Edit Profile (opens in new tab) Cai, Xiao-Chuan Co-Author Distance Author ID: cai.xiao-chuan Published as: Cai, Xiao-Chuan; Cai, X.-C.; Cai, Xiao-Chuan. more...less Homepage: https://www.colorado.edu/faculty/cai/ External Links: MGP · dblp Documents Indexed: 130 Publications since 1990, including 1 Additional arXiv Preprint 7 Contributions as Editor Co-Authors: 101 Co-Authors with 122 Joint Publications 3,803 Co-Co-Authors all top 5 Co-Authors 8 single-authored 21 Keyes, David Elliot 14 Chen, Rongliang 13 Yang, Chao 12 Hwang, Fengnan 10 Luo, Li 9 Sarkis, Marcus V. 8 Yang, Haijian 7 Yan, Zhengzheng 6 Dryja, Maksymilian 6 Gropp, William D. 5 Widlund, Olof B. 5 Zou, Jun 4 Barker, Andrew T. 4 Deng, Xiaomao 4 Huang, Jizu 4 Klawonn, Axel 4 Prudencio, Ernesto E. 4 Wu, Yuqi 4 Zhao, Yubo 3 Kong, Fande 3 Li, Shishun 3 Liao, Ziju 3 Liu, Si 3 Marcinkowski, Leszek 3 Wang, Xiaoping 2 Benzi, Michele 2 Bialecki, Bernard 2 Chen, Xingding 2 Duff, Iain S. 2 Elman, Howard C. 2 Farhat, Charbel H. 2 Gong, Shihua 2 Jin, Chao 2 Jordan, Kirk E. 2 Kelley, Tim 2 Kilmer, Misha Elena 2 Kim, Hyea Hyun 2 Leyffer, Sven 2 Liu, Lulu 2 Liu, Yingzhi 2 Manteuffel, Thomas A. 2 McCormick, Steve Fahrney 2 Murillo, Maria 2 Ovtchinnikov, Serguei 2 Qin, Shanlin 2 Shiu, Wen-Shin 2 Silvester, David J. 2 Tidriri, M. Driss 2 Tuminaro, Ray S. 2 Walker, Homer F. 2 Woodward, Carol S. 2 Yavneh, Irad 2 Young, David P. 2 Zhang, Qian 2 Zhao, Tao 1 Benner, Peter 1 Brenner, Susanne Cecelia 1 Cao, Jianwen 1 Casarin, Mario A. 1 Cheng, Yu-Lun 1 Cong, Cui 1 de Oliveira-Filho, Waldyr Lopes 1 Dobrian, Florin 1 Elliott, Frank W. jun. 1 Fairweather, Graeme 1 Finol, Ender 1 Freund, Roland W. 1 Gander, Martin Jakob 1 Goossens, Serge 1 Gu, Linyan 1 Gustafson, Karl Edwin 1 Halpern, Laurence 1 Haynes, Ronald D. 1 Jiang, Yi 1 Kheyfets, Vitaly 1 Knoll, Dana A. 1 Lee, Chang-Ock 1 Li, Congming 1 Li, Jingwei 1 Li, Xuefeng 1 Lin, Hsin-Lun 1 Liu, Jia 1 Livshits, Irene 1 MacLachlan, Scott P. 1 Mandel, Jan 1 Mathew, Tarek P. A. 1 Melvin, Robin G. 1 Olson, Luke N. 1 Park, Eun-Jae 1 Pernice, Michael 1 Roose, Dirk 1 Saad, Yousef 1 Shadid, John N. 1 Shao, Xinping 1 Su, Yi-Cheng 1 Suwito, Wan 1 Szyld, Daniel B. 1 Tsao, Chia-Wen 1 Vassilevski, Panayot Spirov 1 Wang, Jingyuan ...and 9 more Co-Authors all top 5 Serials 28 SIAM Journal on Scientific Computing 13 Journal of Computational Physics 7 SIAM Journal on Numerical Analysis 6 Journal of Scientific Computing 6 Numerical Linear Algebra with Applications 5 ETNA. Electronic Transactions on Numerical Analysis 5 Communications in Computational Physics 4 Computers and Fluids 2 Computer Physics Communications 2 International Journal for Numerical Methods in Fluids 2 International Journal for Numerical Methods in Engineering 2 Journal of Computational and Applied Mathematics 2 Numerische Mathematik 2 Lecture Notes in Computational Science and Engineering 2 Inverse Problems and Imaging 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 International Journal for Numerical and Analytical Methods in Geomechanics 1 Mathematics of Computation 1 SIAM Journal on Scientific and Statistical Computing 1 Computational Mechanics 1 Applications of Mathematics 1 Numerical Algorithms 1 International Journal of Computer Mathematics 1 East-West Journal of Numerical Mathematics 1 International Journal of Numerical Analysis and Modeling 1 Cubo 1 Contemporary Mathematics 1 Communications in Applied Mathematics and Computational Science all top 5 Fields 120 Numerical analysis (65-XX) 63 Fluid mechanics (76-XX) 52 Partial differential equations (35-XX) 16 Biology and other natural sciences (92-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 9 Mechanics of deformable solids (74-XX) 8 Operations research, mathematical programming (90-XX) 7 General and overarching topics; collections (00-XX) 4 Computer science (68-XX) 4 Geophysics (86-XX) 4 Systems theory; control (93-XX) 3 Probability theory and stochastic processes (60-XX) 2 Quantum theory (81-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 History and biography (01-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 110 Publications have been cited 1,578 times in 760 Documents Cited by ▼ Year ▼ A restricted additive Schwarz preconditioner for general sparse linear systems. Zbl 0944.65031 Cai, Xiao-Chuan; Sarkis, Marcus 199 1999 Nonlinearly preconditioned inexact Newton algorithms. Zbl 1015.65058 Cai, Xiao-Chuan; Keyes, David E. 88 2002 Additive Schwarz algorithms for parabolic convection-diffusion equations. Zbl 0737.65078 Cai, Xiao-Chuan 82 1991 Domain decomposition algorithms for indefinite elliptic problems. Zbl 0746.65085 Cai, Xiao-Chuan; Widlund, Olof B. 81 1992 Multiplicative Schwarz methods for parabolic problems. Zbl 0803.65096 Cai, Xiao-Chuan 62 1994 Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation. Zbl 0917.76035 Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.; Melvin, Robin G.; Young, David P. 55 1998 A parallel nonlinear additive Schwarz preconditioned inexact Newton algorithm for incompressible Navier-Stokes equations. Zbl 1267.76083 Hwang, Feng-Nan; Cai, Xiao-Chuan 44 2005 Scalable parallel methods for monolithic coupling in fluid-structure interaction with application to blood flow modeling. Zbl 1253.76137 Barker, Andrew T.; Cai, Xiao-Chuan 43 2010 Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems. Zbl 0787.65016 Cai, Xiao-Chuan; Widlund, Olof B. 36 1993 Inexact Newton methods with restricted additive Schwarz based nonlinear elimination for problems with high local nonlinearity. Zbl 1227.65045 Cai, Xiao-Chuan; Li, Xuefeng 33 2011 A fully implicit domain decomposition based ALE framework for three-dimensional fluid-structure interaction with application in blood flow computation. Zbl 1349.76552 Wu, Yuqi; Cai, Xiao-Chuan 33 2014 Restricted additive Schwarz preconditioners with harmonic overlap for symmetric positive definite linear systems. Zbl 1052.65036 Cai, Xiao-Chuan; Dryja, Maksymilian; Sarkis, Marcus 31 2003 Nonlinear additive Schwarz preconditioners and application in computational fluid dynamics. Zbl 1025.76040 Cai, Xiao-Chuan; Keyes, David E.; Marcinkowski, Leszek 31 2002 A class of parallel two-level nonlinear Schwarz preconditioned inexact Newton algorithms. Zbl 1173.76385 Hwang, Feng-Nan; Cai, Xiao-Chuan 30 2007 A fully implicit parallel algorithm for simulating the nonlinear electrical activity of the heart. Zbl 1114.65112 Murillo, Maria; Cai, Xiao-Chuan. 28 2004 Newton-Krylov-Schwarz methods in CFD. Zbl 0876.76059 Cai, X.-C.; Gropp, W. D.; Keyes, D. E.; Tidriri, M. D. 24 1994 A minimum overlap restricted additive Schwarz preconditioner and applications in 3D flow simulations. Zbl 0936.76036 Cai, Xiao-Chuan; Farhat, Charbel; Sarkis, Marcus 23 1998 A parallel adaptive nonlinear elimination preconditioned inexact Newton method for transonic full potential equation. Zbl 1390.76271 Hwang, Feng-Nan; Su, Yi-Cheng; Cai, Xiao-Chuan 20 2015 A fully implicit domain decomposition algorithm for shallow water equations on the cubed-sphere. Zbl 1410.76309 Yang, Chao; Cao, Jianwen; Cai, Xiao-Chuan 19 2010 Two-level Newton and hybrid Schwarz preconditioners for fluid-structure interaction. Zbl 1214.92014 Barker, Andrew T.; Cai, Xiao-Chuan 19 2010 Overlapping Schwarz algorithms for solving Helmholtz’s equation. Zbl 0909.65104 Cai, Xiao-Chuan; Casarin, Mario A.; Elliott, Frank W. jun.; Widlund, Olof B. 19 1998 A preconditioned GMRES method for nonsymmetric or indefinite problems. Zbl 0766.65034 Xu, Jinchao; Cai, Xiao-Chuan 19 1992 Nonlinear preconditioning techniques for full-space Lagrange-Newton solution of PDE-constrained optimization problems. Zbl 1348.65103 Yang, Haijian; Hwang, Feng-Nan; Cai, Xiao-Chuan 19 2016 Two-level nonlinear elimination based preconditioners for inexact Newton methods with application in shocked duct flow calculation. Zbl 1205.65180 Hwang, Feng-Nan; Lin, Hsin-Lun; Cai, Xiao-Chuan 18 2010 Overlapping domain decomposition algorithms for general sparse matrices. Zbl 0851.65083 Cai, Xiao-Chuan; Saad, Yousef 18 1996 Parallel full space SQP Lagrange-Newton-Krylov-Schwarz algorithms for PDE-constrained optimization problems. Zbl 1092.49024 Prudencio, Ernesto E.; Byrd, Richard; Cai, Xiao-Chuan 18 2006 Parallel multilevel restricted Schwarz preconditioners with pollution removing for PDE-constrained optimization. Zbl 1357.76020 Prudencio, Ernesto E.; Cai, Xiao-Chuan 17 2007 Domain decomposition methods for monotone nonlinear elliptic problems. Zbl 0817.65127 Cai, Xiao-Chuan; Dryja, Maksymilian 17 1994 Overlapping nonmatching grid mortar element methods for elliptic problems. Zbl 0927.65131 Cai, Xiao-Chuan; Dryja, Maksymilian; Sarkis, Marcus 16 1998 A highly scalable multilevel Schwarz method with boundary geometry preserving coarse spaces for 3D elasticity problems on domains with complex geometry. Zbl 1380.65404 Kong, Fande; Cai, Xiao-Chuan 16 2016 A scalable nonlinear fluid-structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D. Zbl 1376.76022 Kong, Fande; Cai, Xiao-Chuan 15 2017 A parallel space-time domain decomposition method for unsteady source inversion problems. Zbl 1332.65057 Deng, Xiaomao; Cai, Xiao-Chuan; Zou, Jun 15 2015 A scalable fully implicit compressible Euler solver for mesoscale nonhydrostatic simulation of atmospheric flows. Zbl 1305.86005 Yang, Chao; Cai, Xiao-Chuan 15 2014 Two-level space-time domain decomposition methods for three-dimensional unsteady inverse source problems. Zbl 1342.49044 Deng, Xiaomao; Cai, Xiao-Chuan; Zou, Jun 15 2016 Parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere. Zbl 1316.76016 Yang, Chao; Cai, Xiao-Chuan 14 2011 Fully implicit Lagrange-Newton-Krylov-Schwarz algorithms for boundary control of unsteady incompressible flows. Zbl 1253.65145 Yang, Haijian; Prudencio, Ernesto E.; Cai, Xiao-Chuan 14 2012 A fully implicit method for lattice Boltzmann equations. Zbl 1325.76144 Huang, Jizu; Yang, Chao; Cai, Xiao-Chuan 13 2015 Parallel domain decomposition methods for stochastic elliptic equations. Zbl 1149.65007 Jin, Chao; Cai, Xiao-Chuan; Li, Congming 13 2007 Additive Schwarz-based fully coupled implicit methods for resistive Hall magnetohydrodynamic problems. Zbl 1343.76049 Ovtchinnikov, S.; Dobrian, F.; Cai, X.-C.; Keyes, D. E. 12 2007 A nonlinearly preconditioned inexact Newton algorithm for steady state lattice Boltzmann equations. Zbl 1339.65236 Huang, Jizu; Yang, Chao; Cai, Xiao-Chuan 12 2016 Parallel one-shot Lagrange–Newton–Krylov–Schwarz algorithms for shape optimization of steady incompressible flows. Zbl 1256.49034 Chen, Rongliang; Cai, Xiao-Chuan 12 2012 Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids. Zbl 1435.76038 Luo, Li; Liu, Lulu; Cai, Xiao-Chuan; Keyes, David E. 11 2020 Maximum norm analysis of overlapping nonmatching grid discretizations of elliptic equations. Zbl 0963.65125 Cai, Xiao-Chuan; Mathew, Tarek P.; Sarkis, Marcus V. 10 2000 Convergence analysis of two-level space-time additive Schwarz method for parabolic equations. Zbl 1330.65144 Li, Shishun; Cai, Xiao-Chuan 10 2015 A nonlinear additive Schwarz preconditioned inexact Newton method for shocked duct flows. Zbl 1201.76107 Cai, Xiao-Chuan; Keyes, David E.; Young, David P. 10 2002 A comparison of some domain decomposition and ILU preconditioned iterative methods for nonsymmetric elliptic problems. Zbl 0838.65025 Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E. 9 1994 A parallel domain decomposition method for 3D unsteady incompressible flows at high Reynolds number. Zbl 1298.76057 Chen, Rongliang; Wu, Yuqi; Yan, Zhengzheng; Zhao, Yubo; Cai, Xiao-Chuan 9 2014 Parallel domain decomposition methods with mixed order discretization for fully implicit solution of tracer transport problems on the cubed-sphere. Zbl 1299.76165 Yang, Haijian; Yang, Chao; Cai, Xiao-Chuan 9 2014 A nonlinear elimination preconditioned inexact Newton method for heterogeneous hyperelasticity. Zbl 1436.65065 Gong, Shihua; Cai, Xiao-Chuan 9 2019 An optimal two-level overlapping domain decomposition method for elliptic problems in two and three dimensions. Zbl 0771.65083 Cai, Xiao-Chuan 8 1993 An efficient finite element method for simulation of droplet spreading on a topologically rough surface. Zbl 1380.76042 Luo, Li; Wang, Xiao-Ping; Cai, Xiao-Chuan 8 2017 A multilayer nonlinear elimination preconditioned inexact Newton method for steady-state incompressible flow problems in three dimensions. Zbl 1456.76104 Luo, Li; Cai, Xiao-Chuan; Yan, Zhengzheng; Xu, Lei; Keyes, David E. 8 2020 A nonlinear elimination preconditioned inexact Newton method for blood flow problems in human artery with stenosis. Zbl 1453.65109 Luo, Li; Shiu, Wen-Shin; Chen, Rongliang; Cai, Xiao-Chuan 8 2019 The use of pointwise interpolation in domain decomposition methods with nonnested meshes. Zbl 0826.65023 Cai, Xiao-Chuan 7 1995 Improving robustness and parallel scalability of Newton method through nonlinear preconditioning. Zbl 1067.65052 Hwang, Feng-Nan; Cai, Xiao-Chuan 7 2005 Parallel performance of some two-level ASPIN algorithms. Zbl 1066.65057 Marcinkowski, Leszek; Cai, Xiao-Chuan 7 2005 An additive Schwarz algorithm for nonselfadjoint elliptic equations. Zbl 0701.65072 Cai, Xiao-Chuan 7 1990 Parallel two-grid semismooth Newton-Krylov-Schwarz method for nonlinear complementarity problems. Zbl 1217.65116 Yang, Haijian; Cai, Xiao-Chuan 7 2011 Two-level space-time domain decomposition methods for flow control problems. Zbl 1404.65157 Yang, Haijian; Cai, Xiao-Chuan 7 2017 Nonlinear preconditioning strategies for two-phase flows in porous media discretized by a fully implicit discontinuous Galerkin method. Zbl 1490.65203 Luo, Li; Cai, Xiao-Chuan; Keyes, David E. 7 2021 Multilevel space-time additive Schwarz methods for parabolic equations. Zbl 1405.65113 Li, Shishun; Shao, Xinping; Cai, Xiao-Chuan 7 2018 Implicit space-time domain decomposition methods for stochastic parabolic partial differential equations. Zbl 1292.65002 Cong, Cui; Cai, Xiao-Chuan; Gustafson, Karl 7 2014 A parallel two-level method for simulating blood flows in branching arteries with the resistive boundary condition. Zbl 1429.76023 Wu, Yuqi; Cai, Xiao-Chuan 6 2011 NKS method for the implicit solution of a coupled Allen-Cahn/Cahn-Hilliard system. Zbl 1465.35343 Yang, Chao; Cai, Xiao-Chuan; Keyes, David E.; Pernice, Michael 6 2014 One-level Newton-Krylov-Schwarz algorithm for unsteady nonlinear radiation diffusion problem. Zbl 1164.65468 Ovtchinnikov, Serguei; Cai, Xiao-Chuan 6 2004 Parallel overlapping domain decomposition methods for coupled inverse elliptic problems. Zbl 1169.65342 Cai, Xiao-Chuan; Liu, Si; Zou, Jun 6 2009 A preconditioned recycling GMRES solver for stochastic Helmholtz problems. Zbl 1364.65278 Jin, Chao; Cai, Xiao-Chuan 6 2009 A comparison of some domain decomposition algorithms for nonsymmetric ellliptic problems. Zbl 0770.65079 Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E. 5 1992 Parallel fully coupled Schwarz preconditioners for saddle point problems. Zbl 1112.65026 Hwang, Feng-Nan; Cai, Xiao-Chuan 5 2006 Some observations on the \(l^2\) convergence of the additive Schwarz preconditioned GMRES method. Zbl 1071.65529 Cai, Xiao-Chuan; Zou, Jun 5 2002 NKS for fully coupled fluid-structure interaction with application. Zbl 1284.74029 Barker, Andrew T.; Cai, Xiao-Chuan 4 2009 An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation. Zbl 0798.65105 Bialecki, Bernard; Cai, X.-C.; Dryja, M.; Fairweather, G. 4 1994 \(H^ 1\)-norm error bounds for piecewise Hermite bicubic orthogonal spline collocation schemes for elliptic boundary value problems. Zbl 0809.65107 Bialecki, Bernard; Cai, Xiao-Chuan 4 1994 Parallel two-level domain decomposition based Jacobi-Davidson algorithms for pyramidal quantum dot simulation. Zbl 1378.65110 Zhao, Tao; Hwang, Feng-Nan; Cai, Xiao-Chuan 4 2016 Effective two-level domain decomposition preconditioners for elastic crack problems modeled by extended finite element method. Zbl 1473.65294 Chen, Xingding; Cai, Xiao-Chuan 4 2020 Parallel implicit methods for aerodynamics. Zbl 0818.76065 Cai, X.-C.; Gropp, W. D.; Keyes, D. E.; Tidriri, M. D. 3 1994 An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems. Zbl 1099.65031 Cai, Xiao-Chuan; Marcinkowski, Leszek; Vassilevski, Panayot S. 3 2005 A parallel domain decomposition algorithm for large scale image denoising. Zbl 1427.65401 Chen, Rongliang; Huang, Jizu; Cai, Xiao-Chuan 3 2019 Additive Schwarz methods for hyperbolic equations. Zbl 0909.65062 Wu, Yunhai; Cai, Xiao-Chuan; Keyes, David E. 2 1998 Nonlinear overlapping domain decomposition methods. Zbl 1183.65053 Cai, Xiao-Chuan 2 2009 Local multiplicative Schwarz algorithms for steady and unsteady convection-diffusion equations. Zbl 0913.65083 Cai, X.-C.; Sarkis, M. 2 1998 A parallel domain decomposition-based implicit method for the Cahn-Hilliard-cook phase-field equation in 3D. Zbl 1351.76199 Zheng, Xiang; Yang, Chao; Cai, Xiao-Chuan; Keyes, David 2 2015 A parallel two-level domain decomposition based one-shot method for shape optimization problems. Zbl 1352.76046 Chen, Rongliang; Cai, Xiao-Chuan 2 2014 A parallel domain decomposition algorithm for simulating blood flow with incompressible Navier-Stokes equations with resistive boundary condition. Zbl 1373.76222 Wu, Yuqi; Cai, Xiao-Chuan 2 2012 A domain decomposition based Jacobi-Davidson algorithm for quantum dot simulation. Zbl 1343.82056 Zhao, Tao; Hwang, Feng-Nan; Cai, Xiao-Chuan 2 2016 RASHO: A restricted additive Schwarz preconditioner with harmonic overlap. Zbl 1026.65034 Cai, X.-C.; Dryja, M.; Sarkis, M. 2 2002 A recycling preconditioning method with auxiliary tip subspace for elastic crack propagation simulation using XFEM. Zbl 07517739 Chen, Xingding; Cai, Xiao-Chuan 2 2022 A parallel multilevel domain decomposition method for source identification problems governed by elliptic equations. Zbl 1471.65180 Deng, Xiaomao; Liao, Zi-Ju; Cai, Xiao-Chuan 2 2021 Summation pollution of principal component analysis and an improved algorithm for location sensitive data. Zbl 07478603 Li, Jingwei; Cai, Xiao-Chuan 2 2021 Mixed order discretization based two-level Schwarz preconditioners for a tracer transport problem on the cubed-sphere. Zbl 1390.86038 Yang, Haijian; Yang, Chao; Cai, Xiao-Chuan 2 2015 A highly parallel implicit domain decomposition method for the simulation of the left ventricle on unstructured meshes. Zbl 1468.74066 Jiang, Yi; Chen, Rongliang; Cai, Xiao-Chuan 2 2020 A nonlinear elimination preconditioned Newton method with applications in arterial wall simulation. Zbl 1450.65146 Gong, Shihua; Cai, Xiao-Chuan 2 2018 Newton-Krylov-Schwarz method for a spherical shallow water model. Zbl 1430.76408 Yang, Chao; Cai, Xiao-Chuan 1 2011 Domain decomposition methods for a complementarity problem. Zbl 1217.65115 Yang, Haijian; Cai, Xiao-Chuan 1 2011 Domain decomposition methods 10. The 10th international conference, Boulder, CO, USA, August 10–14, 1997. Zbl 0895.00045 1 1998 A family of overlapping Schwarz algorithms for nonsymmetric and indefinite elliptic problems. Zbl 0854.65113 Cai, Xiao-Chuan 1 1995 A parallel well-balanced finite volume method for shallow water equations with topography on the cubed-sphere. Zbl 1222.76065 Yang, Chao; Cai, Xiao-Chuan 1 2011 Numerical solution for consolidation and desiccation of soft soils. Zbl 1112.74439 Yao, Daniel T. C.; de Oliveira-Filho, Waldyr Lopes; Cai, Xiao-Chuan; Znidarcic, Dobroslav 1 2002 Parallel Newton-Krylov-Schwarz method for solving the anisotropic bidomain equations from the excitation of the heart model. Zbl 1048.92011 Murillo, M.; Cai, X.-C. 1 2002 Domain decomposition methods for PDE constrained optimization problems. Zbl 1118.65341 Prudencio, Ernesto; Byrd, Richard; Cai, Xiao-Chuan 1 2005 \(\mathrm{PIN}^{\mathcal{L}}\): preconditioned inexact Newton with learning capability for nonlinear system of equations. Zbl 1524.76136 Luo, Li; Cai, Xiao-Chuan 1 2023 A recycling preconditioning method with auxiliary tip subspace for elastic crack propagation simulation using XFEM. Zbl 07517739 Chen, Xingding; Cai, Xiao-Chuan 2 2022 Decomposition and composition of deep convolutional neural networks and training acceleration via sub-network transfer learning. Zbl 1524.68316 Gu, Linyan; Zhang, Wei; Liu, Jia; Cai, Xiao-Chuan 1 2022 A nonlinear elimination preconditioned inexact Newton algorithm. Zbl 1492.65144 Liu, Lulu; Hwang, Feng-Nan; Luo, Li; Cai, Xiao-Chuan; Keyes, David E. 1 2022 An efficient two-level overlapping domain decomposition method for recovering unsteady sources of 3D parabolic problems. Zbl 1524.65477 Deng, Xiaomao; Liao, Zi-Ju; Cai, Xiao-Chuan 1 2022 Large eddy simulation of the wind flow in a realistic full-scale urban community with a scalable parallel algorithm. Zbl 1516.76045 Yan, Zhengzheng; Chen, Rongliang; Cai, Xiao-Chuan 1 2022 Nonlinear preconditioning strategies for two-phase flows in porous media discretized by a fully implicit discontinuous Galerkin method. Zbl 1490.65203 Luo, Li; Cai, Xiao-Chuan; Keyes, David E. 7 2021 A parallel multilevel domain decomposition method for source identification problems governed by elliptic equations. Zbl 1471.65180 Deng, Xiaomao; Liao, Zi-Ju; Cai, Xiao-Chuan 2 2021 Summation pollution of principal component analysis and an improved algorithm for location sensitive data. Zbl 07478603 Li, Jingwei; Cai, Xiao-Chuan 2 2021 A central-line coarse preconditioner for Stokes flows in artery-like domains. Zbl 1464.76057 Liu, Yingzhi; Cai, Xiao-Chuan 1 2021 Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids. Zbl 1435.76038 Luo, Li; Liu, Lulu; Cai, Xiao-Chuan; Keyes, David E. 11 2020 A multilayer nonlinear elimination preconditioned inexact Newton method for steady-state incompressible flow problems in three dimensions. Zbl 1456.76104 Luo, Li; Cai, Xiao-Chuan; Yan, Zhengzheng; Xu, Lei; Keyes, David E. 8 2020 Effective two-level domain decomposition preconditioners for elastic crack problems modeled by extended finite element method. Zbl 1473.65294 Chen, Xingding; Cai, Xiao-Chuan 4 2020 A highly parallel implicit domain decomposition method for the simulation of the left ventricle on unstructured meshes. Zbl 1468.74066 Jiang, Yi; Chen, Rongliang; Cai, Xiao-Chuan 2 2020 A nonlinear elimination preconditioned inexact Newton method for heterogeneous hyperelasticity. Zbl 1436.65065 Gong, Shihua; Cai, Xiao-Chuan 9 2019 A nonlinear elimination preconditioned inexact Newton method for blood flow problems in human artery with stenosis. Zbl 1453.65109 Luo, Li; Shiu, Wen-Shin; Chen, Rongliang; Cai, Xiao-Chuan 8 2019 A parallel domain decomposition algorithm for large scale image denoising. Zbl 1427.65401 Chen, Rongliang; Huang, Jizu; Cai, Xiao-Chuan 3 2019 Multilevel space-time additive Schwarz methods for parabolic equations. Zbl 1405.65113 Li, Shishun; Shao, Xinping; Cai, Xiao-Chuan 7 2018 A nonlinear elimination preconditioned Newton method with applications in arterial wall simulation. Zbl 1450.65146 Gong, Shihua; Cai, Xiao-Chuan 2 2018 A scalable nonlinear fluid-structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D. Zbl 1376.76022 Kong, Fande; Cai, Xiao-Chuan 15 2017 An efficient finite element method for simulation of droplet spreading on a topologically rough surface. Zbl 1380.76042 Luo, Li; Wang, Xiao-Ping; Cai, Xiao-Chuan 8 2017 Two-level space-time domain decomposition methods for flow control problems. Zbl 1404.65157 Yang, Haijian; Cai, Xiao-Chuan 7 2017 Nonlinear preconditioning techniques for full-space Lagrange-Newton solution of PDE-constrained optimization problems. Zbl 1348.65103 Yang, Haijian; Hwang, Feng-Nan; Cai, Xiao-Chuan 19 2016 A highly scalable multilevel Schwarz method with boundary geometry preserving coarse spaces for 3D elasticity problems on domains with complex geometry. Zbl 1380.65404 Kong, Fande; Cai, Xiao-Chuan 16 2016 Two-level space-time domain decomposition methods for three-dimensional unsteady inverse source problems. Zbl 1342.49044 Deng, Xiaomao; Cai, Xiao-Chuan; Zou, Jun 15 2016 A nonlinearly preconditioned inexact Newton algorithm for steady state lattice Boltzmann equations. Zbl 1339.65236 Huang, Jizu; Yang, Chao; Cai, Xiao-Chuan 12 2016 Parallel two-level domain decomposition based Jacobi-Davidson algorithms for pyramidal quantum dot simulation. Zbl 1378.65110 Zhao, Tao; Hwang, Feng-Nan; Cai, Xiao-Chuan 4 2016 A domain decomposition based Jacobi-Davidson algorithm for quantum dot simulation. Zbl 1343.82056 Zhao, Tao; Hwang, Feng-Nan; Cai, Xiao-Chuan 2 2016 Simulation of cavity flows by an implicit domain decomposition algorithm for the lattice Boltzmann equations. Zbl 1383.76386 Huang, Jizu; Yang, Chao; Cai, Xiao-Chuan 1 2016 A parallel adaptive nonlinear elimination preconditioned inexact Newton method for transonic full potential equation. Zbl 1390.76271 Hwang, Feng-Nan; Su, Yi-Cheng; Cai, Xiao-Chuan 20 2015 A parallel space-time domain decomposition method for unsteady source inversion problems. Zbl 1332.65057 Deng, Xiaomao; Cai, Xiao-Chuan; Zou, Jun 15 2015 A fully implicit method for lattice Boltzmann equations. Zbl 1325.76144 Huang, Jizu; Yang, Chao; Cai, Xiao-Chuan 13 2015 Convergence analysis of two-level space-time additive Schwarz method for parabolic equations. Zbl 1330.65144 Li, Shishun; Cai, Xiao-Chuan 10 2015 A parallel domain decomposition-based implicit method for the Cahn-Hilliard-cook phase-field equation in 3D. Zbl 1351.76199 Zheng, Xiang; Yang, Chao; Cai, Xiao-Chuan; Keyes, David 2 2015 Mixed order discretization based two-level Schwarz preconditioners for a tracer transport problem on the cubed-sphere. Zbl 1390.86038 Yang, Haijian; Yang, Chao; Cai, Xiao-Chuan 2 2015 A fully implicit domain decomposition based ALE framework for three-dimensional fluid-structure interaction with application in blood flow computation. Zbl 1349.76552 Wu, Yuqi; Cai, Xiao-Chuan 33 2014 A scalable fully implicit compressible Euler solver for mesoscale nonhydrostatic simulation of atmospheric flows. Zbl 1305.86005 Yang, Chao; Cai, Xiao-Chuan 15 2014 A parallel domain decomposition method for 3D unsteady incompressible flows at high Reynolds number. Zbl 1298.76057 Chen, Rongliang; Wu, Yuqi; Yan, Zhengzheng; Zhao, Yubo; Cai, Xiao-Chuan 9 2014 Parallel domain decomposition methods with mixed order discretization for fully implicit solution of tracer transport problems on the cubed-sphere. Zbl 1299.76165 Yang, Haijian; Yang, Chao; Cai, Xiao-Chuan 9 2014 Implicit space-time domain decomposition methods for stochastic parabolic partial differential equations. Zbl 1292.65002 Cong, Cui; Cai, Xiao-Chuan; Gustafson, Karl 7 2014 NKS method for the implicit solution of a coupled Allen-Cahn/Cahn-Hilliard system. Zbl 1465.35343 Yang, Chao; Cai, Xiao-Chuan; Keyes, David E.; Pernice, Michael 6 2014 A parallel two-level domain decomposition based one-shot method for shape optimization problems. Zbl 1352.76046 Chen, Rongliang; Cai, Xiao-Chuan 2 2014 A scalable numerical method for simulating flows around high-speed train under crosswind conditions. Zbl 1373.76107 Yan, Zhengzheng; Chen, Rongliang; Zhao, Yubo; Cai, Xiao-Chuan 1 2014 Parallel fully implicit two-grid methods for distributed control of unsteady incompressible flows. Zbl 1455.76050 Yang, Haijian; Cai, Xiao-Chuan 1 2013 Fully implicit Lagrange-Newton-Krylov-Schwarz algorithms for boundary control of unsteady incompressible flows. Zbl 1253.65145 Yang, Haijian; Prudencio, Ernesto E.; Cai, Xiao-Chuan 14 2012 Parallel one-shot Lagrange–Newton–Krylov–Schwarz algorithms for shape optimization of steady incompressible flows. Zbl 1256.49034 Chen, Rongliang; Cai, Xiao-Chuan 12 2012 A parallel domain decomposition algorithm for simulating blood flow with incompressible Navier-Stokes equations with resistive boundary condition. Zbl 1373.76222 Wu, Yuqi; Cai, Xiao-Chuan 2 2012 Inexact Newton methods with restricted additive Schwarz based nonlinear elimination for problems with high local nonlinearity. Zbl 1227.65045 Cai, Xiao-Chuan; Li, Xuefeng 33 2011 Parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere. Zbl 1316.76016 Yang, Chao; Cai, Xiao-Chuan 14 2011 Parallel two-grid semismooth Newton-Krylov-Schwarz method for nonlinear complementarity problems. Zbl 1217.65116 Yang, Haijian; Cai, Xiao-Chuan 7 2011 A parallel two-level method for simulating blood flows in branching arteries with the resistive boundary condition. Zbl 1429.76023 Wu, Yuqi; Cai, Xiao-Chuan 6 2011 Newton-Krylov-Schwarz method for a spherical shallow water model. Zbl 1430.76408 Yang, Chao; Cai, Xiao-Chuan 1 2011 Domain decomposition methods for a complementarity problem. Zbl 1217.65115 Yang, Haijian; Cai, Xiao-Chuan 1 2011 A parallel well-balanced finite volume method for shallow water equations with topography on the cubed-sphere. Zbl 1222.76065 Yang, Chao; Cai, Xiao-Chuan 1 2011 Scalable parallel methods for monolithic coupling in fluid-structure interaction with application to blood flow modeling. Zbl 1253.76137 Barker, Andrew T.; Cai, Xiao-Chuan 43 2010 A fully implicit domain decomposition algorithm for shallow water equations on the cubed-sphere. Zbl 1410.76309 Yang, Chao; Cao, Jianwen; Cai, Xiao-Chuan 19 2010 Two-level Newton and hybrid Schwarz preconditioners for fluid-structure interaction. Zbl 1214.92014 Barker, Andrew T.; Cai, Xiao-Chuan 19 2010 Two-level nonlinear elimination based preconditioners for inexact Newton methods with application in shocked duct flow calculation. Zbl 1205.65180 Hwang, Feng-Nan; Lin, Hsin-Lun; Cai, Xiao-Chuan 18 2010 Parallel overlapping domain decomposition methods for coupled inverse elliptic problems. Zbl 1169.65342 Cai, Xiao-Chuan; Liu, Si; Zou, Jun 6 2009 A preconditioned recycling GMRES solver for stochastic Helmholtz problems. Zbl 1364.65278 Jin, Chao; Cai, Xiao-Chuan 6 2009 NKS for fully coupled fluid-structure interaction with application. Zbl 1284.74029 Barker, Andrew T.; Cai, Xiao-Chuan 4 2009 Nonlinear overlapping domain decomposition methods. Zbl 1183.65053 Cai, Xiao-Chuan 2 2009 A class of parallel two-level nonlinear Schwarz preconditioned inexact Newton algorithms. Zbl 1173.76385 Hwang, Feng-Nan; Cai, Xiao-Chuan 30 2007 Parallel multilevel restricted Schwarz preconditioners with pollution removing for PDE-constrained optimization. Zbl 1357.76020 Prudencio, Ernesto E.; Cai, Xiao-Chuan 17 2007 Parallel domain decomposition methods for stochastic elliptic equations. Zbl 1149.65007 Jin, Chao; Cai, Xiao-Chuan; Li, Congming 13 2007 Additive Schwarz-based fully coupled implicit methods for resistive Hall magnetohydrodynamic problems. Zbl 1343.76049 Ovtchinnikov, S.; Dobrian, F.; Cai, X.-C.; Keyes, D. E. 12 2007 Parallel full space SQP Lagrange-Newton-Krylov-Schwarz algorithms for PDE-constrained optimization problems. Zbl 1092.49024 Prudencio, Ernesto E.; Byrd, Richard; Cai, Xiao-Chuan 18 2006 Parallel fully coupled Schwarz preconditioners for saddle point problems. Zbl 1112.65026 Hwang, Feng-Nan; Cai, Xiao-Chuan 5 2006 A parallel nonlinear additive Schwarz preconditioned inexact Newton algorithm for incompressible Navier-Stokes equations. Zbl 1267.76083 Hwang, Feng-Nan; Cai, Xiao-Chuan 44 2005 Improving robustness and parallel scalability of Newton method through nonlinear preconditioning. Zbl 1067.65052 Hwang, Feng-Nan; Cai, Xiao-Chuan 7 2005 Parallel performance of some two-level ASPIN algorithms. Zbl 1066.65057 Marcinkowski, Leszek; Cai, Xiao-Chuan 7 2005 An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems. Zbl 1099.65031 Cai, Xiao-Chuan; Marcinkowski, Leszek; Vassilevski, Panayot S. 3 2005 Domain decomposition methods for PDE constrained optimization problems. Zbl 1118.65341 Prudencio, Ernesto; Byrd, Richard; Cai, Xiao-Chuan 1 2005 A fully implicit parallel algorithm for simulating the nonlinear electrical activity of the heart. Zbl 1114.65112 Murillo, Maria; Cai, Xiao-Chuan. 28 2004 One-level Newton-Krylov-Schwarz algorithm for unsteady nonlinear radiation diffusion problem. Zbl 1164.65468 Ovtchinnikov, Serguei; Cai, Xiao-Chuan 6 2004 Restricted additive Schwarz preconditioners with harmonic overlap for symmetric positive definite linear systems. Zbl 1052.65036 Cai, Xiao-Chuan; Dryja, Maksymilian; Sarkis, Marcus 31 2003 Nonlinearly preconditioned inexact Newton algorithms. Zbl 1015.65058 Cai, Xiao-Chuan; Keyes, David E. 88 2002 Nonlinear additive Schwarz preconditioners and application in computational fluid dynamics. Zbl 1025.76040 Cai, Xiao-Chuan; Keyes, David E.; Marcinkowski, Leszek 31 2002 A nonlinear additive Schwarz preconditioned inexact Newton method for shocked duct flows. Zbl 1201.76107 Cai, Xiao-Chuan; Keyes, David E.; Young, David P. 10 2002 Some observations on the \(l^2\) convergence of the additive Schwarz preconditioned GMRES method. Zbl 1071.65529 Cai, Xiao-Chuan; Zou, Jun 5 2002 RASHO: A restricted additive Schwarz preconditioner with harmonic overlap. Zbl 1026.65034 Cai, X.-C.; Dryja, M.; Sarkis, M. 2 2002 Numerical solution for consolidation and desiccation of soft soils. Zbl 1112.74439 Yao, Daniel T. C.; de Oliveira-Filho, Waldyr Lopes; Cai, Xiao-Chuan; Znidarcic, Dobroslav 1 2002 Parallel Newton-Krylov-Schwarz method for solving the anisotropic bidomain equations from the excitation of the heart model. Zbl 1048.92011 Murillo, M.; Cai, X.-C. 1 2002 Maximum norm analysis of overlapping nonmatching grid discretizations of elliptic equations. Zbl 0963.65125 Cai, Xiao-Chuan; Mathew, Tarek P.; Sarkis, Marcus V. 10 2000 A restricted additive Schwarz preconditioner for general sparse linear systems. Zbl 0944.65031 Cai, Xiao-Chuan; Sarkis, Marcus 199 1999 Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation. Zbl 0917.76035 Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.; Melvin, Robin G.; Young, David P. 55 1998 A minimum overlap restricted additive Schwarz preconditioner and applications in 3D flow simulations. Zbl 0936.76036 Cai, Xiao-Chuan; Farhat, Charbel; Sarkis, Marcus 23 1998 Overlapping Schwarz algorithms for solving Helmholtz’s equation. Zbl 0909.65104 Cai, Xiao-Chuan; Casarin, Mario A.; Elliott, Frank W. jun.; Widlund, Olof B. 19 1998 Overlapping nonmatching grid mortar element methods for elliptic problems. Zbl 0927.65131 Cai, Xiao-Chuan; Dryja, Maksymilian; Sarkis, Marcus 16 1998 Additive Schwarz methods for hyperbolic equations. Zbl 0909.65062 Wu, Yunhai; Cai, Xiao-Chuan; Keyes, David E. 2 1998 Local multiplicative Schwarz algorithms for steady and unsteady convection-diffusion equations. Zbl 0913.65083 Cai, X.-C.; Sarkis, M. 2 1998 Domain decomposition methods 10. The 10th international conference, Boulder, CO, USA, August 10–14, 1997. Zbl 0895.00045 1 1998 Overlapping domain decomposition algorithms for general sparse matrices. Zbl 0851.65083 Cai, Xiao-Chuan; Saad, Yousef 18 1996 The use of pointwise interpolation in domain decomposition methods with nonnested meshes. Zbl 0826.65023 Cai, Xiao-Chuan 7 1995 A family of overlapping Schwarz algorithms for nonsymmetric and indefinite elliptic problems. Zbl 0854.65113 Cai, Xiao-Chuan 1 1995 Multiplicative Schwarz methods for parabolic problems. Zbl 0803.65096 Cai, Xiao-Chuan 62 1994 Newton-Krylov-Schwarz methods in CFD. Zbl 0876.76059 Cai, X.-C.; Gropp, W. D.; Keyes, D. E.; Tidriri, M. D. 24 1994 Domain decomposition methods for monotone nonlinear elliptic problems. Zbl 0817.65127 Cai, Xiao-Chuan; Dryja, Maksymilian 17 1994 A comparison of some domain decomposition and ILU preconditioned iterative methods for nonsymmetric elliptic problems. Zbl 0838.65025 Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E. 9 1994 An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation. Zbl 0798.65105 Bialecki, Bernard; Cai, X.-C.; Dryja, M.; Fairweather, G. 4 1994 ...and 10 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,203 Authors 52 Cai, Xiao-Chuan 31 Yang, Haijian 27 Yang, Chao 18 Yang, Danping 17 Keyes, David Elliot 16 Chen, Rongliang 16 Hwang, Fengnan 14 Gander, Martin Jakob 13 Pavarino, Luca Franco 12 Dolean, Victorita 12 Klawonn, Axel 12 Nataf, Frédéric 12 Sun, Shuyu 11 Rheinbach, Oliver 10 Heinlein, Alexander 10 Huang, Jizu 10 Jolivet, Pierre 10 Scacchi, Simone 9 Xu, Jinchao 9 Xu, Xuejun 8 Lanser, Martin 8 Li, Shishun 8 Liu, Lulu 8 Luo, Li 8 Szyld, Daniel B. 8 Zhang, Jiansong 7 Farhat, Charbel H. 7 Ma, Keying 7 Sun, Tongjun 7 Tromeur-Dervout, Damien 7 Yan, Zhengzheng 6 Bukač, Martina 6 Chen, Zhangxin 6 Graham, Ivan G. 6 Haynes, Ronald D. 6 Hu, Qiya 6 Marcinkowski, Leszek 6 Quarteroni, Alfio M. 6 Shu, Shi 6 Spence, Euan A. 6 Tournier, Pierre-Henri 6 Zou, Jun 5 Berenguer, Laurent 5 Bialecki, Bernard 5 Jun, Younbae 5 Krause, Rolf H. 5 Li, Yiteng 5 Liu, Hui 5 Magoulès, Frédéric 5 Miranville, Alain M. 5 Rahman, Talal 5 Tai, Xuecheng 5 Tu, Xuemin 5 Vassilevski, Panayot Spirov 5 Zhang, Hui 4 Chen, Jinru 4 Chung, Tsz Shun Eric 4 Daas, Hussam Al 4 Demkowicz, Leszek F. 4 Deng, Xiaomao 4 di Serafino, Daniela 4 Fu, Shubin 4 Gunzburger, Max D. 4 Jiang, Jiamin 4 Kwok, Felix 4 Li, Lingxiao 4 Lin, Paul T. 4 Loneland, Atle 4 Mai, Tsun-Zee 4 Makki, Ahmad 4 Maute, Kurt 4 Monica Huynh, Ngoc Mai 4 Shadid, John N. 4 Shang, Yueqiang 4 Tchelepi, Hamdi A. 4 van Zuijlen, Alexander H. 4 Widlund, Olof B. 4 Wu, Yuqi 4 Zampini, Stefano 4 Zheng, Weiying 4 Zhong, Liuqiang 3 An, Hengbin 3 Antonietti, Paola Francesca 3 Badia, Santiago 3 Berger-Vergiat, Luc 3 Bijl, Hester 3 Biros, George 3 Blom, David S. 3 Boulaaras, Salah Mahmoud 3 Boulbrachene, Messaoud 3 Brenner, Konstantin 3 Čanić, Sunčica 3 Chen, Xingding 3 Cheng, Tianpei 3 D’Ambra, Pasqua 3 de Sturler, Eric 3 Filippone, Salvatore 3 Glowinski, Roland 3 Gosselet, Pierre 3 Guo, Hui ...and 1,103 more Authors all top 5 Cited in 105 Serials 100 Journal of Computational Physics 65 SIAM Journal on Scientific Computing 57 Computer Methods in Applied Mechanics and Engineering 39 Computers & Mathematics with Applications 32 Journal of Computational and Applied Mathematics 30 Applied Mathematics and Computation 28 Computers and Fluids 25 Applied Numerical Mathematics 22 Journal of Scientific Computing 21 Mathematics of Computation 16 International Journal for Numerical Methods in Engineering 15 Numerical Algorithms 14 Numerical Linear Algebra with Applications 13 Communications in Computational Physics 11 Numerische Mathematik 10 SIAM Journal on Numerical Analysis 9 Computational Mechanics 9 Numerical Methods for Partial Differential Equations 9 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 7 International Journal for Numerical Methods in Fluids 7 Mathematics and Computers in Simulation 7 Mathematical Problems in Engineering 6 Computer Physics Communications 6 International Journal of Computer Mathematics 6 ETNA. 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Real World Applications 1 Mathematical Modelling and Analysis 1 Journal of Applied Mathematics 1 Communications on Pure and Applied Analysis 1 International Journal of Computational Methods 1 Advances in Difference Equations 1 Journal of Computational Acoustics 1 Boundary Value Problems 1 SIAM Journal on Imaging Sciences 1 Mathematical Geosciences ...and 5 more Serials all top 5 Cited in 35 Fields 628 Numerical analysis (65-XX) 259 Fluid mechanics (76-XX) 252 Partial differential equations (35-XX) 101 Mechanics of deformable solids (74-XX) 65 Biology and other natural sciences (92-XX) 36 Calculus of variations and optimal control; optimization (49-XX) 28 Optics, electromagnetic theory (78-XX) 27 Computer science (68-XX) 21 Operations research, mathematical programming (90-XX) 18 Geophysics (86-XX) 16 Statistical mechanics, structure of matter (82-XX) 10 Probability theory and stochastic processes (60-XX) 8 Ordinary differential equations (34-XX) 7 Systems theory; control (93-XX) 5 Integral equations (45-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Approximations and expansions (41-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Real functions (26-XX) 3 Statistics (62-XX) 3 Information and communication theory, circuits (94-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Operator theory (47-XX) 2 Quantum theory (81-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Mechanics of particles and systems (70-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX) Citations by Year