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## Cai, Xiao-Chuan

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 Author ID: cai.xiao-chuan Published as: Cai, Xiao-Chuan; Cai, X.-C.; Cai, Xiao-Chuan. Homepage: https://www.colorado.edu/faculty/cai/ External Links: MGP · dblp
 Documents Indexed: 119 Publications since 1990, including 2 Books
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#### Co-Authors

 8 single-authored 18 Keyes, David Elliot 13 Yang, Chao 11 Hwang, Fengnan 9 Chen, Rongliang 9 Sarkis, Marcus V. 8 Yang, Haijian 7 Luo, Li 6 Dryja, Maksymilian 6 Gropp, William D. 5 Yan, Zhengzheng 5 Zou, Jun 4 Barker, Andrew T. 4 Huang, Jizu 4 Prudencio, Ernesto E. 4 Widlund, Olof B. 4 Wu, Yuqi 3 Deng, Xiaomao 3 Liu, Si 3 Marcinkowski, Leszek 3 Wang, Xiaoping 3 Zhao, Yubo 2 Benzi, Michele 2 Bialecki, Bernard 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 E. 2 Klawonn, Axel 2 Kong, Fande 2 Leyffer, Sven 2 Li, Shishun 2 Manteuffel, Thomas A. 2 McCormick, Steve Fahrney 2 Murillo, Maria 2 Ovtchinnikov, Serguei 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 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 Freund, Roland W. 1 Gander, Martin Jakob 1 Goossens, Serge 1 Gustafson, Karl Edwin 1 Jiang, Yi 1 Kim, Hyea Hyun 1 Knoll, Dana A. 1 Lee, Chang-Ock 1 Li, Congming 1 Li, Xuefeng 1 Liao, Ziju 1 Lin, Hsin-Lun 1 Liu, Jia 1 Liu, Lulu 1 Liu, Yingzhi 1 Livshits, Irene 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 Wu, Yunhai 1 Xi, Yunping 1 Xu, Jinchao 1 Xu, Lei 1 Yao, Daniel T. C. 1 Zheng, Xiang 1 Znidarcic, Dobroslav
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#### Serials

 25 SIAM Journal on Scientific Computing 10 Journal of Computational Physics 6 SIAM Journal on Numerical Analysis 6 Journal of Scientific Computing 5 Numerical Linear Algebra with Applications 3 Computers and Fluids 3 ETNA. Electronic Transactions on Numerical Analysis 3 Communications in Computational Physics 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 Inverse Problems and Imaging 1 Computer Methods in Applied Mechanics and Engineering 1 Computer Physics Communications 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 Lecture Notes in Computational Science and Engineering 1 Communications in Applied Mathematics and Computational Science
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#### Fields

 107 Numerical analysis (65-XX) 54 Fluid mechanics (76-XX) 50 Partial differential equations (35-XX) 14 Biology and other natural sciences (92-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 8 Operations research, mathematical programming (90-XX) 7 Mechanics of deformable solids (74-XX) 5 General and overarching topics; collections (00-XX) 4 Geophysics (86-XX) 3 Probability theory and stochastic processes (60-XX) 3 Systems theory; control (93-XX) 2 Computer science (68-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)

#### Citations contained in zbMATH Open

92 Publications have been cited 1,099 times in 566 Documents Cited by Year
A restricted additive Schwarz preconditioner for general sparse linear systems. Zbl 0944.65031
Cai, Xiao-Chuan; Sarkis, Marcus
1999
Domain decomposition algorithms for indefinite elliptic problems. Zbl 0746.65085
Cai, Xiao-Chuan; Widlund, Olof B.
1992
Additive Schwarz algorithms for parabolic convection-diffusion equations. Zbl 0737.65078
Cai, Xiao-Chuan
1991
Nonlinearly preconditioned inexact Newton algorithms. Zbl 1015.65058
Cai, Xiao-Chuan; Keyes, David E.
2002
Multiplicative Schwarz methods for parabolic problems. Zbl 0803.65096
Cai, Xiao-Chuan
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.
1998
A parallel nonlinear additive Schwarz preconditioned inexact Newton algorithm for incompressible Navier-Stokes equations. Zbl 1267.76083
Hwang, Feng-Nan; Cai, Xiao-Chuan
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
2010
Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems. Zbl 0787.65016
Cai, Xiao-Chuan; Widlund, Olof B.
1993
A class of parallel two-level nonlinear Schwarz preconditioned inexact Newton algorithms. Zbl 1173.76385
Hwang, Feng-Nan; Cai, Xiao-Chuan
2007
Nonlinear additive Schwarz preconditioners and application in computational fluid dynamics. Zbl 1025.76040
Cai, Xiao-Chuan; Keyes, David E.; Marcinkowski, Leszek
2002
A fully implicit parallel algorithm for simulating the nonlinear electrical activity of the heart. Zbl 1114.65112
Murillo, Maria; Cai, Xiao-Chuan.
2004
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
2014
A minimum overlap restricted additive Schwarz preconditioner and applications in 3D flow simulations. Zbl 0936.76036
Cai, Xiao-Chuan; Farhat, Charbel; Sarkis, Marcus
1998
Restricted additive Schwarz preconditioners with harmonic overlap for symmetric positive definite linear systems. Zbl 1052.65036
Cai, Xiao-Chuan; Dryja, Maksymilian; Sarkis, Marcus
2003
Newton-Krylov-Schwarz methods in CFD. Zbl 0876.76059
Cai, X.-C.; Gropp, W. D.; Keyes, D. E.; Tidriri, M. D.
1994
Inexact Newton methods with restricted additive Schwarz based nonlinear elimination for problems with high local nonlinearity. Zbl 1227.65045
Cai, Xiao-Chuan; Li, Xuefeng
2011
A preconditioned GMRES method for nonsymmetric or indefinite problems. Zbl 0766.65034
Xu, Jinchao; Cai, Xiao-Chuan
1992
Overlapping Schwarz algorithms for solving Helmholtz’s equation. Zbl 0909.65104
Cai, Xiao-Chuan; Casarin, Mario A.; Elliott, Frank W. jun.; Widlund, Olof B.
1998
Overlapping nonmatching grid mortar element methods for elliptic problems. Zbl 0927.65131
Cai, Xiao-Chuan; Dryja, Maksymilian; Sarkis, Marcus
1998
A fully implicit domain decomposition algorithm for shallow water equations on the cubed-sphere. Zbl 1410.76309
Yang, Chao; Cao, Jianwen; Cai, Xiao-Chuan
2010
Two-level Newton and hybrid Schwarz preconditioners for fluid-structure interaction. Zbl 1214.92014
Barker, Andrew T.; Cai, Xiao-Chuan
2010
Domain decomposition methods for monotone nonlinear elliptic problems. Zbl 0817.65127
Cai, Xiao-Chuan; Dryja, Maksymilian
1994
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
2006
Overlapping domain decomposition algorithms for general sparse matrices. Zbl 0851.65083
1996
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
2015
A parallel space-time domain decomposition method for unsteady source inversion problems. Zbl 1332.65057
Deng, Xiaomao; Cai, Xiao-Chuan; Zou, Jun
2015
Two-level space-time domain decomposition methods for three-dimensional unsteady inverse source problems. Zbl 1342.49044
Deng, Xiaomao; Cai, Xiao-Chuan; Zou, Jun
2016
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.
2007
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
2010
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
2011
Parallel domain decomposition methods for stochastic elliptic equations. Zbl 1149.65007
Jin, Chao; Cai, Xiao-Chuan; Li, Congming
2007
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.
1994
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
2012
Parallel one-shot Lagrange–Newton–Krylov–Schwarz algorithms for shape optimization of steady incompressible flows. Zbl 1256.49034
Chen, Rongliang; Cai, Xiao-Chuan
2012
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
2014
Maximum norm analysis of overlapping nonmatching grid discretizations of elliptic equations. Zbl 0963.65125
Cai, Xiao-Chuan; Mathew, Tarek P.; Sarkis, Marcus V.
2000
Parallel multilevel restricted Schwarz preconditioners with pollution removing for PDE-constrained optimization. Zbl 1357.76020
Prudencio, Ernesto E.; Cai, Xiao-Chuan
2007
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
2014
A scalable fully implicit compressible Euler solver for mesoscale nonhydrostatic simulation of atmospheric flows. Zbl 1305.86005
Yang, Chao; Cai, Xiao-Chuan
2014
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
2017
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
2016
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
2016
An optimal two-level overlapping domain decomposition method for elliptic problems in two and three dimensions. Zbl 0771.65083
Cai, Xiao-Chuan
1993
The use of pointwise interpolation in domain decomposition methods with nonnested meshes. Zbl 0826.65023
Cai, Xiao-Chuan
1995
A nonlinear additive Schwarz preconditioned inexact Newton method for shocked duct flows. Zbl 1201.76107
Cai, Xiao-Chuan; Keyes, David E.; Young, David P.
2002
Ovtchinnikov, Serguei; Cai, Xiao-Chuan
2004
Cai, Xiao-Chuan
1990
Convergence analysis of two-level space-time additive Schwarz method for parabolic equations. Zbl 1330.65144
Li, Shishun; Cai, Xiao-Chuan
2015
Parallel performance of some two-level ASPIN algorithms. Zbl 1066.65057
Marcinkowski, Leszek; Cai, Xiao-Chuan
2005
A comparison of some domain decomposition algorithms for nonsymmetric ellliptic problems. Zbl 0770.65079
Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.
1992
Some observations on the $$l^2$$ convergence of the additive Schwarz preconditioned GMRES method. Zbl 1071.65529
Cai, Xiao-Chuan; Zou, Jun
2002
Parallel fully coupled Schwarz preconditioners for saddle point problems. Zbl 1112.65026
Hwang, Feng-Nan; Cai, Xiao-Chuan
2006
Parallel overlapping domain decomposition methods for coupled inverse elliptic problems. Zbl 1169.65342
Cai, Xiao-Chuan; Liu, Si; Zou, Jun
2009
Parallel two-grid semismooth Newton-Krylov-Schwarz method for nonlinear complementarity problems. Zbl 1217.65116
Yang, Haijian; Cai, Xiao-Chuan
2011
Implicit space-time domain decomposition methods for stochastic parabolic partial differential equations. Zbl 1292.65002
Cong, Cui; Cai, Xiao-Chuan; Gustafson, Karl
2014
A preconditioned recycling GMRES solver for stochastic Helmholtz problems. Zbl 1364.65278
Jin, Chao; Cai, Xiao-Chuan
2009
A fully implicit method for lattice Boltzmann equations. Zbl 1325.76144
Huang, Jizu; Yang, Chao; Cai, Xiao-Chuan
2015
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
2017
An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation. Zbl 0798.65105
Bialecki, Bernard; Cai, X.-C.; Dryja, M.; Fairweather, G.
1994
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
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
2014
Two-level space-time domain decomposition methods for flow control problems. Zbl 1404.65157
Yang, Haijian; Cai, Xiao-Chuan
2017
A nonlinearly preconditioned inexact Newton algorithm for steady state lattice Boltzmann equations. Zbl 1339.65236
Huang, Jizu; Yang, Chao; Cai, Xiao-Chuan
2016
Improving robustness and parallel scalability of Newton method through nonlinear preconditioning. Zbl 1067.65052
Hwang, Feng-Nan; Cai, Xiao-Chuan
2005
$$H^ 1$$-norm error bounds for piecewise Hermite bicubic orthogonal spline collocation schemes for elliptic boundary value problems. Zbl 0809.65107
Bialecki, Bernard; Cai, Xiao-Chuan
1994
Parallel implicit methods for aerodynamics. Zbl 0818.76065
Cai, X.-C.; Gropp, W. D.; Keyes, D. E.; Tidriri, M. D.
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.
2005
A parallel domain decomposition algorithm for large scale image denoising. Zbl 1427.65401
Chen, Rongliang; Huang, Jizu; Cai, Xiao-Chuan
2019
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
2016
A parallel two-level domain decomposition based one-shot method for shape optimization problems. Zbl 1352.76046
Chen, Rongliang; Cai, Xiao-Chuan
2014
Additive Schwarz methods for hyperbolic equations. Zbl 0909.65062
Wu, Yunhai; Cai, Xiao-Chuan; Keyes, David E.
1998
Local multiplicative Schwarz algorithms for steady and unsteady convection-diffusion equations. Zbl 0913.65083
Cai, X.-C.; Sarkis, M.
1998
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.
2020
A nonlinear elimination preconditioned inexact Newton method for heterogeneous hyperelasticity. Zbl 1436.65065
Gong, Shihua; Cai, Xiao-Chuan
2019
RASHO: A restricted additive Schwarz preconditioner with harmonic overlap. Zbl 1026.65034
Cai, X.-C.; Dryja, M.; Sarkis, M.
2002
Nonlinear overlapping domain decomposition methods. Zbl 1183.65053
Cai, Xiao-Chuan
2009
NKS for fully coupled fluid-structure interaction with application. Zbl 1284.74029
Barker, Andrew T.; Cai, Xiao-Chuan
2009
Multilevel space-time additive Schwarz methods for parabolic equations. Zbl 1405.65113
Li, Shishun; Shao, Xinping; Cai, Xiao-Chuan
2018
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
2015
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
2016
A family of overlapping Schwarz algorithms for nonsymmetric and indefinite elliptic problems. Zbl 0854.65113
Cai, Xiao-Chuan
1995
Domain decomposition methods 10. The 10th international conference, Boulder, CO, USA, August 10–14, 1997. Zbl 0895.00045
Mandel, Jan (ed.); Farhat, Charbel (ed.); Cai, Xiao-Chuan (ed.)
1998
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
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.
2002
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
2011
Convergence rate estimate for a domain decomposition method. Zbl 0727.65105
Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.
1991
Newton-Krylov-Schwarz method for a spherical shallow water model. Zbl 1430.76408
Yang, Chao; Cai, Xiao-Chuan
2011
Domain decomposition methods for a complementarity problem. Zbl 1217.65115
Yang, Haijian; Cai, Xiao-Chuan
2011
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
2019
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.
2020
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
2015
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.
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.
2020
A parallel domain decomposition algorithm for large scale image denoising. Zbl 1427.65401
Chen, Rongliang; Huang, Jizu; Cai, Xiao-Chuan
2019
A nonlinear elimination preconditioned inexact Newton method for heterogeneous hyperelasticity. Zbl 1436.65065
Gong, Shihua; Cai, Xiao-Chuan
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
2019
Multilevel space-time additive Schwarz methods for parabolic equations. Zbl 1405.65113
Li, Shishun; Shao, Xinping; Cai, Xiao-Chuan
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
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
2017
Two-level space-time domain decomposition methods for flow control problems. Zbl 1404.65157
Yang, Haijian; Cai, Xiao-Chuan
2017
Two-level space-time domain decomposition methods for three-dimensional unsteady inverse source problems. Zbl 1342.49044
Deng, Xiaomao; Cai, Xiao-Chuan; Zou, Jun
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
2016
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
2016
A nonlinearly preconditioned inexact Newton algorithm for steady state lattice Boltzmann equations. Zbl 1339.65236
Huang, Jizu; Yang, Chao; Cai, Xiao-Chuan
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
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
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
2015
A parallel space-time domain decomposition method for unsteady source inversion problems. Zbl 1332.65057
Deng, Xiaomao; Cai, Xiao-Chuan; Zou, Jun
2015
Convergence analysis of two-level space-time additive Schwarz method for parabolic equations. Zbl 1330.65144
Li, Shishun; Cai, Xiao-Chuan
2015
A fully implicit method for lattice Boltzmann equations. Zbl 1325.76144
Huang, Jizu; Yang, Chao; Cai, Xiao-Chuan
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
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
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
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
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
2014
A scalable fully implicit compressible Euler solver for mesoscale nonhydrostatic simulation of atmospheric flows. Zbl 1305.86005
Yang, Chao; Cai, Xiao-Chuan
2014
Implicit space-time domain decomposition methods for stochastic parabolic partial differential equations. Zbl 1292.65002
Cong, Cui; Cai, Xiao-Chuan; Gustafson, Karl
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
2014
A parallel two-level domain decomposition based one-shot method for shape optimization problems. Zbl 1352.76046
Chen, Rongliang; Cai, Xiao-Chuan
2014
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
2012
Parallel one-shot Lagrange–Newton–Krylov–Schwarz algorithms for shape optimization of steady incompressible flows. Zbl 1256.49034
Chen, Rongliang; Cai, Xiao-Chuan
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
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
2011
Parallel two-grid semismooth Newton-Krylov-Schwarz method for nonlinear complementarity problems. Zbl 1217.65116
Yang, Haijian; Cai, Xiao-Chuan
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
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
2011
Newton-Krylov-Schwarz method for a spherical shallow water model. Zbl 1430.76408
Yang, Chao; Cai, Xiao-Chuan
2011
Domain decomposition methods for a complementarity problem. Zbl 1217.65115
Yang, Haijian; Cai, Xiao-Chuan
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
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
2010
Two-level Newton and hybrid Schwarz preconditioners for fluid-structure interaction. Zbl 1214.92014
Barker, Andrew T.; Cai, Xiao-Chuan
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
2010
Parallel overlapping domain decomposition methods for coupled inverse elliptic problems. Zbl 1169.65342
Cai, Xiao-Chuan; Liu, Si; Zou, Jun
2009
A preconditioned recycling GMRES solver for stochastic Helmholtz problems. Zbl 1364.65278
Jin, Chao; Cai, Xiao-Chuan
2009
Nonlinear overlapping domain decomposition methods. Zbl 1183.65053
Cai, Xiao-Chuan
2009
NKS for fully coupled fluid-structure interaction with application. Zbl 1284.74029
Barker, Andrew T.; Cai, Xiao-Chuan
2009
A class of parallel two-level nonlinear Schwarz preconditioned inexact Newton algorithms. Zbl 1173.76385
Hwang, Feng-Nan; Cai, Xiao-Chuan
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.
2007
Parallel domain decomposition methods for stochastic elliptic equations. Zbl 1149.65007
Jin, Chao; Cai, Xiao-Chuan; Li, Congming
2007
Parallel multilevel restricted Schwarz preconditioners with pollution removing for PDE-constrained optimization. Zbl 1357.76020
Prudencio, Ernesto E.; Cai, Xiao-Chuan
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
2006
Parallel fully coupled Schwarz preconditioners for saddle point problems. Zbl 1112.65026
Hwang, Feng-Nan; Cai, Xiao-Chuan
2006
A parallel nonlinear additive Schwarz preconditioned inexact Newton algorithm for incompressible Navier-Stokes equations. Zbl 1267.76083
Hwang, Feng-Nan; Cai, Xiao-Chuan
2005
Parallel performance of some two-level ASPIN algorithms. Zbl 1066.65057
Marcinkowski, Leszek; Cai, Xiao-Chuan
2005
Improving robustness and parallel scalability of Newton method through nonlinear preconditioning. Zbl 1067.65052
Hwang, Feng-Nan; Cai, Xiao-Chuan
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.
2005
A fully implicit parallel algorithm for simulating the nonlinear electrical activity of the heart. Zbl 1114.65112
Murillo, Maria; Cai, Xiao-Chuan.
2004
Ovtchinnikov, Serguei; Cai, Xiao-Chuan
2004
Restricted additive Schwarz preconditioners with harmonic overlap for symmetric positive definite linear systems. Zbl 1052.65036
Cai, Xiao-Chuan; Dryja, Maksymilian; Sarkis, Marcus
2003
Nonlinearly preconditioned inexact Newton algorithms. Zbl 1015.65058
Cai, Xiao-Chuan; Keyes, David E.
2002
Nonlinear additive Schwarz preconditioners and application in computational fluid dynamics. Zbl 1025.76040
Cai, Xiao-Chuan; Keyes, David E.; Marcinkowski, Leszek
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.
2002
Some observations on the $$l^2$$ convergence of the additive Schwarz preconditioned GMRES method. Zbl 1071.65529
Cai, Xiao-Chuan; Zou, Jun
2002
RASHO: A restricted additive Schwarz preconditioner with harmonic overlap. Zbl 1026.65034
Cai, X.-C.; Dryja, M.; Sarkis, M.
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
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.
2002
Maximum norm analysis of overlapping nonmatching grid discretizations of elliptic equations. Zbl 0963.65125
Cai, Xiao-Chuan; Mathew, Tarek P.; Sarkis, Marcus V.
2000
A restricted additive Schwarz preconditioner for general sparse linear systems. Zbl 0944.65031
Cai, Xiao-Chuan; Sarkis, Marcus
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.
1998
A minimum overlap restricted additive Schwarz preconditioner and applications in 3D flow simulations. Zbl 0936.76036
Cai, Xiao-Chuan; Farhat, Charbel; Sarkis, Marcus
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.
1998
Overlapping nonmatching grid mortar element methods for elliptic problems. Zbl 0927.65131
Cai, Xiao-Chuan; Dryja, Maksymilian; Sarkis, Marcus
1998
Additive Schwarz methods for hyperbolic equations. Zbl 0909.65062
Wu, Yunhai; Cai, Xiao-Chuan; Keyes, David E.
1998
Local multiplicative Schwarz algorithms for steady and unsteady convection-diffusion equations. Zbl 0913.65083
Cai, X.-C.; Sarkis, M.
1998
Domain decomposition methods 10. The 10th international conference, Boulder, CO, USA, August 10–14, 1997. Zbl 0895.00045
Mandel, Jan; Farhat, Charbel; Cai, Xiao-Chuan
1998
Overlapping domain decomposition algorithms for general sparse matrices. Zbl 0851.65083
1996
The use of pointwise interpolation in domain decomposition methods with nonnested meshes. Zbl 0826.65023
Cai, Xiao-Chuan
1995
A family of overlapping Schwarz algorithms for nonsymmetric and indefinite elliptic problems. Zbl 0854.65113
Cai, Xiao-Chuan
1995
Multiplicative Schwarz methods for parabolic problems. Zbl 0803.65096
Cai, Xiao-Chuan
1994
Newton-Krylov-Schwarz methods in CFD. Zbl 0876.76059
Cai, X.-C.; Gropp, W. D.; Keyes, D. E.; Tidriri, M. D.
1994
Domain decomposition methods for monotone nonlinear elliptic problems. Zbl 0817.65127
Cai, Xiao-Chuan; Dryja, Maksymilian
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.
1994
An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation. Zbl 0798.65105
Bialecki, Bernard; Cai, X.-C.; Dryja, M.; Fairweather, G.
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
1994
Parallel implicit methods for aerodynamics. Zbl 0818.76065
Cai, X.-C.; Gropp, W. D.; Keyes, D. E.; Tidriri, M. D.
1994
Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems. Zbl 0787.65016
Cai, Xiao-Chuan; Widlund, Olof B.
1993
An optimal two-level overlapping domain decomposition method for elliptic problems in two and three dimensions. Zbl 0771.65083
Cai, Xiao-Chuan
1993
Domain decomposition algorithms for indefinite elliptic problems. Zbl 0746.65085
Cai, Xiao-Chuan; Widlund, Olof B.
1992
A preconditioned GMRES method for nonsymmetric or indefinite problems. Zbl 0766.65034
Xu, Jinchao; Cai, Xiao-Chuan
1992
A comparison of some domain decomposition algorithms for nonsymmetric ellliptic problems. Zbl 0770.65079
Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.
1992
Additive Schwarz algorithms for parabolic convection-diffusion equations. Zbl 0737.65078
Cai, Xiao-Chuan
1991
Convergence rate estimate for a domain decomposition method. Zbl 0727.65105
Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.
1991
Cai, Xiao-Chuan
1990
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#### Cited by 903 Authors

 48 Cai, Xiao-Chuan 18 Yang, Danping 14 Keyes, David Elliot 14 Yang, Chao 14 Yang, Haijian 12 Hwang, Fengnan 11 Gander, Martin Jakob 10 Nataf, Frédéric 9 Dolean, Victorita 9 Klawonn, Axel 9 Pavarino, Luca Franco 8 Chen, Rongliang 8 Zhang, Jiansong 7 Ma, Keying 7 Sun, Tongjun 7 Xu, Jinchao 7 Xu, Xuejun 6 Chen, Zhangxin 6 Graham, Ivan G. 6 Lanser, Martin 6 Liu, Lulu 6 Luo, Li 6 Rheinbach, Oliver 6 Scacchi, Simone 6 Spence, Euan A. 6 Sun, Shuyu 6 Zou, Jun 5 Bialecki, Bernard 5 Bukač, Martina 5 Farhat, Charbel H. 5 Haynes, Ronald D. 5 Hu, Qiya 5 Huang, Jizu 5 Jun, Younbae 5 Li, Shishun 5 Liu, Hui 5 Marcinkowski, Leszek 5 Quarteroni, Alfio M. 5 Shu, Shi 5 Szyld, Daniel B. 5 Tournier, Pierre-Henri 4 Chen, Jinru 4 di Serafino, Daniela 4 Heinlein, Alexander 4 Krause, Rolf H. 4 Lin, Paul T. 4 Loneland, Atle 4 Mai, Tsun-Zee 4 Rahman, Talal 4 Shadid, John N. 4 Shang, Yueqiang 4 Tai, Xuecheng 4 Tromeur-Dervout, Damien 4 van Zuijlen, Alexander H. 4 Vassilevski, Panayot Spirov 4 Widlund, Olof B. 4 Wu, Yuqi 4 Yan, Zhengzheng 4 Zampini, Stefano 4 Zhang, Hui 4 Zhong, Liuqiang 3 Antonietti, Paola Francesca 3 Badia, Santiago 3 Berenguer, Laurent 3 Bijl, Hester 3 Biros, George 3 Blom, David S. 3 Boulbrachene, Messaoud 3 D’Ambra, Pasqua 3 Demkowicz, Leszek F. 3 Deng, Xiaomao 3 Filippone, Salvatore 3 Glowinski, Roland 3 Gosselet, Pierre 3 Gunzburger, Max D. 3 Guo, Hui 3 Halpern, Laurence 3 Houzeaux, Guillaume 3 Huang, Weizhang 3 Jiang, Daijun 3 Jolivet, Pierre 3 Karniadakis, George Em 3 Kimn, Jung-Han 3 Kong, Fande 3 Kwok, Felix 3 Lanteri, Stéphane 3 Li, Lingxiao 3 Li, Weidong 3 Li, Yiteng 3 Liu, Xingping 3 Magoulès, Frédéric 3 Maute, Kurt 3 Mehl, Miriam 3 Pasciak, Joseph E. 3 Rapetti, Francesca 3 Rey, Christian A. 3 Rui, Hongxing 3 Sala, Marzio 3 Sarkis, Marcus V. 3 Shao, Xinping ...and 803 more Authors
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#### Cited in 92 Serials

 70 Journal of Computational Physics 45 SIAM Journal on Scientific Computing 43 Computer Methods in Applied Mechanics and Engineering 30 Applied Mathematics and Computation 29 Journal of Computational and Applied Mathematics 23 Computers & Mathematics with Applications 21 Applied Numerical Mathematics 20 Computers and Fluids 20 Mathematics of Computation 20 Journal of Scientific Computing 14 Numerical Linear Algebra with Applications 12 International Journal for Numerical Methods in Engineering 11 Numerical Algorithms 10 Numerische Mathematik 9 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 8 SIAM Journal on Numerical Analysis 8 Numerical Methods for Partial Differential Equations 7 International Journal for Numerical Methods in Fluids 7 Mathematics and Computers in Simulation 6 Computational Mechanics 5 BIT 5 International Journal of Computer Mathematics 5 Mathematical Problems in Engineering 5 Inverse Problems and Imaging 4 Computational Geosciences 3 Applicable Analysis 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 ETNA. Electronic Transactions on Numerical Analysis 3 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 3 Discrete and Continuous Dynamical Systems. Series B 3 Computational Methods in Applied Mathematics 3 Journal of Numerical Mathematics 3 Acta Numerica 3 International Journal for Numerical Methods in Biomedical Engineering 2 Mathematical Biosciences 2 Calcolo 2 Computing 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Journal of Integral Equations and Applications 2 Linear Algebra and its Applications 2 SIAM Review 2 Computational Optimization and Applications 2 Advances in Computational Mathematics 2 Computing and Visualization in Science 2 Communications in Nonlinear Science and Numerical Simulation 2 Archives of Computational Methods in Engineering 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Applied Mathematics and Computing 2 Boletim da Sociedade Paranaense de Matemática. Terceira Série 2 Discrete and Continuous Dynamical Systems. Series S 2 SIAM/ASA Journal on Uncertainty Quantification 1 Computer Physics Communications 1 Inverse Problems 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Fluid Mechanics 1 Numerical Functional Analysis and Optimization 1 Parallel Computing 1 Acta Mathematicae Applicatae Sinica. English Series 1 Journal of Symbolic Computation 1 Applied Mathematics Letters 1 SIAM Journal on Matrix Analysis and Applications 1 Science in China. Series A 1 Applications of Mathematics 1 Computational Mathematics and Mathematical Physics 1 Applied Mathematical Modelling 1 Applicable Algebra in Engineering, Communication and Computing 1 SIAM Journal on Optimization 1 Applied Mathematics. Series B (English Edition) 1 Communications in Numerical Methods in Engineering 1 International Journal of Numerical Methods for Heat & Fluid Flow 1 Journal of Inverse and Ill-Posed Problems 1 Engineering Analysis with Boundary Elements 1 Journal of Difference Equations and Applications 1 International Journal of Computational Fluid Dynamics 1 Journal of Inequalities and Applications 1 European Journal of Mechanics. B. Fluids 1 Applied Sciences 1 Nonlinear Analysis. Real World Applications 1 Mathematical Modelling and Analysis 1 Journal of Applied Mathematics 1 Communications on Pure and Applied Analysis 1 Multiscale Modeling & Simulation 1 International Journal of Computational Methods 1 Advances in Difference Equations 1 Journal of Computational Acoustics 1 GAMM-Mitteilungen 1 Mathematical Geosciences 1 Advances in Numerical Analysis 1 Advances in Applied Mathematics and Mechanics 1 EURO Journal on Computational Optimization 1 Mathematics in Engineering 1 Electronic Research Archive
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#### Cited in 34 Fields

 472 Numerical analysis (65-XX) 207 Partial differential equations (35-XX) 185 Fluid mechanics (76-XX) 74 Mechanics of deformable solids (74-XX) 44 Biology and other natural sciences (92-XX) 26 Calculus of variations and optimal control; optimization (49-XX) 24 Optics, electromagnetic theory (78-XX) 16 Computer science (68-XX) 16 Operations research, mathematical programming (90-XX) 14 Geophysics (86-XX) 11 Statistical mechanics, structure of matter (82-XX) 9 Probability theory and stochastic processes (60-XX) 5 Ordinary differential equations (34-XX) 5 Integral equations (45-XX) 5 Systems theory; control (93-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Approximations and expansions (41-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Functional analysis (46-XX) 2 Operator theory (47-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistics (62-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Information and communication theory, circuits (94-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 General topology (54-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX)