Edit Profile (opens in new tab) Patera, Anthony T. Compute Distance To: Compute Author ID: patera.anthony-t Published as: Patera, Anthony T.; Patera, A. T.; Patera, A.; Patera, Anthony Documents Indexed: 134 Publications since 1981 2 Contributions as Editor Co-Authors: 95 Co-Authors with 131 Joint Publications 2,551 Co-Co-Authors all top 5 Co-Authors 4 single-authored 34 Maday, Yvon 17 Rønquist, Einar M. 12 Huynh, Dinh Bao Phuong 12 Knezevic, David J. 12 Nguyen, Ngoc Cuong 9 Yano, Masayuki 7 Eftang, Jens L. 7 Orszag, Steven Alan 6 Urban, Karsten 6 Veroy, Karen 5 Fischer, Paul F. 5 Grepl, Martin A. 5 Machiels, Luc 5 Paraschivoiu, Marius 5 Rozza, Gianluigi 4 Cruz, Manuel E. 4 Ho, Lee-Wing 4 Karniadakis, George Em 4 Penn, James D. 4 Peraire, Jaume 4 Prud’homme, Christophe 4 Rovas, Dimitrios V. 4 Yeşilyurt, Serhat 3 Anagnostou, George 3 Bernardi, Christine 3 Ghaddar, Chahid K. 3 Le Bris, Claude 3 Liu, Gui-Rong 3 Taddei, Tommaso 3 Turinici, Gabriel 2 Ballani, Jonas 2 Benner, Peter 2 Boyaval, Sébastien 2 Deville, Michel O. 2 Dewey, Daniel 2 Korczak, Karol Z. 2 Magen, Michael 2 Nguyen, Loi 2 Ohlberger, Mario 2 Oliveira, Ivan B. 2 Peraire, Jaime 2 Smetana, Kathrin 1 Barrault, Maxime 1 Basdevant, Claude 1 Bègue, Catherine 1 Bhouri, Mohamed Aziz 1 Buffa, Annalisa 1 Cancès, Eric 1 Chakir, Rachida 1 Charpentier, Isabelle 1 Chen, Yanlai 1 Dapogny, Charles 1 Debit, Naïma 1 Fick, Lambert 1 Glas, Silke 1 Gurfinkel Castillo, Mariano E. 1 Haasdonk, Bernard 1 Hadjiconstantinou, Nicolas G. 1 Haldenwang, Pierre 1 Hesthaven, Jan S. 1 Hoang, K. C. 1 Hussaini, M. Yousuff 1 Huynh, Phuong 1 Japhet, Caroline 1 Jung, Nadine 1 Kambourides, Miltos E. 1 Khoo, Boo Cheong 1 Kopriva, David Alan 1 Lacroix, J. M. 1 Lam, Khin-Yong 1 Lelièvre, Tony 1 Lewis, Robert Michael 1 Lohmann, Boris 1 Mavriplis, Catherine 1 Mavriplis, Cathy 1 Meiron, Dan 1 Mikic, B. B. 1 Montavon, Jean-Baptiste 1 Mula, Olga 1 Mund, Ernest H. 1 Muñoz, Rafael 1 Orlandi, Paolo 1 Otto, John 1 Ouazzani, Jalil 1 Pantz, Olivier 1 Pau, George Shu Heng 1 Pau, S. H. 1 Pedercini, Matteo 1 Peterson, John W. 1 Peyret, Roger 1 Sorensen, Danny C. 1 Sulem, Catherine 1 Sulem, Pierre-Louis 1 Vallaghé, Sylvain 1 Zahm, Olivier all top 5 Serials 19 Computer Methods in Applied Mechanics and Engineering 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 SIAM Journal on Scientific Computing 7 Journal of Computational Physics 7 International Journal for Numerical Methods in Engineering 6 International Journal for Numerical Methods in Fluids 4 Journal of Scientific Computing 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Journal of Fluid Mechanics 3 Archives of Computational Methods in Engineering 2 Computers and Fluids 2 International Journal of Heat and Mass Transfer 2 Mathematical and Computer Modelling of Dynamical Systems 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 Communications on Pure and Applied Mathematics 1 Computers and Structures 1 Mathematics of Computation 1 Calcolo 1 Journal of Computational and Applied Mathematics 1 Mathematics and Computers in Simulation 1 Numerische Mathematik 1 Numerical Heat Transfer 1 Applied Numerical Mathematics 1 Finite Elements in Analysis and Design 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Advances in Computational Mathematics 1 Computing and Visualization in Science 1 International Journal of Computational Fluid Dynamics 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Optimization and Engineering 1 Foundations of Computational Mathematics 1 Communications on Pure and Applied Analysis 1 Inverse Problems in Science and Engineering 1 MS&A. Modeling, Simulation and Applications all top 5 Fields 99 Numerical analysis (65-XX) 58 Partial differential equations (35-XX) 51 Fluid mechanics (76-XX) 15 Mechanics of deformable solids (74-XX) 13 Classical thermodynamics, heat transfer (80-XX) 7 Statistics (62-XX) 6 Systems theory; control (93-XX) 5 Computer science (68-XX) 4 Approximations and expansions (41-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Operations research, mathematical programming (90-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 General and overarching topics; collections (00-XX) 2 Operator theory (47-XX) 2 Probability theory and stochastic processes (60-XX) 2 Quantum theory (81-XX) 2 Biology and other natural sciences (92-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 120 Publications have been cited 4,260 times in 2,296 Documents Cited by ▼ Year ▼ A spectral element method for fluid dynamics: Laminar flow in a channel expansion. Zbl 0535.76035Patera, Anthony T. 431 1984 An ‘empirical interpolation’ method: Application to efficient reduced-basis discretization of partial differential equations. Zbl 1061.65118Barrault, Maxime; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T. 421 2004 Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics. Zbl 1304.65251Rozza, G.; Huynh, D. B. P.; Patera, A. T. 335 2008 A new nonconforming approach to domain decomposition: The mortar element method. Zbl 0797.65094Bernardi, C.; Maday, Y.; Patera, A. T. 271 1994 Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations. Zbl 1142.65078Grepl, Martin A.; Maday, Yvon; Nguyen, Ngoc C.; Patera, Anthony T. 165 2007 Secondary instability of wall-bounded shear flows. Zbl 0556.76039Orszag, Steven A.; Patera, Anthony T. 135 1983 A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. Zbl 1079.65096Grepl, Martin A.; Patera, Anthony T. 122 2005 Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: rigorous reduced-basis a posteriori error bounds. Zbl 1134.76326Veroy, K.; Patera, A. T. 116 2005 A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants. Zbl 1127.65086Huynh, D. B. P.; Rozza, G.; Sen, S.; Patera, A. T. 101 2007 Domain decomposition by the mortar element method. Zbl 0799.65124Bernardi, C.; Maday, Y.; Patera, A. T. 100 1993 A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations. Zbl 0907.65102Paraschivoiu, Marius; Peraire, Jaime; Patera, Anthony T. 85 1997 An operator-integration-factor splitting method for time-dependent problems: Application to incompressible fluid flow. Zbl 0724.76070Maday, Y.; Patera, Anthony T.; Rønquist, Einar M. 84 1990 A priori convergence of the greedy algorithm for the parametrized reduced basis method. Zbl 1272.65084Buffa, Annalisa; Maday, Yvon; Patera, Anthony T.; Prud’homme, Christophe; Turinici, Gabriel 72 2012 A general multipurpose interpolation procedure: The magic points. Zbl 1184.65020Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T.; Pau, S. H. 67 2009 Spectral and finite difference solutions of the Burgers equations. Zbl 0612.76031Basdevant, C.; Deville, M.; Haldenwang, P.; Lacroix, J. M.; Ouazzani, J.; Peyret, R.; Orlandi, P.; Patera, A. T. 67 1986 An “\(hp\)” certified reduced basis method for parametrized elliptic partial differential equations. Zbl 1228.35097Eftang, Jens L.; Patera, Anthony T.; Rønquist, Einar M. 52 2010 A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations. Zbl 1014.65115Maday, Yvon; Patera, Anthony T.; Turinici, Gabriel 48 2002 Spectral element multigrid. I: Formulation and numerical results. Zbl 0666.65055Rønquist, Einar M.; Patera, Anthony T. 48 1987 Reduced basis techniques for stochastic problems. Zbl 1269.65005Boyaval, S.; Le Bris, C.; Lelièvre, T.; Maday, Y.; Nguyen, N. C.; Patera, A. T. 47 2010 Analysis of iterative methods for the steady and unsteady Stokes problem: Application to spectral element discretizations. Zbl 0769.76047Maday, Yvon; Meiron, Dan; Patera, Anthony T.; Rønquist, Einar M. 46 1993 Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems. Zbl 0960.65063Machiels, Luc; Maday, Yvon; Oliveira, Ivan B.; Patera, Anthony T.; Rovas, Dimitrios V. 45 2000 Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation. Zbl 1178.65109Nguyen, Ngoc-Cuong; Rozza, Gianluigi; Patera, Anthony T. 45 2009 An isoparametric spectral element method for solution of the Navier-Stokes equations in complex geometry. Zbl 0581.76036Korczak, Karol Z.; Patera, Anthony T. 44 1986 An improved error bound for reduced basis approximation of linear parabolic problems. Zbl 1320.65129Urban, Karsten; Patera, Anthony T. 44 2014 A ‘best points’ interpolation method for efficient approximation of parametrized functions. Zbl 1163.65009Nguyen, N. C.; Patera, A. T.; Peraire, J. 43 2008 A natural-norm successive constraint method for inf-sup lower bounds. Zbl 1231.76208Huynh, D. B. P.; Knezevic, D. J.; Chen, Y.; Hesthaven, J. S.; Patera, A. T. 41 2010 A static condensation reduced basis element method: approximation and {a posteriori} error estimation. Zbl 1276.65082Huynh, Dinh Bao Phuong; Knezevic, David J.; Patera, Anthony T. 40 2013 Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations. Zbl 1009.65066Maday, Yvon; Patera, Anthony T.; Turinici, G. 37 2002 Reduced-basis approximation of the viscous Burgers equation: Rigorous a posteriori error bounds. Zbl 1036.65075Veroy, Karen; Prud’homme, Christophe; Patera, Anthony T. 37 2003 “Natural norm” a posteriori error estimators for reduced basis approximations. Zbl 1100.65094Sen, S.; Veroy, K.; Huynh, D. B. P.; Deparis, S.; Nguyen, N. C.; Patera, A. T. 36 2006 A Legendre spectral element method for simulation of unsteady incompressible viscous free-surface flows. Zbl 0722.76052Ho, Lee-Wing; Patera, Anthony T. 35 1990 A blackbox reduced-basis output bound method for noncoercive linear problems. Zbl 1006.65124Maday, Y.; Patera, A. T.; Rovas, D. V. 33 2002 A hierarchical duality approach to bounds for the outputs of partial differential equations. Zbl 0953.76054Paraschivoiu, Marius; Patera, Anthony T. 33 1998 Numerical simulation of singular solutions to the two-dimensional cubic Schrödinger equation. Zbl 0543.65081Sulem, P. L.; Sulem, C.; Patera, A. 31 1984 A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics. Zbl 1352.65529Maday, Yvon; Patera, Anthony T.; Penn, James D.; Yano, Masayuki 31 2015 A stabilized POD model for turbulent flows over a range of Reynolds numbers: optimal parameter sampling and constrained projection. Zbl 1415.76387Fick, Lambert; Maday, Yvon; Patera, Anthony T.; Taddei, Tommaso 27 2018 An \(hp\) certified reduced basis method for parametrized parabolic partial differential equations. Zbl 1302.65223Eftang, Jens L.; Knezevic, David J.; Patera, Anthony T. 27 2011 Un cadre général pour l’obtention de bornes a posteriori sur des résultats en sortie d’équations aux dérivées partielles; application aux problèmes de valeurs propres. (A general formulation for a posteriori bounds for output functionals of partial differential equations; application to the eigenvalue problem.) Zbl 0933.65129Maday, Yvon; Patera, Anthony T.; Peraire, Jaume 26 1999 A reduced basis approach for variational problems with stochastic parameters: application to heat conduction with variable Robin coefficient. Zbl 1230.80013Boyaval, Sébastien; Le Bris, Claude; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T. 26 2009 A Legendre spectral element method for the Stefan problem. Zbl 0632.65126Rønquist, Einar M.; Patera, Anthony T. 23 1987 Reduced basis approximation and a posteriori error estimation for the parametrized unsteady Boussinesq equations. Zbl 1279.76023Knezevic, David J.; Nguyen, Ngoc-Cuong; Patera, Anthony T. 22 2011 Port reduction in parametrized component static condensation: approximation and a posteriori error estimation. Zbl 1352.65495Eftang, Jens L.; Patera, Anthony T. 22 2013 A new error bound for reduced basis approximation of parabolic partial differential equations. Zbl 1242.35157Urban, Karsten; Patera, Anthony T. 21 2012 A posteriori error estimation for reduced-basis approximation of parametrized elliptic coercive partial differential equations: convex inverse bound conditioners. Zbl 1092.35031Veroy, Karen; Rovas, Dimitrios V.; Patera, Anthony T. 21 2002 Finite-amplitude stability of axisymmetric pipe flow. Zbl 0518.76037Patera, Anthony T.; Orszag, Steven A. 21 1981 The generalized empirical interpolation method: stability theory on Hilbert spaces with an application to the Stokes equation. Zbl 1423.76346Maday, Y.; Mula, O.; Patera, A. T.; Yano, M. 20 2015 A posteriori error bounds for the empirical interpolation method. Zbl 1190.65018Eftang, Jens L.; Grepl, Martin A.; Patera, Anthony T. 19 2010 A space-time \(hp\)-interpolation-based certified reduced basis method for Burgers’ equation. Zbl 1295.65098Yano, Masayuki; Patera, Anthony T.; Urban, Karsten 19 2014 A posteriori finite-element output bounds for the incompressible Navier-Stokes equations: Application to a natural convection problem. Zbl 1002.76069Machiels, L.; Peraire, J.; Patera, A. T. 18 2001 A “flux-free” nodal Neumann subproblem approach to output bounds for partial differential equations. Zbl 0946.65101Machiels, Luc; Maday, Yvon; Patera, Anthony T. 18 2000 Reduced basis approximation and a posteriori error estimation for stress intensity factors. Zbl 1194.74413Huynh, D. B. P.; Patera, A. T. 18 2007 A parallel Monte Carlo finite-element procedure for the analysis of multicomponent random media. Zbl 0823.73063Cruz, Manuel E.; Patera, Anthony T. 17 1995 Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations. Zbl 1171.65404Oliveira, I. B.; Patera, A. T. 17 2007 Variational formulation of three-dimensional viscous free-surface flows: Natural imposition of surface tension boundary conditions. Zbl 0739.76057Ho, Lee-Wing; Patera, Anthony T. 17 1991 Asymptotic a posteriori finite element bounds for the outputs of noncoercive problems: The Helmholtz and Burgers equations. Zbl 0943.65124Peraire, Jaume; Patera, Anthony T. 17 1999 Parallel spectral element solution of the Stokes problem. Zbl 0709.76106Fischer, Paul F.; Patera, Anthony T. 16 1991 A static condensation reduced basis element method: complex problems. Zbl 1286.65160Huynh, D. B. P.; Knezevic, D. J.; Patera, A. T. 16 2013 Nonconforming mortar element methods: Application to spectral discretizations. Zbl 0692.65055Maday, Yvon; Mavriplis, Cathy; Patera, Anthony T. 15 1989 Inverse identification of thermal parameters using reduced-basis method. Zbl 1137.74361Liu, G. R.; Lee, J. H.; Patera, A. T.; Yang, Z. L.; Lam, K. Y. 15 2005 Model reduction of parametrized systems. Selected contributions based on the presentations at the MoRePaS conference, SISSA, Trieste, Italy, October 13–16, 2015. Zbl 1381.65001 15 2017 A mathematical and computational framework for reliable real-time solution of parametrized partial differential equations. Zbl 1024.65104Prud’homme, Christophe; Rovas, Dimitrios V.; Veroy, Karen; Patera, Anthony T. 13 2002 A posteriori finite element error bounds for nonlinear outputs of the Helmholtz equation. Zbl 0964.65119Sarrate, J.; Peraire, J.; Patera, A. 13 1999 A posteriori bounds for linear functional outputs of Crouzeix-Raviart finite element discretizations of the incompressible Stokes problem. Zbl 0974.76047Paraschivoiu, Marius; Patera, Anthony T. 13 2000 Parallel simulation of viscous incompressible flows. Zbl 0802.76065Fischer, Paul F.; Patera, Anthony T. 13 1994 Optimal local approximation spaces for component-based static condensation procedures. Zbl 1457.65216Smetana, Kathrin; Patera, Anthony T. 13 2016 A general output bound result: application to discretization and iteration error estimation and control. Zbl 1012.65110Patera, Anthony T.; Rønquist, Einar M. 12 2001 PBDW state estimation: noisy observations; configuration-adaptive background spaces; physical interpretations. Zbl 1342.82116Maday, Yvon; Patera, Anthony T.; Penn, James D.; Yano, Masayuki 12 2015 Numerical analysis of a posteriori finite element bounds for linear functional outputs. Zbl 1012.65109Maday, Yvon; Patera, Anthony T. 11 2000 A certified reduced basis method for the Fokker-Planck equation of dilute polymeric fluids: FENE dumbbells in extensional flow. Zbl 1226.82051Knezevic, David J.; Patera, Anthony T. 11 2010 Certified rapid solution of partial differential equations for real-time parameter estimation and optimization. Zbl 1228.65223Grepl, Martin A.; Nguyen, Ngoc C.; Veroy, Karen; Patera, Anthony T.; Liu, Gui R. 10 2007 Output bounds for reduced-order approximations of elliptic partial differential equations. Zbl 0984.65118Machiels, L.; Maday, Y.; Patera, A. T. 10 2001 Recent advances in parallel spectral element simulation of unsteady incompressible flows. Zbl 0668.76039Fischer, Paul F.; Ho, Lee-Wing; Karniadakis, George E.; Rønquist, Einar M.; Patera, Anthony T. 10 1988 A space-time variational approach to hydrodynamic stability theory. Zbl 1371.76054Yano, Masayuki; Patera, Anthony T. 10 2013 Rapid identification of material properties of the interface tissue in dental implant systems using reduced basis method. Zbl 1300.92047Hoang, K. C.; Khoo, B. C.; Liu, G. R.; Nguyen, N. C.; Patera, A. T. 9 2013 Reduced basis approximation and a posteriori error estimation for a Boltzmann model. Zbl 1178.76236Patera, Anthony T.; Rønquist, Einar M. 9 2007 Output bound approximations for partial differential equations; application to the incompressible Navier-Stokes equations. Zbl 0988.76052Machiels, L.; Peraire, J.; Patera, A. T. 9 1999 The static condensation reduced basis element method for a mixed-mean conjugate heat exchanger model. Zbl 1298.80016Vallaghé, Sylvain; Patera, Anthony T. 9 2014 Non-conforming spectral element-finite element approximations for partial differential equations. Zbl 0697.65080Bègue, C.; Bernardi, C.; Debit, N.; Maday, Y.; Karniadakis, G. E.; Mavriplis, C.; Patera, A. T. 8 1989 A model-data weak formulation for simultaneous estimation of state and model bias. (Estimation de la variable d’état et du biais de modèle par une formulation faible incorporant les données.) Zbl 1281.65148Yano, Masayuki; Penn, James D.; Patera, Anthony T. 8 2013 Fast direct Poisson solvers for high-order finite element discretizations in rectangularly decomposable domains. Zbl 0623.65111Patera, Anthony T. 8 1986 Feasibility and competitiveness of a reduced basis approach for rapid electronic structure calculations in quantum chemistry. Zbl 1330.81022Cancès, Éric; Le Bris, Claude; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T.; Pau, George Shu Heng 8 2007 A two-step certified reduced basis method. Zbl 1244.65172Eftang, J. L.; Huynh, D. B. P.; Knezevic, D. J.; Patera, A. T. 7 2012 High-fidelity real-time simulation on deployed platforms. Zbl 1452.65429Huynh, D. B. P.; Knezevic, D. J.; Peterson, J. W.; Patera, A. T. 7 2011 A high-order Lagrangian-decoupling method for the incompressible Navier- Stokes equations. Zbl 0722.76038Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Rønquist, Einar M. 7 1990 A computational procedure for part design. Zbl 0763.73079Anagnostou, George; Rønquist, Einar M.; Patera, Anthony T. 7 1992 Spectral collocation methods. Zbl 0671.65093Hussaini, M. Y.; Kopriva, D. A.; Patera, A. T. 7 1989 An LP empirical quadrature procedure for parametrized functions. (Une procédure de quadrature empirique par programmation linéaire pour les fonctions à paramètres.) Zbl 1377.65074Patera, Anthony T.; Yano, Masayuki 7 2017 A localization strategy for data assimilation; application to state estimation and parameter estimation. Zbl 1426.65144Taddei, Tommaso; Patera, Anthony T. 6 2018 Certified reduced basis model validation: a frequentistic uncertainty framework. Zbl 1239.93120Huynh, D. B. P.; Knezevic, D. J.; Patera, A. T. 6 2012 A general Lagrangian formulation for the computation of a posteriori finite element bounds. Zbl 1141.76426Patera, Anthony T.; Peraire, Jaume 6 2003 Reduced-basis output bounds for approximately parametrized elliptic coercive partial differential equations. Zbl 1064.65140Prud’homme, C.; Patera, A. T. 6 2004 A Legendre spectral element method for the incompressible Navier-Stokes equations. Zbl 0684.76030Rønquist, Einar M.; Patera, Anthony T. 6 1988 An LP empirical quadrature procedure for reduced basis treatment of parametrized nonlinear PDEs. Zbl 1440.65238Yano, Masayuki; Patera, Anthony T. 6 2019 Fast bounds for outputs of parallel differential equations. Zbl 0924.65057Paraschivoiu, Marius; Peraire, Jaime; Maday, Yvon; Patera, Anthony T. 5 1998 Regression on parametric manifolds: Estimation of spatial fields, functional outputs, and parameters from noisy data. Zbl 1245.65010Patera, Anthony T.; Rønquist, Einar M. 5 2012 Approximation of parametric derivatives by the empirical interpolation method. Zbl 1284.65041Eftang, Jens L.; Grepl, Martin A.; Patera, Anthony T.; Rønquist, Einar M. 5 2013 On the mortar element method: Generalizations and implementation. Zbl 0704.65077Anagnostou, George; Maday, Yvon; Mavriplis, Catherine; Patera, Anthony T. 5 1990 Subcritical transition to turbulence in planar shear flows. Zbl 0492.76063Orszag, Steven A.; Patera, Anthony T. 5 1981 Randomized residual-based error estimators for parametrized equations. Zbl 1411.65148Smetana, Kathrin; Zahm, Olivier; Patera, Anthony T. 5 2019 Simulation-based classification; a model-order-reduction approach for structural health monitoring. Zbl 1390.74078Taddei, T.; Penn, J. D.; Yano, M.; Patera, A. T. 4 2018 An LP empirical quadrature procedure for reduced basis treatment of parametrized nonlinear PDEs. Zbl 1440.65238Yano, Masayuki; Patera, Anthony T. 6 2019 Randomized residual-based error estimators for parametrized equations. Zbl 1411.65148Smetana, Kathrin; Zahm, Olivier; Patera, Anthony T. 5 2019 A stabilized POD model for turbulent flows over a range of Reynolds numbers: optimal parameter sampling and constrained projection. Zbl 1415.76387Fick, Lambert; Maday, Yvon; Patera, Anthony T.; Taddei, Tommaso 27 2018 A localization strategy for data assimilation; application to state estimation and parameter estimation. Zbl 1426.65144Taddei, Tommaso; Patera, Anthony T. 6 2018 Simulation-based classification; a model-order-reduction approach for structural health monitoring. Zbl 1390.74078Taddei, T.; Penn, J. D.; Yano, M.; Patera, A. T. 4 2018 A component-based hybrid reduced basis/finite element method for solid mechanics with local nonlinearities. Zbl 1439.74387Ballani, J.; Huynh, D. B. P.; Knezevic, D. J.; Nguyen, L.; Patera, A. T. 3 2018 Model reduction of parametrized systems. Selected contributions based on the presentations at the MoRePaS conference, SISSA, Trieste, Italy, October 13–16, 2015. Zbl 1381.65001 15 2017 An LP empirical quadrature procedure for parametrized functions. (Une procédure de quadrature empirique par programmation linéaire pour les fonctions à paramètres.) Zbl 1377.65074Patera, Anthony T.; Yano, Masayuki 7 2017 Optimal local approximation spaces for component-based static condensation procedures. Zbl 1457.65216Smetana, Kathrin; Patera, Anthony T. 13 2016 A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics. Zbl 1352.65529Maday, Yvon; Patera, Anthony T.; Penn, James D.; Yano, Masayuki 31 2015 The generalized empirical interpolation method: stability theory on Hilbert spaces with an application to the Stokes equation. Zbl 1423.76346Maday, Y.; Mula, O.; Patera, A. T.; Yano, M. 20 2015 PBDW state estimation: noisy observations; configuration-adaptive background spaces; physical interpretations. Zbl 1342.82116Maday, Yvon; Patera, Anthony T.; Penn, James D.; Yano, Masayuki 12 2015 An improved error bound for reduced basis approximation of linear parabolic problems. Zbl 1320.65129Urban, Karsten; Patera, Anthony T. 44 2014 A space-time \(hp\)-interpolation-based certified reduced basis method for Burgers’ equation. Zbl 1295.65098Yano, Masayuki; Patera, Anthony T.; Urban, Karsten 19 2014 The static condensation reduced basis element method for a mixed-mean conjugate heat exchanger model. Zbl 1298.80016Vallaghé, Sylvain; Patera, Anthony T. 9 2014 A static condensation reduced basis element method: approximation and {a posteriori} error estimation. Zbl 1276.65082Huynh, Dinh Bao Phuong; Knezevic, David J.; Patera, Anthony T. 40 2013 Port reduction in parametrized component static condensation: approximation and a posteriori error estimation. Zbl 1352.65495Eftang, Jens L.; Patera, Anthony T. 22 2013 A static condensation reduced basis element method: complex problems. Zbl 1286.65160Huynh, D. B. P.; Knezevic, D. J.; Patera, A. T. 16 2013 A space-time variational approach to hydrodynamic stability theory. Zbl 1371.76054Yano, Masayuki; Patera, Anthony T. 10 2013 Rapid identification of material properties of the interface tissue in dental implant systems using reduced basis method. Zbl 1300.92047Hoang, K. C.; Khoo, B. C.; Liu, G. R.; Nguyen, N. C.; Patera, A. T. 9 2013 A model-data weak formulation for simultaneous estimation of state and model bias. (Estimation de la variable d’état et du biais de modèle par une formulation faible incorporant les données.) Zbl 1281.65148Yano, Masayuki; Penn, James D.; Patera, Anthony T. 8 2013 Approximation of parametric derivatives by the empirical interpolation method. Zbl 1284.65041Eftang, Jens L.; Grepl, Martin A.; Patera, Anthony T.; Rønquist, Einar M. 5 2013 A priori convergence of the greedy algorithm for the parametrized reduced basis method. Zbl 1272.65084Buffa, Annalisa; Maday, Yvon; Patera, Anthony T.; Prud’homme, Christophe; Turinici, Gabriel 72 2012 A new error bound for reduced basis approximation of parabolic partial differential equations. Zbl 1242.35157Urban, Karsten; Patera, Anthony T. 21 2012 A two-step certified reduced basis method. Zbl 1244.65172Eftang, J. L.; Huynh, D. B. P.; Knezevic, D. J.; Patera, A. T. 7 2012 Certified reduced basis model validation: a frequentistic uncertainty framework. Zbl 1239.93120Huynh, D. B. P.; Knezevic, D. J.; Patera, A. T. 6 2012 Regression on parametric manifolds: Estimation of spatial fields, functional outputs, and parameters from noisy data. Zbl 1245.65010Patera, Anthony T.; Rønquist, Einar M. 5 2012 An \(hp\) certified reduced basis method for parametrized parabolic partial differential equations. Zbl 1302.65223Eftang, Jens L.; Knezevic, David J.; Patera, Anthony T. 27 2011 Reduced basis approximation and a posteriori error estimation for the parametrized unsteady Boussinesq equations. Zbl 1279.76023Knezevic, David J.; Nguyen, Ngoc-Cuong; Patera, Anthony T. 22 2011 High-fidelity real-time simulation on deployed platforms. Zbl 1452.65429Huynh, D. B. P.; Knezevic, D. J.; Peterson, J. W.; Patera, A. T. 7 2011 A Laplace transform certified reduced basis method; application to the heat equation and wave equation. (Une méthode de bases réduites certifiée utilisant la transformation de Laplace; Application à l’équation de la chaleur et à l’équation des ondes.) Zbl 1215.65156Huynh, D. B. Phuong; Knezevic, David J.; Patera, Anthony T. 4 2011 An \(hp\) certified reduced basis method for parametrized parabolic partial differential equations. Zbl 1216.65128Eftang, Jens L.; Patera, Anthony T.; Rønquist, Einar M. 3 2011 Model order reduction and error estimation with an application to the parameter-dependent eddy current equation. Zbl 1303.93052Jung, Nadine; Patera, Anthony T.; Haasdonk, Bernard; Lohmann, Boris 2 2011 An “\(hp\)” certified reduced basis method for parametrized elliptic partial differential equations. Zbl 1228.35097Eftang, Jens L.; Patera, Anthony T.; Rønquist, Einar M. 52 2010 Reduced basis techniques for stochastic problems. Zbl 1269.65005Boyaval, S.; Le Bris, C.; Lelièvre, T.; Maday, Y.; Nguyen, N. C.; Patera, A. T. 47 2010 A natural-norm successive constraint method for inf-sup lower bounds. Zbl 1231.76208Huynh, D. B. P.; Knezevic, D. J.; Chen, Y.; Hesthaven, J. S.; Patera, A. T. 41 2010 A posteriori error bounds for the empirical interpolation method. Zbl 1190.65018Eftang, Jens L.; Grepl, Martin A.; Patera, Anthony T. 19 2010 A certified reduced basis method for the Fokker-Planck equation of dilute polymeric fluids: FENE dumbbells in extensional flow. Zbl 1226.82051Knezevic, David J.; Patera, Anthony T. 11 2010 A general multipurpose interpolation procedure: The magic points. Zbl 1184.65020Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T.; Pau, S. H. 67 2009 Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation. Zbl 1178.65109Nguyen, Ngoc-Cuong; Rozza, Gianluigi; Patera, Anthony T. 45 2009 A reduced basis approach for variational problems with stochastic parameters: application to heat conduction with variable Robin coefficient. Zbl 1230.80013Boyaval, Sébastien; Le Bris, Claude; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T. 26 2009 Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics. Zbl 1304.65251Rozza, G.; Huynh, D. B. P.; Patera, A. T. 335 2008 A ‘best points’ interpolation method for efficient approximation of parametrized functions. Zbl 1163.65009Nguyen, N. C.; Patera, A. T.; Peraire, J. 43 2008 Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations. Zbl 1142.65078Grepl, Martin A.; Maday, Yvon; Nguyen, Ngoc C.; Patera, Anthony T. 165 2007 A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants. Zbl 1127.65086Huynh, D. B. P.; Rozza, G.; Sen, S.; Patera, A. T. 101 2007 Reduced basis approximation and a posteriori error estimation for stress intensity factors. Zbl 1194.74413Huynh, D. B. P.; Patera, A. T. 18 2007 Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations. Zbl 1171.65404Oliveira, I. B.; Patera, A. T. 17 2007 Certified rapid solution of partial differential equations for real-time parameter estimation and optimization. Zbl 1228.65223Grepl, Martin A.; Nguyen, Ngoc C.; Veroy, Karen; Patera, Anthony T.; Liu, Gui R. 10 2007 Reduced basis approximation and a posteriori error estimation for a Boltzmann model. Zbl 1178.76236Patera, Anthony T.; Rønquist, Einar M. 9 2007 Feasibility and competitiveness of a reduced basis approach for rapid electronic structure calculations in quantum chemistry. Zbl 1330.81022Cancès, Éric; Le Bris, Claude; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T.; Pau, George Shu Heng 8 2007 “Natural norm” a posteriori error estimators for reduced basis approximations. Zbl 1100.65094Sen, S.; Veroy, K.; Huynh, D. B. P.; Deparis, S.; Nguyen, N. C.; Patera, A. T. 36 2006 A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. Zbl 1079.65096Grepl, Martin A.; Patera, Anthony T. 122 2005 Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: rigorous reduced-basis a posteriori error bounds. Zbl 1134.76326Veroy, K.; Patera, A. T. 116 2005 Inverse identification of thermal parameters using reduced-basis method. Zbl 1137.74361Liu, G. R.; Lee, J. H.; Patera, A. T.; Yang, Z. L.; Lam, K. Y. 15 2005 An ‘empirical interpolation’ method: Application to efficient reduced-basis discretization of partial differential equations. Zbl 1061.65118Barrault, Maxime; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T. 421 2004 Reduced-basis output bounds for approximately parametrized elliptic coercive partial differential equations. Zbl 1064.65140Prud’homme, C.; Patera, A. T. 6 2004 Reduced-basis approximation of the viscous Burgers equation: Rigorous a posteriori error bounds. Zbl 1036.65075Veroy, Karen; Prud’homme, Christophe; Patera, Anthony T. 37 2003 A general Lagrangian formulation for the computation of a posteriori finite element bounds. Zbl 1141.76426Patera, Anthony T.; Peraire, Jaume 6 2003 A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations. Zbl 1014.65115Maday, Yvon; Patera, Anthony T.; Turinici, Gabriel 48 2002 Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations. Zbl 1009.65066Maday, Yvon; Patera, Anthony T.; Turinici, G. 37 2002 A blackbox reduced-basis output bound method for noncoercive linear problems. Zbl 1006.65124Maday, Y.; Patera, A. T.; Rovas, D. V. 33 2002 A posteriori error estimation for reduced-basis approximation of parametrized elliptic coercive partial differential equations: convex inverse bound conditioners. Zbl 1092.35031Veroy, Karen; Rovas, Dimitrios V.; Patera, Anthony T. 21 2002 A mathematical and computational framework for reliable real-time solution of parametrized partial differential equations. Zbl 1024.65104Prud’homme, Christophe; Rovas, Dimitrios V.; Veroy, Karen; Patera, Anthony T. 13 2002 A posteriori finite-element output bounds for the incompressible Navier-Stokes equations: Application to a natural convection problem. Zbl 1002.76069Machiels, L.; Peraire, J.; Patera, A. T. 18 2001 A general output bound result: application to discretization and iteration error estimation and control. Zbl 1012.65110Patera, Anthony T.; Rønquist, Einar M. 12 2001 Output bounds for reduced-order approximations of elliptic partial differential equations. Zbl 0984.65118Machiels, L.; Maday, Y.; Patera, A. T. 10 2001 Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems. Zbl 0960.65063Machiels, Luc; Maday, Yvon; Oliveira, Ivan B.; Patera, Anthony T.; Rovas, Dimitrios V. 45 2000 A “flux-free” nodal Neumann subproblem approach to output bounds for partial differential equations. Zbl 0946.65101Machiels, Luc; Maday, Yvon; Patera, Anthony T. 18 2000 A posteriori bounds for linear functional outputs of Crouzeix-Raviart finite element discretizations of the incompressible Stokes problem. Zbl 0974.76047Paraschivoiu, Marius; Patera, Anthony T. 13 2000 Numerical analysis of a posteriori finite element bounds for linear functional outputs. Zbl 1012.65109Maday, Yvon; Patera, Anthony T. 11 2000 A posteriori finite element bounds for sensitivity derivatives of partial-differential-equation outputs. Zbl 0946.65100Lewis, Robert Michael; Patera, Anthony T.; Peraire, Jaume 3 2000 A variationally consistent finite element approach to the two-fluid internal contact-line problem. Zbl 0998.76048Hadjiconstantinou, Nicolas G.; Patera, Anthony T. 1 2000 Un cadre général pour l’obtention de bornes a posteriori sur des résultats en sortie d’équations aux dérivées partielles; application aux problèmes de valeurs propres. (A general formulation for a posteriori bounds for output functionals of partial differential equations; application to the eigenvalue problem.) Zbl 0933.65129Maday, Yvon; Patera, Anthony T.; Peraire, Jaume 26 1999 Asymptotic a posteriori finite element bounds for the outputs of noncoercive problems: The Helmholtz and Burgers equations. Zbl 0943.65124Peraire, Jaume; Patera, Anthony T. 17 1999 A posteriori finite element error bounds for nonlinear outputs of the Helmholtz equation. Zbl 0964.65119Sarrate, J.; Peraire, J.; Patera, A. 13 1999 Output bound approximations for partial differential equations; application to the incompressible Navier-Stokes equations. Zbl 0988.76052Machiels, L.; Peraire, J.; Patera, A. T. 9 1999 Bounds evaluation for outputs of eigenvalue problems approximated by the overlapping modal synthesis method. Zbl 0941.65110Charpentier, Isabelle; Maday, Yvon; Patera, Anthony T. 2 1999 A hierarchical duality approach to bounds for the outputs of partial differential equations. Zbl 0953.76054Paraschivoiu, Marius; Patera, Anthony T. 33 1998 Fast bounds for outputs of parallel differential equations. Zbl 0924.65057Paraschivoiu, Marius; Peraire, Jaime; Maday, Yvon; Patera, Anthony T. 5 1998 Variational bound finite element methods for three-dimensional creeping porous media and sedimentation flows. Zbl 0910.76037Pedercini, Matteo; Patera, Anthony T.; Cruz, Manuel E. 3 1998 A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations. Zbl 0907.65102Paraschivoiu, Marius; Peraire, Jaime; Patera, Anthony T. 85 1997 Three-dimensional ribbing instability in symmetric forward-roll film-coating processes. Zbl 0892.76028Gurfinkel Castillo, Mariano E.; Patera, Anthony T. 2 1997 Bayesian-validated computer-simulation surrogates for optimization and design: Error estimates and applications. Zbl 1017.65506Otto, John; Paraschivoiu, Marius; Yesilyurt, Serhat; Patera, Anthony T. 2 1997 Bayesian-validated surrogates for noisy computer simulations; application to random media. Zbl 0870.65145Yeşilyurt, Serhat; Ghaddar, Chahid K.; Cruz, Manuel E.; Patera, Anthony T. 4 1996 A parallel Monte Carlo finite-element procedure for the analysis of multicomponent random media. Zbl 0823.73063Cruz, Manuel E.; Patera, Anthony T. 17 1995 Surrogates for numerical simulations; optimization of eddy-promoter heat exchangers. Zbl 0852.76074Yeşilyurt, Serhat; Patera, Anthony T. 3 1995 A variational-bound nip-element method for geometrically stiff problems; application to thermal composites and porous media. Zbl 0826.73076Cruz, Manuel E.; Ghaddar, Chahid K.; Patera, Anthony T. 3 1995 A new nonconforming approach to domain decomposition: The mortar element method. Zbl 0797.65094Bernardi, C.; Maday, Y.; Patera, A. T. 271 1994 Parallel simulation of viscous incompressible flows. Zbl 0802.76065Fischer, Paul F.; Patera, Anthony T. 13 1994 Domain decomposition by the mortar element method. Zbl 0799.65124Bernardi, C.; Maday, Y.; Patera, A. T. 100 1993 Analysis of iterative methods for the steady and unsteady Stokes problem: Application to spectral element discretizations. Zbl 0769.76047Maday, Yvon; Meiron, Dan; Patera, Anthony T.; Rønquist, Einar M. 46 1993 A general estimate for the thermal time-to-steady-state for a solid body suddenly immersed in a fluid stream. Zbl 0769.73006Maday, Y.; Patera, Anthony T. 2 1993 Spectral element and lattice gas methods for incompressible fluid dynamics. Zbl 1189.76379Karniadakis, George Em; Orszag, Steven A.; Rønquist, Einar M.; Patera, Anthony T. 2 1993 A computational procedure for part design. Zbl 0763.73079Anagnostou, George; Rønquist, Einar M.; Patera, Anthony T. 7 1992 Spectral element multigrid methods. Zbl 0785.65111Maday, Y.; Muñoz, R.; Patera, A.; Rønquist, E. 2 1992 Variational formulation of three-dimensional viscous free-surface flows: Natural imposition of surface tension boundary conditions. Zbl 0739.76057Ho, Lee-Wing; Patera, Anthony T. 17 1991 Parallel spectral element solution of the Stokes problem. Zbl 0709.76106Fischer, Paul F.; Patera, Anthony T. 16 1991 An operator-integration-factor splitting method for time-dependent problems: Application to incompressible fluid flow. Zbl 0724.76070Maday, Y.; Patera, Anthony T.; Rønquist, Einar M. 84 1990 A Legendre spectral element method for simulation of unsteady incompressible viscous free-surface flows. Zbl 0722.76052Ho, Lee-Wing; Patera, Anthony T. 35 1990 A high-order Lagrangian-decoupling method for the incompressible Navier- Stokes equations. Zbl 0722.76038Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Rønquist, Einar M. 7 1990 ...and 20 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,187 Authors 71 Patera, Anthony T. 64 Rozza, Gianluigi 61 Maday, Yvon 40 Quarteroni, Alfio M. 34 Karniadakis, George Em 26 Fischer, Paul F. 26 Hesthaven, Jan S. 24 Haasdonk, Bernard 23 Díez, Pedro 23 Wohlmuth, Barbara I. 22 Manzoni, Andrea 22 Willcox, Karen E. 21 Nguyen, Ngoc Cuong 20 Benner, Peter 19 Bernardi, Christine 19 Huerta, Antonio 19 Rønquist, Einar M. 18 Farhat, Charbel H. 18 Veroy, Karen 17 Carlberg, Kevin T. 17 Grepl, Martin A. 17 Peherstorfer, Benjamin 17 Urban, Karsten 16 Chen, Yanlai 16 Ohlberger, Mario 15 Chamoin, Ludovic 15 Dehghan Takht Fooladi, Mehdi 15 Ladevèze, Pierre 15 Nouy, Anthony 15 Parés, Núria 15 Phillips, Timothy N. 15 Volkwein, Stefan 15 Yano, Masayuki 14 Ballarin, Francesco 14 Chinesta, Francisco 14 Henningson, Dan S. 14 Rapetti, Francesca 13 Abdulle, Assyr 13 Stabile, Giovanni 12 Chen, Jinru 12 Chung, Tsz Shun Eric 12 Efendiev, Yalchin R. 12 Iliescu, Traian 12 Jiang, Lijian 12 Navon, Ionel Michael 12 Schlatter, Philipp 12 Taddei, Tommaso 11 Chen, Peng 11 Deville, Michel O. 11 Huynh, Dinh Bao Phuong 10 Amsallem, David 10 Bertoluzza, Silvia 10 Bordas, Stéphane Pierre Alain 10 Deparis, Simone 10 Dušek, Jan 10 Knezevic, David J. 10 Li, Huiyuan 10 Paraschivoiu, Marius 10 Schwab, Christoph 10 Seshaiyer, Padmanabhan 10 Wall, Wolfgang A. 9 Ben Belgacem, Faker 9 Cohen, Albert 9 Fang, Fangxin 9 Gervasio, Paola 9 Luo, Zhendong 9 Narayan, Akil C. 9 Prud’homme, Christophe 9 Sherwin, Spencer J. 9 Wheeler, Mary Fanett 8 Chacón Rebollo, Tomás 8 Duczek, Sascha 8 Feng, Lihong 8 Fidkowski, Krzysztof J. 8 Giraldo, Francis X. 8 Gugercin, Serkan 8 Gunzburger, Max D. 8 Hanifi, Ardeshir 8 Hou, Thomas Yizhao 8 Karasözen, Bülent 8 Kopriva, David Alan 8 Kutz, J. Nathan 8 Li, Qiuqi 8 López, Juan Manuel 8 Marques, Francisco 8 Mula, Olga 8 Néron, David 8 Oden, John Tinsley 8 Orszag, Steven Alan 8 Pain, Christopher C. 8 Prudhomme, Serge 8 Rave, Stephan David 8 Smetana, Kathrin 8 Uzunca, Murat 8 Vohralík, Martin 8 Yotov, Ivan 7 Alla, Alessandro 7 Babuška, Ivo 7 Barone, Matthew F. 7 Brunton, Steven L. ...and 3,087 more Authors all top 5 Cited in 203 Serials 361 Computer Methods in Applied Mechanics and Engineering 284 Journal of Computational Physics 96 Journal of Fluid Mechanics 88 International Journal for Numerical Methods in Engineering 85 Journal of Scientific Computing 83 SIAM Journal on Scientific Computing 82 Computers and Fluids 56 Computers & Mathematics with Applications 56 Computational Mechanics 51 Applied Numerical Mathematics 50 Journal of Computational and Applied Mathematics 44 Physics of Fluids 43 Advances in Computational Mathematics 37 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 36 Comptes Rendus. 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Series B 2 Acta Applicandae Mathematicae 2 Mathematical and Computer Modelling 2 Annals of Operations Research ...and 103 more Serials all top 5 Cited in 42 Fields 1,493 Numerical analysis (65-XX) 938 Fluid mechanics (76-XX) 639 Partial differential equations (35-XX) 409 Mechanics of deformable solids (74-XX) 84 Systems theory; control (93-XX) 71 Calculus of variations and optimal control; optimization (49-XX) 70 Statistics (62-XX) 70 Optics, electromagnetic theory (78-XX) 68 Classical thermodynamics, heat transfer (80-XX) 66 Computer science (68-XX) 55 Approximations and expansions (41-XX) 55 Probability theory and stochastic processes (60-XX) 51 Geophysics (86-XX) 48 Biology and other natural sciences (92-XX) 46 Operations research, mathematical programming (90-XX) 41 Dynamical systems and ergodic theory (37-XX) 30 Statistical mechanics, structure of matter (82-XX) 25 Ordinary differential equations (34-XX) 23 Linear and multilinear algebra; matrix theory (15-XX) 14 Harmonic analysis on Euclidean spaces (42-XX) 12 Quantum theory (81-XX) 11 Operator theory (47-XX) 11 Mechanics of particles and systems (70-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 10 Functional analysis (46-XX) 10 Information and communication theory, circuits (94-XX) 6 Integral equations (45-XX) 4 General and overarching topics; collections (00-XX) 4 Combinatorics (05-XX) 4 Functions of a complex variable (30-XX) 4 Relativity and gravitational theory (83-XX) 3 History and biography (01-XX) 3 Real functions (26-XX) 3 Mathematics education (97-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Integral transforms, operational calculus (44-XX) 2 Differential geometry (53-XX) 2 Astronomy and astrophysics (85-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Global analysis, analysis on manifolds (58-XX) Citations by Year