien, M.; Le Bris, C.
2020
Local precised approximation in multiscale problems with local defects. Zbl 1411.35024
Blanc, Xavier; Josien, Marc; Le Bris, Claude
2019
Parabolic equations with irregular data and related issues. Applications to stochastic differential equations. Zbl 07046231
Le Bris, Claude; Lions, Pierre-Louis
2019
On correctors for linear elliptic homogenization in the presence of local defects: the case of advection-diffusion. Zbl 1416.35092
Blanc, X.; Le Bris, Claude; Lions, P.-L.
2019
On correctors for linear elliptic homogenization in the presence of local defects. Zbl 1423.35092
Blanc, X.; Le Bris, C.; Lions, P.-L.
2018
On the best constant matrix approximating an oscillatory matrix-valued coefficient in divergence-form operators. Zbl 1419.35020
Le Bris, Claude; Legoll, Frédéric; Lemaire, Simon
2018
Examples of computational approaches for elliptic, possibly multiscale PDEs with random inputs. Zbl 1406.35496
Le Bris, Claude; Legoll, Frédéric
2017
A numerical comparison of some multiscale finite element approaches for advection-dominated problems in heterogeneous media. Zbl 1373.65083
Le Bris, Claude; Legoll, Frédéric; Madiot, François
2017
Special quasirandom structures: a selection approach for stochastic homogenization. Zbl 1334.35450
Le Bris, Claude; Legoll, Frédéric; Minvielle, William
2016
Some variance reduction methods for numerical stochastic homogenization. Zbl 1353.82006
Blanc, X.; Le Bris, C.; Legoll, F.
2016
Stabilization of non-coercive problems using the invariant measure. Zbl 1344.65113
Le Bris, Claude; Legoll, Frédéric; Madiot, François
2016
Local profiles for elliptic problems at different scales: defects in, and interfaces between periodic structures. Zbl 1333.35003
Blanc, X.; Le Bris, C.; Lions, P.-L.
2015
Local profiles and elliptic problems at different scales with defects. Zbl 1312.35054
Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis
2015
An MsFEM type approach for perforated domains. Zbl 1316.35021
Le Bris, Claude; Legoll, Frédéric; Lozinski, Alexei
2014
Multiscale finite element approach for “weakly” random problems and related issues. Zbl 1300.65007
Le Bris, Claude; Legoll, Frédéric; Thomines, Florian
2014
Homogenization theory and multiscale numerical approaches for disordered media: some recent contributions. Zbl 1331.35035
Le Bris, Claude
2014
Symmetric parareal algorithms for Hamiltonian systems. Zbl 1269.65133
Dai, Xiaoying; Le Bris, Claude; Legoll, Frédéric; Maday, Yvon
2013
MsFEM à la Crouzeix-Raviart for highly oscillatory elliptic problems. Zbl 1275.35021
Le Bris, Claude; Legoll, Frédéric; Lozinski, Alexei
2013
Mathematical modeling of point defects in materials science. Zbl 1282.35035
Cancès, Eric; Le Bris, Claude
2013
Coarse approximation of an elliptic problme with higly oscillatory coefficients. Zbl 1270.35064
Le Bris, Claude; Legoll, Frédéric; Li, Kun
2013
Symplectic schemes for highly oscillatory Hamiltonian systems: The homogenization approach beyond the constant frequency case. Zbl 1261.65131
Dobson, Matthew; Le Bris, Claude; Legoll, Frédéric
2013
Elements of mathematical foundations for numerical approaches for weakly random homogenization problems. Zbl 1373.35027
Anantharaman, A.; Le Bris, C.
2012
A possible homogenization approach for the numerical simulation of periodic microstructures with defects. Zbl 1255.74051
Blanc, X.; Le Bris, C.; Lions, P.-L.
2012
A mathematical formalization of the parallel replica dynamics. Zbl 1243.82045
Le Bris, Claude; Lelièvre, Tony; Luskin, Mitchell; Perez, Danny
2012
Variance reduction in stochastic homogenization using antithetic variables. Zbl 1260.35260
Blanc, X.; Costaouec, R.; Le Bris, C.; Legoll, F.
2012
Micro-macro models for viscoelastic fluids: modelling, mathematics and numerics. Zbl 1377.76006
Le Bris, Claude; Lelièvre, Tony
2012
Variance reduction in stochastic homogenization: the technique of antithetic variables. Zbl 1245.65050
Blanc, Xavier; Costaouec, Ronan; Le Bris, Claude; Legoll, Frédéric
2012
A reduced basis approach for some weakly stochastic multiscale problems. Zbl 1269.35002
Le Bris, Claude; Thomines, Florian
2012
Periodic long-time behaviour for an approximate model of nematic polymers. Zbl 1250.35031
He, Lingbing; Le Bris, Claude; Lelièvre, Tony
2012
From the Newton equation to the wave equation in some simple cases. Zbl 1259.35163
Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis
2012
A numerical approach related to defect-type theories for some weakly random problems in homogenization. Zbl 1233.35014
Anantharaman, A.; Le Bris, C.
2011
A new proof of the uniqueness of the flow for ordinary differential equations with $$BV$$ vector fields. Zbl 1227.34013
Hauray, Maxime; Le Bris, Claude
2011
Reduced basis techniques for stochastic problems. Zbl 1269.65005
Boyaval, S.; Le Bris, C.; Lelièvre, T.; Maday, Y.; Nguyen, N. C.; Patera, A. T.
2010
Some numerical approaches for weakly random homogenization. Zbl 1311.74101
Le Bris, Claude
2010
Improving on computation of homogenized coefficients in the periodic and quasi-periodic settings. Zbl 1262.65115
Blanc, Xavier; Le Bris, Claude
2010
Variance reduction in stochastic homogenization: proof of concept, using antithetic variables. Zbl 1242.60039
Costaouec, Ronan; Le Bris, Claude; Legoll, Frédéric
2010
Finite-temperature coarse-graining of one-dimensional models: mathematical analysis and computational approaches. Zbl 1204.37081
Blanc, X.; Le Bris, C.; Legoll, F.; Patz, C.
2010
Homogenization of a weakly randomly perturbed periodic material. Zbl 1193.35008
Anantharaman, Arnaud; Le Bris, Claude
2010
Integrators for highly oscillatory Hamiltonian systems: an homogenization approach. Zbl 1259.37051
Le Bris, Claude; Legoll, Frédéric
2010
Numerical approximation of a class of problems in stochastic homogenization. Zbl 1180.65166
Costaouec, Ronan; Le Bris, Claude; Legoll, Frédéric
2010
Beyond multiscale and multiphysics: multimaths for model coupling. Zbl 1264.82099
Blanc, Xavier; Le Bris, Claude; Legoll, Frédéric; Lelièvre, Tony
2010
Analysis of a quadratic programming decomposition algorithm. Zbl 1208.65082
Bencteux, G.; Cancés, E.; Hager, W. W.; Le Bris, C.
2010
Results and questions on a nonlinear approximation approach for solving high-dimensional partial differential equations. Zbl 1191.65156
Le Bris, C.; Lelièvre, T.; Maday, Y.
2009
A reduced basis approach for variational problems with stochastic parameters: application to heat conduction with variable Robin coefficient. Zbl 1230.80013
Boyaval, Sébastien; Le Bris, Claude; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T.
2009
Multiscale modelling of complex fluids: a mathematical initiation. Zbl 1157.76002
Le Bris, Claude; Lelièvre, Tony
2009
Existence and uniqueness of solutions to Fokker-Planck type equations with irregular coefficients. Zbl 1157.35301
Le Bris, C.; Lions, P.-L.
2008
Analysis of some discretization schemes for constrained stochastic differential equations. Zbl 1142.65308
Lelièvre, Tony; Le Bris, Claude; Vanden-Eijnden, Eric
2008
Molecular simulation and related topics: some open mathematical problems. Zbl 1158.35100
Cancès, Eric; Le Bris, C.; Lions, P.-L.
2008
Domain decomposition and electronic structure computations: a promising approach. Zbl 1147.81022
Bencteux, Guy; Barrault, Maxime; Cancès, Eric; Hager, William W.; Le Bris, Claude
2008
The energy of some microscopic stochastic lattices. Zbl 1173.82308
Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis
2007
Stochastic homogenization and random lattices. Zbl 1129.60055
Blanc, X.; Le Bris, C.; Lions, P.-L.
2007
Atomistic to continuum limits for computational materials science. Zbl 1144.82018
Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis
2007
Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics: the convex case. Zbl 1177.65091
Blanc, Xavier; Le Bris, Claude; Legoll, Frédéric
2007
Feasibility and competitiveness of a reduced basis approach for rapid electronic structure calculations in quantum chemistry. Zbl 1330.81022
Cancès, Éric; Le Bris, Claude; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T.; Pau, George Shu Heng
2007
Two remarks on generalized flows for ordinary differential equations. Zbl 1132.34043
Hauray, Maxime; Le Bris, Claude; Lions, Pierre-Louis
2007
Multilevel domain decomposition for electronic structure calculations. Zbl 1147.81021
Barrault, M.; Cancès, E.; Hager, W. W.; Le Bris, C.
2007
Derivation of simplectic numerical schemes for highly oscillatory Hamiltonian systems. Zbl 1110.65117
Le Bris, Claude; Legoll, Frédéric
2007
Hamiltonian identification for quantum systems: well-posedness and numerical approaches. Zbl 1123.93040
Le Bris, Claude; Mirrahimi, Mazyar; Rabitz, Herschel; Turinici, Gabriel
2007
Mathematical methods for the magnetohydrodynamics of liquid metals. Zbl 1107.76001
Gerbeau, Jean-Frédéric; Le Bris, Claude; Lelièvre, Tony
2006
Long-time asymptotics of a multiscale model for polymeric fluid flows. Zbl 1089.76006
Jourdain, Benjamin; Le Bris, Claude; Lelièvre, Tony; Otto, Félix
2006
A variant of stochastic homogenization theory for elliptic operators. Zbl 1103.35014
Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis
2006
Discrete to continuum limit for some models of stochastic lattices of atoms. Zbl 1095.74006
Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis
2006
Convergence to equilibrium of a multiscale model for suspensions. Zbl 1107.35022
Cancès, Eric; Le Bris, Claude
2006
Mathematical methods in quantum chemistry. An introduction. Zbl 1167.81001
Cancès, Eric; Le Bris, Claude; Maday, Yvon
2006
From atoms to crystals: a mathematical journey. Zbl 1136.81371
Le Bris, Claude; Lions, Pierre-Louis
2005
Computational chemistry from the perspective of numerical analysis. Zbl 1119.65390
Le Bris, Claude
2005
Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics. Zbl 1330.74066
Blanc, Xavier; Le Bris, Claude; Legoll, Frédéric
2005
Well-posedness of a multiscale model for concentrated suspensions. Zbl 1236.35118
Cancès, Eric; Catto, Isabelle; Gati, Yousra; Le Bris, Claude
2005
Long-time averaging for integrable Hamiltonian dynamics. Zbl 1084.65126
Cancès, Eric; Castella, François; Chartier, Philippe; Faou, Erwan; Le Bris, Claude; Legoll, Frédéric; Turinici, Gabriel
2005
A definition of interface energies using atomistic models. Zbl 1117.74006
Blanc, Xavier; Le Bris, Claude
2005
Coupling PDEs and SDEs: the illustrative example of the multiscale simulation of viscoelastic flows. Zbl 1077.76004
Jourdain, Benjamin; Le Bris, Claude; Leli\`vre, Tony
2005
An elementary argument regarding the long-time behavior of the solution to a stochastic differential equation. Zbl 1120.76003
Jourdain, Benjamin; Le Bris, Claude; Lelièvre, Tony
2005
Multi-scale analysis. Modeling and simulation. Zbl 1109.76002
Le Bris, Claude
2005
Existence of solution for a micro-macro model of polymeric fluid: The FENE model. Zbl 1047.76004
Jourdain, Benjamin; Lelièvre, Tony; Le Bris, Claude
2004
Renormalized solutions of some transport equations with partially $$W^{1,1}$$ velocities and applications. Zbl 1170.35364
Le Bris, C.; Lions, P.-L.
2004
On a variance reduction technique for micro–macro simulations of polymeric fluids. Zbl 1143.76333
Jourdain, Benjamin; Le Bris, Claude; Lelièvre, Tony
2004
Mathematical remarks on the optimized effective potential problem. Zbl 1224.35102
Ben-Haj-Yedder, Adel; Cances, Eric; Le Bris, Claude
2004
Modeling and simulation of the industrial production of aluminium: The nonlinear approach. Zbl 1100.76536
Gerbeau, J.-F.; Lelièvre, T.; Le Bris, C.
2004
Computational quantum chemistry: a primer. Zbl 1070.81534
Cancès, Eric; Defranceschi, Mireille; Kutzelnigg, Werner; Le Bris, Claude; Maday, Yvon
2003
Handbook of Numerical Analysis X. Special volume: Computational chemistry. Zbl 1052.81001
Le Bris, Claude (ed.)
2003
A definition of the ground state energy for systems composed of infinitely many particles. Zbl 1035.82004
Blanc, X.; Le Bris, C.; Lions, P. L.
2003
Simulations of MHD flows with moving interfaces. Zbl 1118.76359
Gerbeau, J.-F.; Lelièvre, T.; Le Bris, C.
2003
Quantum control: Mathematical and numerical challenges. CRM workshop, October 6–11, 2002, Montréal, Canada. Zbl 1030.00043
Bandrauk, André D. (ed.); Delfour, Michel C. (ed.); Le Bris, Claude (ed.)
2003
From molecular models to continuum mechanics. Zbl 1028.74005
Blanc, X.; Le Bris, C.; Lions, P.-L.
2002
On some periodic Hartree-type models for crystals. Zbl 1005.81101
Catto, I.; Le Bris, C.; Lions, P.-L.
2002
Numerical analysis of micro-macro simulations of polymeric fluid flows: A simple case. Zbl 1041.76003
Jourdain, Benjamin; Lelièvre, Tony; Le Bris, Claude
2002
Periodicity of the infinite-volume ground state of a one-dimensional quantum model. Zbl 0992.82043
Blanc, X.; Le Bris, C.
2002
Optimal laser control of molecular systems: Methodology and results. Zbl 1017.92050
Auger, A.; Ben Haj Yedder, A.; Cances, E.; Le Bris, C.; Dion, C. M.; Keller, A.; Atabek, O.
2002
Towards reduced basis approaches in ab initio electronic structure computations. Zbl 0998.81122
Cancès, Eric; LeBris, Claude; Maday, Yvon; Turinici, Gabriel
2002
Characterization of functions on $$\mathbb{R}^3$$ with bounded Newtonian potential. Zbl 0995.35028
Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis
2002
Numerical approaches for molecular simulation. Zbl 1056.81087
Le Bris, Claude
2002
On the thermodynamic limit for Hartree-Fock type models. Zbl 0994.35115
Catto, I.; Le Bris, C.; Lions, P.-L.
2001
Convergence of molecular models to continuum mechanics models. Zbl 0986.74006
Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis
2001
Mathematical study of a coupled system arising in magnetohydrodynamics. Zbl 0995.35049
Gerbeau, J.-F.; Le Bris, C.
2001
On the convergence of SCF algorithms for the Hartree-Fock equations. Zbl 1090.65548
Cancès, Eric; Le Bris, Claude
2000
Bilinear optimal control of a Schrödinger equation. Zbl 0953.49005
Cancès, Eric; Le Bris, Claude; Pilot, Mathieu
2000
Mathematical models and methods for ab initio quantum chemistry. Zbl 0979.00023
Defranceschi, M. (ed.); Le Bris, C. (ed.)
2000
Comparison between two numerical methods for a magnetostatic problem. Zbl 0969.78003
Gerbeau, J.-F.; Le Bris, C.
2000
Thomas-Fermi type theories for polymers and thin films. Zbl 1223.35263
Blanc, X.; Le Bris, C.
2000
Control theory applied to quantum chemistry: Some tracks. Zbl 0996.81116
Le Bris, Claude
2000
...and 17 more Documents
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#### Cited by 1,289 Authors

 55 Le Bris, Claude 26 Cancès, Eric 25 Legoll, Frédéric 24 Lelièvre, Tony 23 Ortner, Christoph 21 Blanc, Xavier 18 Lions, Pierre-Louis 16 Lewin, Mathieu 16 Luskin, Mitchell 16 Süli, Endre E. 14 He, Yinnian 13 Lu, Jianfeng 12 Chinesta, Francisco 12 E, Weinan 11 Röckner, Michael 11 Shaposhnikov, Stanislav V. 11 Wu, Shulin 11 Zhang, Guodong 10 Nouy, Anthony 9 Barrett, John W. 9 Braides, Andrea 9 Chung, Tsz Shun Eric 9 Cicalese, Marco 9 Efendiev, Yalchin R. 9 Ehrlacher, Virginie 8 Bogachev, Vladimir Igorevich 8 Dobson, Matthew 8 Jabin, Pierre-Emmanuel 8 Maday, Yvon 8 Masmoudi, Nader 7 Ammar, Amine 7 Beauchard, Karine 7 Chen, Huajie 7 Chen, Peng 7 Gloria, Antoine 7 Khoromskij, Boris N. 7 Linke, Alexander 7 Luo, Dejun 7 Nguyen, Ngoc Cuong 7 Shapeev, Alexander V. 7 Vasilyeva, Maria V. 6 Alicandro, Roberto 6 Boyaval, Sébastien 6 Fan, Jishan 6 Li, Yuan 6 Quarteroni, Alfio M. 6 Rozza, Gianluigi 6 Schmidt, Bernd 6 Schneider, Reinhold 5 Ambrosio, Luigi 5 An, Rong 5 Bardos, Claude Williams 5 Baudouin, Lucie 5 Chamoin, Ludovic 5 Cueto, Elias 5 Feng, Xinlong 5 Gerbeau, Jean-Frédéric 5 Lahbabi, Salma 5 Li, Yongsheng 5 Mauser, Norbert Julius 5 Panasenko, Grigory P. 5 Patera, Anthony T. 5 Samaey, Giovanni 5 Sharma, Basant Lal 5 Stoltz, Gabriel 5 Zhai, Xiaoping 5 Zhou, Aihui 4 Amirat, Youcef Aït 4 Borzì, Alfio 4 Catto, Isabelle 4 Chupin, Laurent 4 Ciuperca, Ionel Sorin 4 Dong, Xiaojing 4 He, Xiaoming 4 Hou, Thomas Yizhao 4 Jourdain, Benjamin 4 Knezevic, David J. 4 Komech, Aleksandr I. 4 Levitt, Antoine 4 Lévy, Guillaume 4 Lin, Fang Hua 4 Manita, Oxana A. 4 Mao, Shipeng 4 Martínez, José Mario 4 Minvielle, William 4 Moroz, Vitaly 4 Owhadi, Houman 4 Razafimandimby, Paul André 4 Ruf, Matthias 4 Schwab, Christoph 4 Su, Haiyan 4 Tan, Zhong 4 Theil, Florian 4 Wang, Jun 4 Wang, Yanjin 4 Wen, Zaiwen 4 Yang, Jinjin 4 Yang, Xiaofeng 4 Zhang, Pingwen 4 Zhang, Xicheng ...and 1,189 more Authors
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#### Cited in 204 Serials

 51 Archive for Rational Mechanics and Analysis 46 Computer Methods in Applied Mechanics and Engineering 46 Journal of Computational Physics 33 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 30 Journal of Differential Equations 30 Multiscale Modeling & Simulation 26 Journal of Scientific Computing 25 Journal of Mathematical Analysis and Applications 25 Comptes Rendus. Mathématique. Académie des Sciences, Paris 23 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 19 Journal de Mathématiques Pures et Appliquées. Neuvième Série 18 Journal of Computational and Applied Mathematics 16 SIAM Journal on Mathematical Analysis 15 Communications in Mathematical Physics 15 SIAM Journal on Scientific Computing 14 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 14 Applied Numerical Mathematics 13 Journal of Mathematical Physics 13 Numerische Mathematik 13 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 13 Communications in Partial Differential Equations 12 Computers & Mathematics with Applications 12 Calculus of Variations and Partial Differential Equations 11 Archives of Computational Methods in Engineering 9 Journal of Functional Analysis 8 Journal of Statistical Physics 8 Mathematics of Computation 7 Applicable Analysis 7 Journal of the Mechanics and Physics of Solids 7 Mathematical Methods in the Applied Sciences 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Nonlinear Analysis. Real World Applications 6 International Journal for Numerical Methods in Engineering 6 SIAM Journal on Numerical Analysis 6 Numerical Methods for Partial Differential Equations 6 Advances in Computational Mathematics 6 Foundations of Computational Mathematics 5 Computers and Fluids 5 Computer Physics Communications 5 Communications on Pure and Applied Mathematics 5 International Journal for Numerical Methods in Fluids 5 Nonlinearity 5 Advances in Mathematics 5 Applied Mathematics and Computation 5 Chinese Annals of Mathematics. Series B 5 Computational Mechanics 5 Applied Mathematics Letters 5 SIAM Journal on Applied Mathematics 5 Journal of Nonlinear Science 5 Continuum Mechanics and Thermodynamics 5 Journal of Mathematical Chemistry 5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 5 Science China. Mathematics 5 SIAM/ASA Journal on Uncertainty Quantification 4 Acta Applicandae Mathematicae 4 SIAM Journal on Matrix Analysis and Applications 4 Bulletin of the American Mathematical Society. New Series 4 Discrete and Continuous Dynamical Systems 4 Mathematical Problems in Engineering 4 Doklady Mathematics 4 Acta Mathematica Sinica. English Series 4 Discrete and Continuous Dynamical Systems. Series B 4 Networks and Heterogeneous Media 4 Discrete and Continuous Dynamical Systems. Series S 4 Kinetic and Related Models 3 Journal of Fluid Mechanics 3 BIT 3 Physica D 3 Acta Mathematicae Applicatae Sinica. English Series 3 Constructive Approximation 3 Journal of Non-Newtonian Fluid Mechanics 3 Stochastic Processes and their Applications 3 Journal of Dynamics and Differential Equations 3 Journal of Mathematical Sciences (New York) 3 Numerical Linear Algebra with Applications 3 Mathematics and Mechanics of Solids 3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 3 Annales Henri Poincaré 3 Journal of Evolution Equations 3 Communications on Pure and Applied Analysis 3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 The Annals of Probability 2 Automatica 2 Inventiones Mathematicae 2 Journal of Optimization Theory and Applications 2 Mathematics and Computers in Simulation 2 Memoirs of the American Mathematical Society 2 Quarterly of Applied Mathematics 2 Probability Theory and Related Fields 2 European Journal of Applied Mathematics 2 Potential Analysis 2 Computational Optimization and Applications 2 NoDEA. Nonlinear Differential Equations and Applications 2 Bulletin des Sciences Mathématiques 2 Mathematical Physics, Analysis and Geometry 2 Journal of Inequalities and Applications 2 Mathematical and Computer Modelling of Dynamical Systems 2 Journal of Mathematical Fluid Mechanics 2 European Journal of Mechanics. A. Solids ...and 104 more Serials
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#### Cited in 41 Fields

 509 Partial differential equations (35-XX) 346 Numerical analysis (65-XX) 286 Fluid mechanics (76-XX) 183 Statistical mechanics, structure of matter (82-XX) 151 Mechanics of deformable solids (74-XX) 120 Probability theory and stochastic processes (60-XX) 120 Quantum theory (81-XX) 71 Calculus of variations and optimal control; optimization (49-XX) 31 Ordinary differential equations (34-XX) 29 Dynamical systems and ergodic theory (37-XX) 25 Operator theory (47-XX) 25 Biology and other natural sciences (92-XX) 22 Optics, electromagnetic theory (78-XX) 20 Systems theory; control (93-XX) 18 Mechanics of particles and systems (70-XX) 17 Statistics (62-XX) 16 Global analysis, analysis on manifolds (58-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 15 Operations research, mathematical programming (90-XX) 11 Approximations and expansions (41-XX) 11 Functional analysis (46-XX) 11 Classical thermodynamics, heat transfer (80-XX) 9 Computer science (68-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Real functions (26-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 Integral equations (45-XX) 6 Information and communication theory, circuits (94-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Number theory (11-XX) 2 Group theory and generalizations (20-XX) 2 Difference and functional equations (39-XX) 2 Astronomy and astrophysics (85-XX) 1 Category theory; homological algebra (18-XX) 1 Potential theory (31-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 1 Relativity and gravitational theory (83-XX)