Edit Profile (opens in new tab) Keyes, David Elliot Compute Distance To: Compute Author ID: keyes.david-e Published as: Keyes, David E.; Keyes, David; Keyes, D. E.; Keyes, D. more...less Homepage: https://www.kaust.edu.sa/en/study/faculty/david-keyes External Links: MGP · ORCID · Wikidata · dblp · GND · IdRef · theses.fr Documents Indexed: 111 Publications since 1987 15 Contributions as Editor Co-Authors: 162 Co-Authors with 117 Joint Publications 4,921 Co-Co-Authors all top 5 Co-Authors 5 single-authored 21 Gropp, William D. 20 Cai, Xiao-Chuan 14 Turkiyyah, George M. 11 Ltaief, Hatem 8 Genton, Marc G. 7 Liu, Lulu 6 Luo, Li 5 Boukaram, Wajih-Halim 4 Cao, Jian 4 Knoll, Dana A. 4 Litvinenko, Alexander 4 Smith, Barry F. 4 Widlund, Olof B. 3 Gao, Longfei 3 Ghattas, Omar N. 3 Kaushik, Dinesh K. 3 Knio, Omar M. 3 McHugh, Paul R. 3 Périaux, Jacques F. 3 Smooke, Mitchell D. 3 Sukkari, Dalal 3 Sun, Ying 3 Tidriri, M. Driss 3 Young, David P. 3 Zampini, Stefano 2 Abdulah, Sameh 2 Atassi, Hafiz M. 2 Biegler, Lorenz T. 2 Boukharfane, Radouan 2 Chan, Tony Fan-Cheong 2 Charara, Ali 2 Chávez, Gustavo 2 Dalcín, Lisandro D. 2 Del Rey Fernández, David C. 2 Ecer, Akin 2 Fox, Pat 2 He, Yuan 2 Heinkenschloss, Matthias 2 Hiriyur, Badri 2 Huang, Huang 2 Jardin, Stephen C. 2 Kane, James H. 2 Kelley, Carl T. 2 Logashenko, Dmitry 2 McInnes, Lois Curfman 2 Melvin, Robin G. 2 Parsani, Matteo 2 Prasad, K. Guru 2 Satofuka, Nobuyuki 2 Stoica, Ion Lucretiu 2 Sultan, Florin 2 Susan-Resiga, Romeo F. 2 Tempone, Raúl F. 2 Tuminaro, Ray S. 2 van Bloemen Waanders, Bart G. 2 Waisman, Haim 2 Wittum, Gabriel 2 Yang, Chao 2 Yokota, Rio 2 Yuan, Xuefei 1 Abdelfattah, Ahmad 1 Abduljabbar, Mustafa 1 Ahmadia, Aron J. 1 Al Farhan, Mohammed 1 Al-Harthi, Noha 1 Al Jahdali, R. 1 Alzahrani, Hasnaa 1 Ambartsumyan, Ilona 1 Ashcraft, C. Cleveland 1 Bağci, Hakan 1 Balakrishna, C. K. 1 Benzi, Michele 1 Berger-Vergiat, Luc 1 Bhattacharjee, Amitava 1 Bieterman, Michael B. 1 Biros, George 1 Boman, Erik G. 1 Bui-Thanh, Tan 1 Carpenter, Mark H. 1 Chefter, J. G. 1 Chen, Rongliang 1 Chen, Rui 1 Chen, Yuxin 1 Coffey, Todd S. 1 Debit, Naïma 1 Discacciati, Marco 1 Dobrian, Florin 1 Duff, Iain S. 1 Elman, Howard C. 1 Ern, Alexandre 1 Esposito, Aniello 1 Fang, Fuhui 1 Fendell, Francis E. 1 Freund, Roland W. 1 Garbey, Marc 1 Germaschewski, Kai 1 Giovangigli, Vincent 1 Grauer, Rainer 1 Hager, Georg 1 Herrera, Ismael ...and 70 more Co-Authors all top 5 Serials 18 SIAM Journal on Scientific Computing 9 Journal of Computational Physics 5 ACM Transactions on Mathematical Software 4 SIAM Journal on Scientific and Statistical Computing 3 International Journal for Numerical Methods in Fluids 3 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 3 International Journal for Numerical Methods in Engineering 3 Lecture Notes in Computational Science and Engineering 2 AIAA Journal 2 Computers & Mathematics with Applications 2 Computer Physics Communications 2 Journal of Computational and Applied Mathematics 2 SIAM Journal on Numerical Analysis 2 Computational Statistics and Data Analysis 2 Advances in Computational Mathematics 2 Journal of Agricultural, Biological, and Environmental Statistics 2 Statistics and Computing 1 Computer Methods in Applied Mechanics and Engineering 1 Inverse Problems 1 Numerische Mathematik 1 Parallel Computing 1 Applied Numerical Mathematics 1 Journal of Parallel and Distributed Computing 1 IMPACT of Computing in Science and Engineering 1 Numerical Linear Algebra with Applications 1 Computing and Visualization in Science 1 Computational Methods in Applied Mathematics 1 Comptes Rendus. Mécanique. Académie des Sciences, Paris 1 Contemporary Mathematics 1 Computational Science & Engineering 1 GEM - International Journal on Geomathematics 1 Journal of Computational and Graphical Statistics 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Communications on Applied Mathematics and Computation all top 5 Fields 106 Numerical analysis (65-XX) 40 Fluid mechanics (76-XX) 33 Partial differential equations (35-XX) 16 General and overarching topics; collections (00-XX) 16 Computer science (68-XX) 10 Statistics (62-XX) 7 Mechanics of deformable solids (74-XX) 7 Classical thermodynamics, heat transfer (80-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Optics, electromagnetic theory (78-XX) 4 Geophysics (86-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Ordinary differential equations (34-XX) 2 Probability theory and stochastic processes (60-XX) 2 Operations research, mathematical programming (90-XX) 2 Biology and other natural sciences (92-XX) 1 Mathematical logic and foundations (03-XX) 1 Integral equations (45-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 99 Publications have been cited 1,269 times in 931 Documents Cited by ▼ Year ▼ Jacobian-free Newton-Krylov methods: a survey of approaches and applications. Zbl 1036.65045Knoll, D. A.; Keyes, D. E. 426 2004 Nonlinearly preconditioned inexact Newton algorithms. Zbl 1015.65058Cai, Xiao-Chuan; Keyes, David E. 78 2002 Convergence analysis of pseudo-transient continuation. Zbl 0911.65080Kelley, C. T.; Keyes, David E. 64 1998 Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation. Zbl 0917.76035Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.; Melvin, Robin G.; Young, David P. 49 1998 High-performance parallel implicit CFD. Zbl 0971.68191Gropp, W. D.; Kaushik, D. K.; Keyes, D. E.; Smith, B. F. 33 2001 Field-split preconditioned inexact Newton algorithms. Zbl 1328.65122Liu, Lulu; Keyes, David E. 31 2015 A comparison of domain decomposition techniques for elliptic partial differential equations and their parallel implementation. Zbl 0619.65088Keyes, David E.; Gropp, William D. 28 1987 Nonlinear additive Schwarz preconditioners and application in computational fluid dynamics. Zbl 1025.76040Cai, Xiao-Chuan; Keyes, David E.; Marcinkowski, Leszek 28 2002 Pseudotransient continuation and differential-algebraic equations. Zbl 1048.65080Coffey, Todd S.; Kelley, C. T.; Keyes, David E. 28 2003 Preconditioned Krylov solvers for BEA. Zbl 0800.73504Prasad, K. Guru; Kane, J. H.; Keyes, D. E.; Balakrishna, C. 27 1994 Iterative solution techniques in boundary element analysis. Zbl 0825.73901Kane, J. H.; Keyes, D. E.; Prasad, K. Guru 25 1991 Towards polyalgorithmic linear system solvers for nonlinear elliptic problems. Zbl 0807.65027Ern, Alexandre; Giovangigli, Vincent; Keyes, David E.; Smooke, Mitchell D. 21 1994 Real-time PDE-constrained optimization. Zbl 1117.49004 21 2007 Inexact Schwarz-algebraic multigrid preconditioners for crack problems modeled by extended finite element methods. Zbl 1242.74094Berger-Vergiat, Luc; Waisman, Haim; Hiriyur, Badri; Tuminaro, Ray; Keyes, David 21 2012 Newton-Krylov-Schwarz methods in CFD. Zbl 0876.76059Cai, X.-C.; Gropp, W. D.; Keyes, D. E.; Tidriri, M. D. 19 1994 Large-scale inverse problems and quantification of uncertainty. Zbl 1203.62002 18 2011 Numerical solution of confined axisymmetric laminar diffusion flames. Zbl 0696.65087Smooke, M. D.; Mitchell, R. E.; Keyes, D. E. 16 1989 Aerodynamic applications of Newton-Krylov-Schwarz solvers. Zbl 0854.76073Keyes, David E. 14 1995 Modeling wildland fire propagation with level set methods. Zbl 1186.65140Mallet, V.; Keyes, D. E.; Fendell, F. E. 14 2009 A quasi-algebraic multigrid approach to fracture problems based on extended finite elements. Zbl 1390.74181Hiriyur, B.; Tuminaro, R. S.; Waisman, H.; Boman, E. G.; Keyes, D. E. 13 2012 Additive Schwarz-based fully coupled implicit methods for resistive Hall magnetohydrodynamic problems. Zbl 1343.76049Ovtchinnikov, S.; Dobrian, F.; Cai, X.-C.; Keyes, D. E. 11 2007 A note on adaptive nonlinear preconditioning techniques. Zbl 1446.65027Liu, Lulu; Keyes, David E.; Krause, Rolf 11 2018 Complexity of parallel implementation of domain decomposition techniques for elliptic partial differential equations. Zbl 0645.65069Gropp, William D.; Keyes, David E. 10 1988 A nonlinear additive Schwarz preconditioned inexact Newton method for shocked duct flows. Zbl 1201.76107Cai, Xiao-Chuan; Keyes, David E.; Young, David P. 9 2002 Hierarchical matrix operations on GPUs. Matrix-vector multiplication and compression. Zbl 1471.65027Boukaram, Wajih; Turkiyyah, George; Keyes, David 9 2019 A comparison of some domain decomposition and ILU preconditioned iterative methods for nonsymmetric elliptic problems. Zbl 0838.65025Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E. 9 1994 Domain decomposition with local mesh refinement. Zbl 0756.65045Gropp, William D.; Keyes, David E. 9 1992 On the robustness and performance of entropy stable collocated discontinuous Galerkin methods. Zbl 07510039Rojas, Diego; Boukharfane, Radouan; Dalcin, Lisandro; Del Rey Fernández, David C.; Ranocha, Hendrik; Keyes, David E.; Parsani, Matteo 8 2021 Convergence analysis for the multiplicative Schwarz preconditioned inexact Newton algorithm. Zbl 1352.65142Liu, Lulu; Keyes, David E. 8 2016 Fifth international SIAM symposium on domain decomposition methods for partial differential equations, held in Norfolk, Virginia, USA, May 6-8, 1991. Zbl 0758.00015 8 1992 Newton-Krylov methods for low-Mach-number compressible combustion. Zbl 0900.76406Knoll, D. A.; McHugh, P. R.; Keyes, D. E. 7 1996 Hierarchical decompositions for the computation of high-dimensional multivariate normal probabilities. Zbl 07498945Genton, Marc G.; Keyes, David E.; Turkiyyah, George 7 2018 Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids. Zbl 1435.76038Luo, Li; Liu, Lulu; Cai, Xiao-Chuan; Keyes, David E. 7 2020 Accelerated dimension-independent adaptive metropolis. Zbl 1352.65029Chen, Yuxin; Keyes, David; Law, Kody J. H.; Ltaief, Hatem 7 2016 Additive Schwarz methods with nonreflecting boundary conditions for the parallel computation of Helmholtz problems. Zbl 0910.65086McInnes, Lois C.; Susan-Resiga, Romeo F.; Keyes, David E.; Atassi, Hafiz M. 7 1998 Interface preconditionings for domain-decomposed convection-diffusion operators. Zbl 0722.65060Chan, Tony F.; Keyes, David E. 7 1990 A multilayer nonlinear elimination preconditioned inexact Newton method for steady-state incompressible flow problems in three dimensions. Zbl 1456.76104Luo, Li; Cai, Xiao-Chuan; Yan, Zhengzheng; Xu, Lei; Keyes, David E. 6 2020 Flame sheet starting estimates for counterflow diffusion flame problems. Zbl 0656.65111Keyes, D. E.; Smooke, M. D. 6 1987 Smooth and robust solutions for Dirichlet boundary control of fluid-solid conjugate heat transfer problems. Zbl 1351.49033Yan, Yan; Keyes, David E. 6 2015 Newton-Krylov-Schwarz methods: Interfacing sparse linear solvers with nonlinear applications. Zbl 0900.65158Keyes, D. E.; Venkatakrishnan, V. 5 1996 Likelihood approximation with hierarchical matrices for large spatial datasets. Zbl 1507.62110Litvinenko, Alexander; Sun, Ying; Genton, Marc G.; Keyes, David E. 5 2019 Randomized GPU algorithms for the construction of hierarchical matrices from matrix-vector operations. Zbl 07099326Boukaram, Wajih; Turkiyyah, George; Keyes, David 5 2019 Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner. Zbl 1416.65263Gao, Longfei; Keyes, David 5 2019 Hierarchical-block conditioning approximations for high-dimensional multivariate normal probabilities. Zbl 1430.62094Cao, Jian; Genton, Marc G.; Keyes, David E.; Turkiyyah, George M. 5 2019 Domain decomposition methods in computational fluid dynamics. Zbl 0745.76062Gropp, William D.; Keyes, David E. 5 1992 A comparison of some domain decomposition algorithms for nonsymmetric ellliptic problems. Zbl 0770.65079Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E. 5 1992 SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids. Zbl 1412.65075Gao, Longfei; Del Rey Fernández, David C.; Carpenter, Mark; Keyes, David 5 2019 Exaflop/s: the why and the how. (Exaflop/s : pourquoi et comment.) Zbl 1221.00058Keyes, David E. 5 2011 Hierarchical algorithms on hierarchical architectures. Zbl 1462.65048Keyes, D. E.; Ltaief, H.; Turkiyyah, G. 5 2020 Optimized explicit Runge-Kutta schemes for high-order collocated discontinuous Galerkin methods for compressible fluid dynamics. Zbl 07546696Al Jahdali, R.; Dalcin, L.; Boukharfane, R.; Nolasco, I. R.; Keyes, D. E.; Parsani, M. 4 2022 Implicit symmetrized streamfunction formulations of magnetohydrodynamics. Zbl 1149.76028Kang, K. S.; Keyes, D. E. 3 2008 Extreme scale FMM-accelerated boundary integral equation solver for wave scattering. Zbl 1461.65254Abduljabbar, Mustafa; Al Farhan, Mohammed; Al-Harthi, Noha; Chen, Rui; Yokota, Rio; Bagci, Hakan; Keyes, David 3 2019 Competition on spatial statistics for large datasets. Zbl 07603083Huang, Huang; Abdulah, Sameh; Sun, Ying; Ltaief, Hatem; Keyes, David E.; Genton, Marc G. 3 2021 Hierarchical matrix approximations of Hessians arising in inverse problems governed by PDEs. Zbl 1453.65289Ambartsumyan, Ilona; Boukaram, Wajih; Bui-Thanh, Tan; Ghattas, Omar; Keyes, David; Stadler, Georg; Turkiyyah, George; Zampini, Stefano 3 2020 Tucker tensor analysis of Matérn functions in spatial statistics. Zbl 1420.60084Litvinenko, Alexander; Keyes, David; Khoromskaia, Venera; Khoromskij, Boris N.; Matthies, Hermann G. 3 2019 Domain decomposition on parallel computers. Zbl 0703.65078Gropp, William D.; Keyes, David E. 3 1989 Application of Newton-Krylov-Schwarz algorithm to low-Mach-number compressible combustion. Zbl 0900.76422McHugh, P. R.; Knoll, D. A.; Keyes, D. E. 3 1998 Fast multipole preconditioners for sparse matrices arising from elliptic equations. Zbl 1398.65039Ibeid, Huda; Yokota, Rio; Pestana, Jennifer; Keyes, David 3 2018 Domain-based parallelism and problem decomposition methods in computational science and engineering. Zbl 0829.00009 3 1995 Using Krylov-Schwarz methods in an adaptive mesh refinement environment. Zbl 1246.65228Germaschewski, Kai; Bhattacharjee, Amitava; Grauer, Rainer; Keyes, David; Smith, Barry 3 2005 Domain decomposition methods in scientific and engineering computing. Proceedings of the 7th international conference on domain decomposition, October 27-30, 1993, Pennsylvania State University, PA, USA. Zbl 0809.00026 3 1994 Parallel implicit methods for aerodynamics. Zbl 0818.76065Cai, X.-C.; Gropp, W. D.; Keyes, D. E.; Tidriri, M. D. 3 1994 Parallel performance of domain-decomposed preconditioned Krylov methods for PDEs with locally uniform refinement. Zbl 0752.65083Gropp, William D.; Keyes, David E. 3 1992 Domain decomposition methods for the parallel computation of reacting flows. Zbl 0804.76066Keyes, David E. 3 1989 Multicore-optimized wavefront diamond blocking for optimizing stencil updates. Zbl 1331.68286Malas, T.; Hager, G.; Ltaief, H.; Stengel, H.; Wellein, G.; Keyes, D. 3 2015 NKS method for the implicit solution of a coupled Allen-Cahn/Cahn-Hilliard system. Zbl 1465.35343Yang, Chao; Cai, Xiao-Chuan; Keyes, David E.; Pernice, Michael 3 2014 Exploiting low-rank covariance structures for computing high-dimensional normal and Student-\(t\) probabilities. Zbl 1461.62014Cao, Jian; Genton, Marc G.; Keyes, David E.; Turkiyyah, George M. 3 2021 Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients. Zbl 1460.65028Chávez, Gustavo; Turkiyyah, George; Zampini, Stefano; Keyes, David 2 2018 Domain decomposition methods in science and engineering XVII. Selected papers based on the presentations at the 17th international conference on domain decomposition methods, St. Wolfgang/Strobl, Austria, July 3–7, 2006. Zbl 1130.65004 2 2008 Terascale implicit methods for partial differential equations. Zbl 1018.65121Keyes, David E. 2 2002 Hierarchical matrix approximations for space-fractional diffusion equations. Zbl 1506.65142Boukaram, Wajih; Lucchesi, Marco; Turkiyyah, George; Le Maître, Olivier; Knio, Omar; Keyes, David 2 2020 A QDWH-based SVD software framework on distributed-memory manycore systems. Zbl 1471.65023Sukkari, Dalal; Ltaief, Hatem; Esposito, Aniello; Keyes, David 2 2019 Additive Schwarz methods for hyperbolic equations. Zbl 0909.65062Wu, Yunhai; Cai, Xiao-Chuan; Keyes, David E. 2 1998 Domain-decomposable preconditioners for second-order upwind discretizations of multicomponent systems. Zbl 0766.65103Keyes, David E.; Gropp, William D. 2 1991 Parallel computational fluid dynamics. Towards teraflops, optimization and novel formulations. Proceedings of the parallel CFD ’99 conference, Williamsburg, VA, USA, My 23–26, 1999. Zbl 0972.68173 2 2000 Moving grids for magnetic reconnection via Newton-Krylov methods. Zbl 1219.78036Yuan, Xuefei; Jardin, Stephen C.; Keyes, David E. 2 2011 KBLAS: an optimized library for dense matrix-vector multiplication on GPU accelerators. Zbl 1369.65042Abdelfattah, Ahmad; Keyes, David; Ltaief, Hatem 2 2016 A high performance QDWH-SVD solver using hardware accelerators. Zbl 1369.65058Sukkari, Dalal; Ltaief, Hatem; Keyes, David 2 2016 A parallel domain decomposition-based implicit method for the Cahn-Hilliard-cook phase-field equation in 3D. Zbl 1351.76199Zheng, Xiang; Yang, Chao; Cai, Xiao-Chuan; Keyes, David 2 2015 Prospects for CFD on petaflops systems. Zbl 0990.76074Keyes, David E.; Kaushik, Dinesh K.; Smith, Barry F. 1 2000 H2Opus: a distributed-memory multi-GPU software package for non-local operators. Zbl 1492.65003Zampini, Stefano; Boukaram, Wajih; Turkiyyah, George; Knio, Omar; Keyes, David 1 2022 Nonlinear preconditioning strategies for two-phase flows in porous media discretized by a fully implicit discontinuous Galerkin method. Zbl 1490.65203Luo, Li; Cai, Xiao-Chuan; Keyes, David E. 1 2021 Batched triangular dense linear algebra kernels for very small matrix sizes on GPUs. Zbl 1471.65028Charara, Ali; Keyes, David; Ltaief, Hatem 1 2019 Parallel solution of Helmholtz problems using additive Schwarz methods. Zbl 0940.65121McInnes, L. C.; Susan-Resiga, R.; Atassi, H. M.; Keyes, D. E. 1 1998 Domain decomposition on parallel computers. Zbl 0681.68030Gropp, William D.; Keyes, David E. 1 1989 Domain decomposition techniques for the parallel solution of nonsymmetric systems of elliptic boundary value problems. Zbl 0694.65048Keyes, David E.; Gropp, William D. 1 1990 Domain decomposition methods in science and engineering. XIV. Papers from the 14th international conference on domain decomposition methods, Cocoyoc, México, January 6–12, 2002. Zbl 1103.65004 1 2003 On the interaction of architecture and algorithm in the domain-based parallelization of an unstructured-grid incompressible flow code. Zbl 0921.76128Kaushik, Dinesh K.; Keyes, David E.; Smith, Barry F. 1 1998 Convergence rate estimate for a domain decomposition method. Zbl 0727.65105Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E. 1 1991 Parallel domain decomposition and the solution of nonlinear systems of equations. Zbl 0767.65040Gropp, William D.; Keyes, David E. 1 1991 Domain decomposition as a mechanism for using asymptotic methods. Zbl 0808.65124Gropp, William D.; Keyes, David E. 1 1993 Large-scale parameter extraction in electrocardiology models through Born approximation. Zbl 1303.92051He, Yuan; Keyes, David E. 1 2013 Approximate error bounds on solutions of nonlinearly preconditioned PDEs. Zbl 1469.49028Liu, Lulu; Keyes, David E. 1 2021 An \(O(N)\) algorithm for computing expectation of \(N\)-dimensional truncated multi-variate normal distribution. I: Fundamentals. Zbl 07400547Huang, Jingfang; Cao, Jian; Fang, Fuhui; Genton, Marc G.; Keyes, David E.; Turkiyyah, George 1 2021 Redesigning triangular dense matrix computations on GPUs. Zbl 1439.65233Charara, Ali; Ltaief, Hatem; Keyes, David 1 2016 Solution of the 3D density-driven groundwater flow problem with uncertain porosity and permeability. Zbl 1434.76016Litvinenko, Alexander; Logashenko, Dmitry; Tempone, Raul; Wittum, Gabriel; Keyes, David 1 2020 A direct elliptic solver based on hierarchically low-rank Schur complements. Zbl 1367.65149Chávez, Gustavo; Turkiyyah, George; Keyes, David E. 1 2017 Nonlinear multiplicative Schwarz preconditioning in natural convection cavity flow. Zbl 1445.76074Liu, Lulu; Zhang, Wei; Keyes, David E. 1 2017 Numerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton-Krylov-Schwarz. Zbl 1277.49037Yuan, Xuefei; Jardin, Stephen C.; Keyes, David E. 1 2012 Optimized explicit Runge-Kutta schemes for high-order collocated discontinuous Galerkin methods for compressible fluid dynamics. Zbl 07546696Al Jahdali, R.; Dalcin, L.; Boukharfane, R.; Nolasco, I. R.; Keyes, D. E.; Parsani, M. 4 2022 H2Opus: a distributed-memory multi-GPU software package for non-local operators. Zbl 1492.65003Zampini, Stefano; Boukaram, Wajih; Turkiyyah, George; Knio, Omar; Keyes, David 1 2022 On the robustness and performance of entropy stable collocated discontinuous Galerkin methods. Zbl 07510039Rojas, Diego; Boukharfane, Radouan; Dalcin, Lisandro; Del Rey Fernández, David C.; Ranocha, Hendrik; Keyes, David E.; Parsani, Matteo 8 2021 Competition on spatial statistics for large datasets. Zbl 07603083Huang, Huang; Abdulah, Sameh; Sun, Ying; Ltaief, Hatem; Keyes, David E.; Genton, Marc G. 3 2021 Exploiting low-rank covariance structures for computing high-dimensional normal and Student-\(t\) probabilities. Zbl 1461.62014Cao, Jian; Genton, Marc G.; Keyes, David E.; Turkiyyah, George M. 3 2021 Nonlinear preconditioning strategies for two-phase flows in porous media discretized by a fully implicit discontinuous Galerkin method. Zbl 1490.65203Luo, Li; Cai, Xiao-Chuan; Keyes, David E. 1 2021 Approximate error bounds on solutions of nonlinearly preconditioned PDEs. Zbl 1469.49028Liu, Lulu; Keyes, David E. 1 2021 An \(O(N)\) algorithm for computing expectation of \(N\)-dimensional truncated multi-variate normal distribution. I: Fundamentals. Zbl 07400547Huang, Jingfang; Cao, Jian; Fang, Fuhui; Genton, Marc G.; Keyes, David E.; Turkiyyah, George 1 2021 Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids. Zbl 1435.76038Luo, Li; Liu, Lulu; Cai, Xiao-Chuan; Keyes, David E. 7 2020 A multilayer nonlinear elimination preconditioned inexact Newton method for steady-state incompressible flow problems in three dimensions. Zbl 1456.76104Luo, Li; Cai, Xiao-Chuan; Yan, Zhengzheng; Xu, Lei; Keyes, David E. 6 2020 Hierarchical algorithms on hierarchical architectures. Zbl 1462.65048Keyes, D. E.; Ltaief, H.; Turkiyyah, G. 5 2020 Hierarchical matrix approximations of Hessians arising in inverse problems governed by PDEs. Zbl 1453.65289Ambartsumyan, Ilona; Boukaram, Wajih; Bui-Thanh, Tan; Ghattas, Omar; Keyes, David; Stadler, Georg; Turkiyyah, George; Zampini, Stefano 3 2020 Hierarchical matrix approximations for space-fractional diffusion equations. Zbl 1506.65142Boukaram, Wajih; Lucchesi, Marco; Turkiyyah, George; Le Maître, Olivier; Knio, Omar; Keyes, David 2 2020 Solution of the 3D density-driven groundwater flow problem with uncertain porosity and permeability. Zbl 1434.76016Litvinenko, Alexander; Logashenko, Dmitry; Tempone, Raul; Wittum, Gabriel; Keyes, David 1 2020 Hierarchical matrix operations on GPUs. Matrix-vector multiplication and compression. Zbl 1471.65027Boukaram, Wajih; Turkiyyah, George; Keyes, David 9 2019 Likelihood approximation with hierarchical matrices for large spatial datasets. Zbl 1507.62110Litvinenko, Alexander; Sun, Ying; Genton, Marc G.; Keyes, David E. 5 2019 Randomized GPU algorithms for the construction of hierarchical matrices from matrix-vector operations. Zbl 07099326Boukaram, Wajih; Turkiyyah, George; Keyes, David 5 2019 Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner. Zbl 1416.65263Gao, Longfei; Keyes, David 5 2019 Hierarchical-block conditioning approximations for high-dimensional multivariate normal probabilities. Zbl 1430.62094Cao, Jian; Genton, Marc G.; Keyes, David E.; Turkiyyah, George M. 5 2019 SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids. Zbl 1412.65075Gao, Longfei; Del Rey Fernández, David C.; Carpenter, Mark; Keyes, David 5 2019 Extreme scale FMM-accelerated boundary integral equation solver for wave scattering. Zbl 1461.65254Abduljabbar, Mustafa; Al Farhan, Mohammed; Al-Harthi, Noha; Chen, Rui; Yokota, Rio; Bagci, Hakan; Keyes, David 3 2019 Tucker tensor analysis of Matérn functions in spatial statistics. Zbl 1420.60084Litvinenko, Alexander; Keyes, David; Khoromskaia, Venera; Khoromskij, Boris N.; Matthies, Hermann G. 3 2019 A QDWH-based SVD software framework on distributed-memory manycore systems. Zbl 1471.65023Sukkari, Dalal; Ltaief, Hatem; Esposito, Aniello; Keyes, David 2 2019 Batched triangular dense linear algebra kernels for very small matrix sizes on GPUs. Zbl 1471.65028Charara, Ali; Keyes, David; Ltaief, Hatem 1 2019 A note on adaptive nonlinear preconditioning techniques. Zbl 1446.65027Liu, Lulu; Keyes, David E.; Krause, Rolf 11 2018 Hierarchical decompositions for the computation of high-dimensional multivariate normal probabilities. Zbl 07498945Genton, Marc G.; Keyes, David E.; Turkiyyah, George 7 2018 Fast multipole preconditioners for sparse matrices arising from elliptic equations. Zbl 1398.65039Ibeid, Huda; Yokota, Rio; Pestana, Jennifer; Keyes, David 3 2018 Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients. Zbl 1460.65028Chávez, Gustavo; Turkiyyah, George; Zampini, Stefano; Keyes, David 2 2018 A direct elliptic solver based on hierarchically low-rank Schur complements. Zbl 1367.65149Chávez, Gustavo; Turkiyyah, George; Keyes, David E. 1 2017 Nonlinear multiplicative Schwarz preconditioning in natural convection cavity flow. Zbl 1445.76074Liu, Lulu; Zhang, Wei; Keyes, David E. 1 2017 Convergence analysis for the multiplicative Schwarz preconditioned inexact Newton algorithm. Zbl 1352.65142Liu, Lulu; Keyes, David E. 8 2016 Accelerated dimension-independent adaptive metropolis. Zbl 1352.65029Chen, Yuxin; Keyes, David; Law, Kody J. H.; Ltaief, Hatem 7 2016 KBLAS: an optimized library for dense matrix-vector multiplication on GPU accelerators. Zbl 1369.65042Abdelfattah, Ahmad; Keyes, David; Ltaief, Hatem 2 2016 A high performance QDWH-SVD solver using hardware accelerators. Zbl 1369.65058Sukkari, Dalal; Ltaief, Hatem; Keyes, David 2 2016 Redesigning triangular dense matrix computations on GPUs. Zbl 1439.65233Charara, Ali; Ltaief, Hatem; Keyes, David 1 2016 Field-split preconditioned inexact Newton algorithms. Zbl 1328.65122Liu, Lulu; Keyes, David E. 31 2015 Smooth and robust solutions for Dirichlet boundary control of fluid-solid conjugate heat transfer problems. Zbl 1351.49033Yan, Yan; Keyes, David E. 6 2015 Multicore-optimized wavefront diamond blocking for optimizing stencil updates. Zbl 1331.68286Malas, T.; Hager, G.; Ltaief, H.; Stengel, H.; Wellein, G.; Keyes, D. 3 2015 A parallel domain decomposition-based implicit method for the Cahn-Hilliard-cook phase-field equation in 3D. Zbl 1351.76199Zheng, Xiang; Yang, Chao; Cai, Xiao-Chuan; Keyes, David 2 2015 NKS method for the implicit solution of a coupled Allen-Cahn/Cahn-Hilliard system. Zbl 1465.35343Yang, Chao; Cai, Xiao-Chuan; Keyes, David E.; Pernice, Michael 3 2014 Large-scale parameter extraction in electrocardiology models through Born approximation. Zbl 1303.92051He, Yuan; Keyes, David E. 1 2013 Inexact Schwarz-algebraic multigrid preconditioners for crack problems modeled by extended finite element methods. Zbl 1242.74094Berger-Vergiat, Luc; Waisman, Haim; Hiriyur, Badri; Tuminaro, Ray; Keyes, David 21 2012 A quasi-algebraic multigrid approach to fracture problems based on extended finite elements. Zbl 1390.74181Hiriyur, B.; Tuminaro, R. S.; Waisman, H.; Boman, E. G.; Keyes, D. E. 13 2012 Numerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton-Krylov-Schwarz. Zbl 1277.49037Yuan, Xuefei; Jardin, Stephen C.; Keyes, David E. 1 2012 Large-scale inverse problems and quantification of uncertainty. Zbl 1203.62002 18 2011 Exaflop/s: the why and the how. (Exaflop/s : pourquoi et comment.) Zbl 1221.00058Keyes, David E. 5 2011 Moving grids for magnetic reconnection via Newton-Krylov methods. Zbl 1219.78036Yuan, Xuefei; Jardin, Stephen C.; Keyes, David E. 2 2011 Modeling wildland fire propagation with level set methods. Zbl 1186.65140Mallet, V.; Keyes, D. E.; Fendell, F. E. 14 2009 Implicit symmetrized streamfunction formulations of magnetohydrodynamics. Zbl 1149.76028Kang, K. S.; Keyes, D. E. 3 2008 Domain decomposition methods in science and engineering XVII. Selected papers based on the presentations at the 17th international conference on domain decomposition methods, St. Wolfgang/Strobl, Austria, July 3–7, 2006. Zbl 1130.65004 2 2008 Real-time PDE-constrained optimization. Zbl 1117.49004 21 2007 Additive Schwarz-based fully coupled implicit methods for resistive Hall magnetohydrodynamic problems. Zbl 1343.76049Ovtchinnikov, S.; Dobrian, F.; Cai, X.-C.; Keyes, D. E. 11 2007 Using Krylov-Schwarz methods in an adaptive mesh refinement environment. Zbl 1246.65228Germaschewski, Kai; Bhattacharjee, Amitava; Grauer, Rainer; Keyes, David; Smith, Barry 3 2005 Jacobian-free Newton-Krylov methods: a survey of approaches and applications. Zbl 1036.65045Knoll, D. A.; Keyes, D. E. 426 2004 Pseudotransient continuation and differential-algebraic equations. Zbl 1048.65080Coffey, Todd S.; Kelley, C. T.; Keyes, David E. 28 2003 Domain decomposition methods in science and engineering. XIV. Papers from the 14th international conference on domain decomposition methods, Cocoyoc, México, January 6–12, 2002. Zbl 1103.65004 1 2003 Nonlinearly preconditioned inexact Newton algorithms. Zbl 1015.65058Cai, Xiao-Chuan; Keyes, David E. 78 2002 Nonlinear additive Schwarz preconditioners and application in computational fluid dynamics. Zbl 1025.76040Cai, Xiao-Chuan; Keyes, David E.; Marcinkowski, Leszek 28 2002 A nonlinear additive Schwarz preconditioned inexact Newton method for shocked duct flows. Zbl 1201.76107Cai, Xiao-Chuan; Keyes, David E.; Young, David P. 9 2002 Terascale implicit methods for partial differential equations. Zbl 1018.65121Keyes, David E. 2 2002 High-performance parallel implicit CFD. Zbl 0971.68191Gropp, W. D.; Kaushik, D. K.; Keyes, D. E.; Smith, B. F. 33 2001 Parallel computational fluid dynamics. Towards teraflops, optimization and novel formulations. Proceedings of the parallel CFD ’99 conference, Williamsburg, VA, USA, My 23–26, 1999. Zbl 0972.68173 2 2000 Prospects for CFD on petaflops systems. Zbl 0990.76074Keyes, David E.; Kaushik, Dinesh K.; Smith, Barry F. 1 2000 Convergence analysis of pseudo-transient continuation. Zbl 0911.65080Kelley, C. T.; Keyes, David E. 64 1998 Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation. Zbl 0917.76035Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.; Melvin, Robin G.; Young, David P. 49 1998 Additive Schwarz methods with nonreflecting boundary conditions for the parallel computation of Helmholtz problems. Zbl 0910.65086McInnes, Lois C.; Susan-Resiga, Romeo F.; Keyes, David E.; Atassi, Hafiz M. 7 1998 Application of Newton-Krylov-Schwarz algorithm to low-Mach-number compressible combustion. Zbl 0900.76422McHugh, P. R.; Knoll, D. A.; Keyes, D. E. 3 1998 Additive Schwarz methods for hyperbolic equations. Zbl 0909.65062Wu, Yunhai; Cai, Xiao-Chuan; Keyes, David E. 2 1998 Parallel solution of Helmholtz problems using additive Schwarz methods. Zbl 0940.65121McInnes, L. C.; Susan-Resiga, R.; Atassi, H. M.; Keyes, D. E. 1 1998 On the interaction of architecture and algorithm in the domain-based parallelization of an unstructured-grid incompressible flow code. Zbl 0921.76128Kaushik, Dinesh K.; Keyes, David E.; Smith, Barry F. 1 1998 Newton-Krylov methods for low-Mach-number compressible combustion. Zbl 0900.76406Knoll, D. A.; McHugh, P. R.; Keyes, D. E. 7 1996 Newton-Krylov-Schwarz methods: Interfacing sparse linear solvers with nonlinear applications. Zbl 0900.65158Keyes, D. E.; Venkatakrishnan, V. 5 1996 Aerodynamic applications of Newton-Krylov-Schwarz solvers. Zbl 0854.76073Keyes, David E. 14 1995 Domain-based parallelism and problem decomposition methods in computational science and engineering. Zbl 0829.00009 3 1995 Preconditioned Krylov solvers for BEA. Zbl 0800.73504Prasad, K. Guru; Kane, J. H.; Keyes, D. E.; Balakrishna, C. 27 1994 Towards polyalgorithmic linear system solvers for nonlinear elliptic problems. Zbl 0807.65027Ern, Alexandre; Giovangigli, Vincent; Keyes, David E.; Smooke, Mitchell D. 21 1994 Newton-Krylov-Schwarz methods in CFD. Zbl 0876.76059Cai, X.-C.; Gropp, W. D.; Keyes, D. E.; Tidriri, M. D. 19 1994 A comparison of some domain decomposition and ILU preconditioned iterative methods for nonsymmetric elliptic problems. Zbl 0838.65025Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E. 9 1994 Domain decomposition methods in scientific and engineering computing. Proceedings of the 7th international conference on domain decomposition, October 27-30, 1993, Pennsylvania State University, PA, USA. Zbl 0809.00026 3 1994 Parallel implicit methods for aerodynamics. Zbl 0818.76065Cai, X.-C.; Gropp, W. D.; Keyes, D. E.; Tidriri, M. D. 3 1994 Domain decomposition as a mechanism for using asymptotic methods. Zbl 0808.65124Gropp, William D.; Keyes, David E. 1 1993 Domain decomposition with local mesh refinement. Zbl 0756.65045Gropp, William D.; Keyes, David E. 9 1992 Fifth international SIAM symposium on domain decomposition methods for partial differential equations, held in Norfolk, Virginia, USA, May 6-8, 1991. Zbl 0758.00015 8 1992 Domain decomposition methods in computational fluid dynamics. Zbl 0745.76062Gropp, William D.; Keyes, David E. 5 1992 A comparison of some domain decomposition algorithms for nonsymmetric ellliptic problems. Zbl 0770.65079Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E. 5 1992 Parallel performance of domain-decomposed preconditioned Krylov methods for PDEs with locally uniform refinement. Zbl 0752.65083Gropp, William D.; Keyes, David E. 3 1992 Iterative solution techniques in boundary element analysis. Zbl 0825.73901Kane, J. H.; Keyes, D. E.; Prasad, K. Guru 25 1991 Domain-decomposable preconditioners for second-order upwind discretizations of multicomponent systems. Zbl 0766.65103Keyes, David E.; Gropp, William D. 2 1991 Convergence rate estimate for a domain decomposition method. Zbl 0727.65105Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E. 1 1991 Parallel domain decomposition and the solution of nonlinear systems of equations. Zbl 0767.65040Gropp, William D.; Keyes, David E. 1 1991 Interface preconditionings for domain-decomposed convection-diffusion operators. Zbl 0722.65060Chan, Tony F.; Keyes, David E. 7 1990 Domain decomposition techniques for the parallel solution of nonsymmetric systems of elliptic boundary value problems. Zbl 0694.65048Keyes, David E.; Gropp, William D. 1 1990 Numerical solution of confined axisymmetric laminar diffusion flames. Zbl 0696.65087Smooke, M. D.; Mitchell, R. E.; Keyes, D. E. 16 1989 Domain decomposition on parallel computers. Zbl 0703.65078Gropp, William D.; Keyes, David E. 3 1989 Domain decomposition methods for the parallel computation of reacting flows. Zbl 0804.76066Keyes, David E. 3 1989 Domain decomposition on parallel computers. Zbl 0681.68030Gropp, William D.; Keyes, David E. 1 1989 Complexity of parallel implementation of domain decomposition techniques for elliptic partial differential equations. Zbl 0645.65069Gropp, William D.; Keyes, David E. 10 1988 A comparison of domain decomposition techniques for elliptic partial differential equations and their parallel implementation. Zbl 0619.65088Keyes, David E.; Gropp, William D. 28 1987 Flame sheet starting estimates for counterflow diffusion flame problems. Zbl 0656.65111Keyes, D. E.; Smooke, M. D. 6 1987 all cited Publications top 5 cited Publications all top 5 Cited by 1,801 Authors 35 Keyes, David Elliot 32 Cai, Xiao-Chuan 21 Knoll, Dana A. 20 Yang, Haijian 16 Chacón, Luis 14 Yang, Chao 13 Shadid, John N. 13 Smooke, Mitchell D. 11 An, Hengbin 10 Bennett, Beth Anne V. 10 Hwang, Fengnan 9 Badia, Santiago 9 Luo, Xinlong 9 Turkiyyah, George M. 9 Wu, Qingbiao 8 Chen, Rongliang 8 Huang, Jingfang 8 Moroney, Timothy J. 8 Sun, Shuyu 7 Biros, George 7 Lin, Paul T. 7 Liu, Lulu 7 Luo, Li 7 Pawlowski, Roger P. 6 Chen, Minhong 6 Genton, Marc G. 6 Huang, Jizu 6 Kelley, Carl T. 6 Klawonn, Axel 6 Lanser, Martin 6 Park, Hyeongkae 6 Power, Henry 6 Rheinbach, Oliver 6 Schmid, Peter Joseph 6 Taitano, William T. 5 Bijl, Hester 5 Botti, Lorenzo 5 Cheng, Yingda 5 Dalcín, Lisandro D. 5 Farhat, Charbel H. 5 Gander, Martin Jakob 5 Gassner, Gregor J. 5 Kadioglu, Samet Y. 5 Lemieux, Jean-François 5 Mavriplis, Dimitri J. 5 Mo, Zeyao 5 Pagnini, Gianni 5 Parsani, Matteo 5 Salamatova, Victoria Yu. 5 Turner, Ian William 5 van Zuijlen, Alexander H. 5 Vuik, Cornelis 5 Zingg, David W. 4 Berger-Vergiat, Luc 4 Birken, Philipp 4 Cao, Jian 4 Chen, Guangye 4 Coutinho, Alvaro L. 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A. 4 Crivellini, Andrea 4 Ghattas, Omar N. 4 Gropp, William D. 4 Hansen, Glen A. 4 Hennigan, Gary L. 4 Jiang, Jiamin 4 Krause, Rolf H. 4 Le, Duc-Vinh 4 Ltaief, Hatem 4 Nourgaliev, Robert R. 4 Pavarino, Luca Franco 4 Philip, Bobby 4 Qu, Wenzhen 4 Sipp, Denis 4 Tchelepi, Hamdi A. 4 Tuminaro, Ray S. 4 Vassilevski, Panayot Spirov 4 Verdugo, Francesc 4 Waisman, Haim 4 Xiao, Hang 4 Xu, Jinchao 4 Yan, Zhengzheng 4 Zampini, Stefano 3 Babuška, Ivo 3 Bassi, Francesco 3 Benner, Peter 3 Berenguer, Laurent 3 Berrill, Mark A. 3 Bordas, Stéphane Pierre Alain 3 Boukaram, Wajih-Halim 3 Brown, David A. 3 Bu, Sunyoung 3 Bujurke, Nagendrappa M. 3 Christlieb, Andrew J. 3 De, Suvranu 3 Delzanno, Gian Luca 3 Demanet, Laurent 3 Elman, Howard C. 3 Feng, Tao 3 Fischer, Paul F. 3 Geuzaine, Philippe 3 Gosselet, Pierre ...and 1,701 more Authors all top 5 Cited in 140 Serials 232 Journal of Computational Physics 74 Computer Methods in Applied Mechanics and Engineering 48 Computers and Fluids 41 SIAM Journal on Scientific Computing 32 Journal of Computational and Applied Mathematics 22 Journal of Scientific Computing 22 Engineering Analysis with Boundary Elements 21 Computers & Mathematics with Applications 21 International Journal for Numerical Methods in Engineering 21 Applied Numerical Mathematics 18 Applied Mathematics and Computation 16 Computational Mechanics 15 Applied Mathematical Modelling 12 Mathematics of Computation 12 Advances in Computational Mathematics 11 Combustion Theory and Modelling 11 Communications in Computational Physics 10 International Journal for Numerical Methods in Fluids 9 Journal of Fluid Mechanics 9 BIT 9 Computational Geosciences 8 Numerical Algorithms 7 Numerische Mathematik 7 International Journal of Computer Mathematics 7 Computational and Applied Mathematics 6 Numerical Linear Algebra with Applications 6 Archives of Computational Methods in Engineering 6 Communications on Applied Mathematics and Computation 5 Computer Physics Communications 5 Numerical Methods for Partial Differential Equations 5 SIAM Review 5 Communications in Numerical Methods in Engineering 5 Journal of Agricultural, Biological, and Environmental Statistics 5 SIAM/ASA Journal on Uncertainty Quantification 4 Computing 4 Optimization Methods & Software 4 Optimization and Engineering 4 Differential Equations 4 Acta Numerica 4 Journal of Computational and Theoretical Transport 3 Mathematical Methods in the Applied Sciences 3 Journal of Optimization Theory and Applications 3 Mathematical and Computer Modelling 3 SIAM Journal on Matrix Analysis and Applications 3 Journal of Mathematical Imaging and Vision 3 Mathematical Problems in Engineering 3 International Journal of Computational Fluid Dynamics 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 SIAM Journal on Imaging Sciences 3 Philosophical Transactions of the Royal Society of London. 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Mathematical Models & Methods in Applied Sciences ...and 40 more Serials all top 5 Cited in 33 Fields 667 Numerical analysis (65-XX) 396 Fluid mechanics (76-XX) 191 Partial differential equations (35-XX) 129 Mechanics of deformable solids (74-XX) 54 Classical thermodynamics, heat transfer (80-XX) 45 Statistical mechanics, structure of matter (82-XX) 44 Calculus of variations and optimal control; optimization (49-XX) 37 Statistics (62-XX) 37 Operations research, mathematical programming (90-XX) 36 Computer science (68-XX) 35 Geophysics (86-XX) 25 Optics, electromagnetic theory (78-XX) 23 Biology and other natural sciences (92-XX) 17 Probability theory and stochastic processes (60-XX) 14 Ordinary differential equations (34-XX) 11 Information and communication theory, circuits (94-XX) 10 Systems theory; control (93-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 6 Integral equations (45-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Approximations and expansions (41-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Quantum theory (81-XX) 3 Mathematical logic and foundations (03-XX) 3 Real functions (26-XX) 3 Astronomy and astrophysics (85-XX) 2 Potential theory (31-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of particles and systems (70-XX) 2 Relativity and gravitational theory (83-XX) 1 Combinatorics (05-XX) 1 Special functions (33-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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