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## Cai, Yongyong

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 Author ID: cai.yongyong Published as: Cai, Yong Yong; Cai, Yong-Yong; Cai, YongYong; Cai, Yongyong Homepage: http://www.csrc.ac.cn/~yycai External Links: MGP · ResearchGate · dblp
 Documents Indexed: 34 Publications since 2007
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#### Co-Authors

 0 single-authored 15 Bao, Weizhu 3 Jia, Xiaowei 3 Shen, Jie 3 Yin, Jia 2 Ben Abdallah, Naoufel 2 Tang, Qinglin 2 Wang, Hanquan 2 Wang, Yan 2 Yi, Wenfan 2 Zhou, Shulin 1 Castella, François 1 Choi, Heejun 1 Gao, Yali 1 Li, Feng 1 Li, Xianggui 1 Liu, Wei 1 Méhats, Florian 1 Ruan, Xinran 1 Tian, Tonghua 1 Wang, Pengde 1 Wang, Yan 1 Wen, Zaiwen 1 Wu, Xinming 1 Xu, Xiang 1 Yao, Fengping 1 Yuan, Yongjun 1 Zhao, Xiaofei
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#### Serials

 6 SIAM Journal on Numerical Analysis 4 Mathematics of Computation 2 Journal of Computational Physics 2 SIAM Journal on Applied Mathematics 2 SIAM Journal on Scientific Computing 2 Kinetic and Related Models 2 Science China. Mathematics 1 IMA Journal of Numerical Analysis 1 Journal of Functional Analysis 1 Numerische Mathematik 1 Physica D 1 Applied Numerical Mathematics 1 Acta Scientiarum Naturalium Universitatis Pekinensis 1 Journal of Scientific Computing 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 SIAM Journal on Mathematical Analysis 1 Journal of Mathematical Study 1 Acta Mathematica Sinica. English Series 1 Communications in Mathematical Sciences 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 East Asian Journal on Applied Mathematics
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#### Fields

 30 Partial differential equations (35-XX) 26 Numerical analysis (65-XX) 20 Quantum theory (81-XX) 7 Statistical mechanics, structure of matter (82-XX) 3 Fluid mechanics (76-XX) 2 Functional analysis (46-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Mechanics of particles and systems (70-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

26 Publications have been cited 491 times in 300 Documents Cited by Year
Mathematical theory and numerical methods for Bose-Einstein condensation. Zbl 1266.82009
Bao, Weizhu; Cai, Yongyong
2013
Uniform error estimates of finite difference methods for the nonlinear Schrödinger equation with wave operator. Zbl 1246.35188
Bao, Weizhu; Cai, Yongyong
2012
Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation. Zbl 1264.65146
Bao, Weizhu; Cai, Yongyong
2013
Efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates. Zbl 1198.82036
Bao, Weizhu; Cai, Yongyong; Wang, Hanquan
2010
A uniformly accurate multiscale time integrator pseudospectral method for the Klein-Gordon equation in the nonrelativistic limit regime. Zbl 1310.65131
Bao, Weizhu; Cai, Yongyong; Zhao, Xiaofei
2014
Ground states of two-component Bose-Einstein condensates with an internal atomic Josephson junction. Zbl 1290.35236
Bao, Weizhu; Cai, Yongyong
2011
Uniform and optimal error estimates of an exponential wave integrator sine pseudospectral method for the nonlinear Schrödinger equation with wave operator. Zbl 1339.35279
Bao, Weizhu; Cai, Yongyong
2014
Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime. Zbl 1365.65208
Bao, WeiZhu; Cai, YongYong; Jia, XiaoWei; Yin, Jia
2016
Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime. Zbl 1370.81053
Bao, Weizhu; Cai, Yongyong; Jia, Xiaowei; Tang, Qinglin
2017
Existence and uniqueness of weak solutions for a non-uniformly parabolic equation. Zbl 1184.35155
Cai, Yongyong; Zhou, Shulin
2009
Ground states and dynamics of spin-orbit-coupled Bose-Einstein condensates. Zbl 1335.35227
Bao, Weizhu; Cai, Yongyong
2015
A uniformly accurate multiscale time integrator pseudospectral method for the Dirac equation in the nonrelativistic limit regime. Zbl 1346.35171
Bao, Weizhu; Cai, Yongyong; Jia, Xiaowei; Tang, Qinglin
2016
Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows. Zbl 1382.35184
Cai, Yongyong; Choi, Heejun; Shen, Jie
2017
Uniform error estimates of the conservative finite difference method for the Zakharov system in the subsonic limit regime. Zbl 1384.35116
Cai, Yongyong; Yuan, Yongjun
2018
Gross-Pitaevskii-Poisson equations for dipolar Bose-Einstein condensate with anisotropic confinement. Zbl 1246.35187
Bao, Weizhu; Ben Abdallah, Naoufel; Cai, Yongyong
2012
A uniformly accurate (UA) multiscale time integrator pseudospectral method for the nonlinear Dirac equation in the nonrelativistic limit regime. Zbl 1404.35377
Cai, Yongyong; Wang, Yan
2018
Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field model for two-phase incompressible flows. Zbl 1390.35225
Cai, Yongyong; Shen, Jie
2018
A stable scheme and its convergence analysis for a 2D dynamic $$Q$$-tensor model of nematic liquid crystals. Zbl 1368.76048
Cai, Yongyong; Shen, Jie; Xu, Xiang
2017
Second order averaging for the nonlinear Schrödinger equation with strongly anisotropic potential. Zbl 1245.35100
Ben Abdallah, Naoufel; Cai, Yongyong; Castella, Francois; Méhats, Florian
2011
Uniformly accurate nested Picard iterative integrators for the Dirac equation in the nonrelativistic limit regime. Zbl 1421.35307
Cai, Yongyong; Wang, Yan
2019
Numerical methods for Bogoliubov-de Gennes excitations of Bose-Einstein condensates. Zbl 1453.81065
Gao, Yali; Cai, Yongyong
2020
(Semi-)nonrelativisitic limit of the nonlinear Dirac equations. Zbl 07266896
Cai, Yongyong; Wang, Yan
2020
Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime. Zbl 1440.35286
Bao, Weizhu; Cai, Yongyong; Yin, Jia
2020
Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation. Zbl 1440.65090
Li, Xiang-Gui; Cai, Yongyong; Wang, Pengde
2020
Error estimates of finite difference time domain methods for the Klein-Gordon-Dirac system in the nonrelativistic limit regime. Zbl 1406.35345
Cai, Yong-Yong; Yi, Wenfan
2018
Analysis and computation for ground state solutions of Bose-Fermi mixtures at zero temperature. Zbl 1292.35272
Cai, Yongyong; Wang, Hanquan
2013
Numerical methods for Bogoliubov-de Gennes excitations of Bose-Einstein condensates. Zbl 1453.81065
Gao, Yali; Cai, Yongyong
2020
(Semi-)nonrelativisitic limit of the nonlinear Dirac equations. Zbl 07266896
Cai, Yongyong; Wang, Yan
2020
Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime. Zbl 1440.35286
Bao, Weizhu; Cai, Yongyong; Yin, Jia
2020
Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation. Zbl 1440.65090
Li, Xiang-Gui; Cai, Yongyong; Wang, Pengde
2020
Uniformly accurate nested Picard iterative integrators for the Dirac equation in the nonrelativistic limit regime. Zbl 1421.35307
Cai, Yongyong; Wang, Yan
2019
Uniform error estimates of the conservative finite difference method for the Zakharov system in the subsonic limit regime. Zbl 1384.35116
Cai, Yongyong; Yuan, Yongjun
2018
A uniformly accurate (UA) multiscale time integrator pseudospectral method for the nonlinear Dirac equation in the nonrelativistic limit regime. Zbl 1404.35377
Cai, Yongyong; Wang, Yan
2018
Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field model for two-phase incompressible flows. Zbl 1390.35225
Cai, Yongyong; Shen, Jie
2018
Error estimates of finite difference time domain methods for the Klein-Gordon-Dirac system in the nonrelativistic limit regime. Zbl 1406.35345
Cai, Yong-Yong; Yi, Wenfan
2018
Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime. Zbl 1370.81053
Bao, Weizhu; Cai, Yongyong; Jia, Xiaowei; Tang, Qinglin
2017
Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows. Zbl 1382.35184
Cai, Yongyong; Choi, Heejun; Shen, Jie
2017
A stable scheme and its convergence analysis for a 2D dynamic $$Q$$-tensor model of nematic liquid crystals. Zbl 1368.76048
Cai, Yongyong; Shen, Jie; Xu, Xiang
2017
Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime. Zbl 1365.65208
Bao, WeiZhu; Cai, YongYong; Jia, XiaoWei; Yin, Jia
2016
A uniformly accurate multiscale time integrator pseudospectral method for the Dirac equation in the nonrelativistic limit regime. Zbl 1346.35171
Bao, Weizhu; Cai, Yongyong; Jia, Xiaowei; Tang, Qinglin
2016
Ground states and dynamics of spin-orbit-coupled Bose-Einstein condensates. Zbl 1335.35227
Bao, Weizhu; Cai, Yongyong
2015
A uniformly accurate multiscale time integrator pseudospectral method for the Klein-Gordon equation in the nonrelativistic limit regime. Zbl 1310.65131
Bao, Weizhu; Cai, Yongyong; Zhao, Xiaofei
2014
Uniform and optimal error estimates of an exponential wave integrator sine pseudospectral method for the nonlinear Schrödinger equation with wave operator. Zbl 1339.35279
Bao, Weizhu; Cai, Yongyong
2014
Mathematical theory and numerical methods for Bose-Einstein condensation. Zbl 1266.82009
Bao, Weizhu; Cai, Yongyong
2013
Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation. Zbl 1264.65146
Bao, Weizhu; Cai, Yongyong
2013
Analysis and computation for ground state solutions of Bose-Fermi mixtures at zero temperature. Zbl 1292.35272
Cai, Yongyong; Wang, Hanquan
2013
Uniform error estimates of finite difference methods for the nonlinear Schrödinger equation with wave operator. Zbl 1246.35188
Bao, Weizhu; Cai, Yongyong
2012
Gross-Pitaevskii-Poisson equations for dipolar Bose-Einstein condensate with anisotropic confinement. Zbl 1246.35187
Bao, Weizhu; Ben Abdallah, Naoufel; Cai, Yongyong
2012
Ground states of two-component Bose-Einstein condensates with an internal atomic Josephson junction. Zbl 1290.35236
Bao, Weizhu; Cai, Yongyong
2011
Second order averaging for the nonlinear Schrödinger equation with strongly anisotropic potential. Zbl 1245.35100
Ben Abdallah, Naoufel; Cai, Yongyong; Castella, Francois; Méhats, Florian
2011
Efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates. Zbl 1198.82036
Bao, Weizhu; Cai, Yongyong; Wang, Hanquan
2010
Existence and uniqueness of weak solutions for a non-uniformly parabolic equation. Zbl 1184.35155
Cai, Yongyong; Zhou, Shulin
2009
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#### Cited by 379 Authors

 27 Bao, Weizhu 16 Antoine, Xavier 16 Zhao, Xiaofei 15 Wang, Tingchun 14 Cai, Yongyong 12 Tang, Qinglin 11 Li, Xianggui 11 Zeng, Xiaoyu 9 Guo, Yujin 9 Su, Chunmei 8 Lorin, Emmanuel 8 Shi, Dongyang 8 Zhang, Yong 8 Zhou, Huan-Song 7 Schratz, Katharina 7 Wang, Hanquan 7 Zhang, Zhiyue 6 Song, Songhe 6 Wang, Junjun 6 Xie, Jianqiang 6 Zhang, Luming 5 Bögelein, Verena 5 Duzaar, Frank 5 Huang, Chengming 5 Jiang, Chaolong 5 Méhats, Florian 5 Qian, Xu 5 Wang, Pengde 5 Yin, Jia 4 Chern, I-Liang 4 Dong, Xuanchun 4 Duboscq, Romain 4 Henning, Patrick 4 Hua, Dongying 4 Huang, Yunqing 4 Li, Shuai 4 Marcellini, Paolo 4 Ruan, Xinran 4 Wang, Jilu 4 Wang, Yushun 4 Xiao, Aiguo 4 Xu, Zhiguo 4 Zhang, Chao 4 Zhao, Qiang 4 Zhou, Shulin 4 Zhu, Shihui 3 Baumstark, Simon 3 Bellazzini, Jacopo 3 Besse, Christophe 3 Cai, Wentao 3 Carles, Rémi 3 Cui, Jin 3 Gao, Yali 3 Guo, Boling 3 He, Dongdong 3 Jia, Xiaowei 3 Jiang, Jiaping 3 Lakoba, Taras I. 3 Liang, Dong 3 Luo, Yong 3 Ma, Ying 3 Mauser, Norbert Julius 3 Pan, Kejia 3 Scheven, Christoph 3 Tersenov, Alkis Savvich 3 Tersenov, Aris Savvich 3 Wang, Dongling 3 Wang, Jianyun 3 Wei, Juncheng 3 Yan, JingYe 3 Yang, Xiaofeng 3 Yuan, Yongjun 3 Zhu, Xincai 2 Antonelli, Paolo 2 Ávila, Andrés I. 2 Chen, Yanping 2 Chen, Zhangxin 2 Crouseilles, Nicolas 2 Feng, Binhua 2 Guo, Helin 2 Hajaiej, Hichem 2 Hofstätter, Harald 2 Hu, Yunxia 2 Huang, Qiumei 2 Jeanjean, Louis 2 Jeng, B.-W. 2 Jia, Hongen 2 Jiang, Shidong 2 Jin, Shi 2 Koch, Othmar 2 Krämer, Patrick 2 Lemou, Mohammed 2 Levitt, Antoine 2 Li, Dongfang 2 Li, Hongwei 2 Li, Jian 2 Li, Shu-Cun 2 Li, Si-Qi 2 Li, Xueyang 2 Liang, Jiarui ...and 279 more Authors
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#### Cited in 83 Serials

 29 Journal of Computational Physics 16 Applied Mathematics and Computation 16 Journal of Scientific Computing 14 Journal of Computational and Applied Mathematics 13 Applied Numerical Mathematics 12 Computers & Mathematics with Applications 10 SIAM Journal on Numerical Analysis 9 Journal of Mathematical Analysis and Applications 9 Applied Mathematics Letters 8 Journal of Differential Equations 8 SIAM Journal on Scientific Computing 7 Computer Physics Communications 7 Numerische Mathematik 7 Advances in Computational Mathematics 6 Mathematics of Computation 6 Physica D 5 Journal of Mathematical Physics 4 International Journal of Theoretical Physics 4 Numerical Algorithms 4 SIAM Journal on Mathematical Analysis 4 Discrete and Continuous Dynamical Systems 4 Discrete and Continuous Dynamical Systems. Series B 4 Science China. Mathematics 4 East Asian Journal on Applied Mathematics 3 Computer Methods in Applied Mechanics and Engineering 3 BIT 3 Journal of Functional Analysis 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Numerical Methods for Partial Differential Equations 3 Communications in Nonlinear Science and Numerical Simulation 3 Multiscale Modeling & Simulation 3 Advances in Difference Equations 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Kinetic and Related Models 2 Applicable Analysis 2 Archive for Rational Mechanics and Analysis 2 Mathematical Methods in the Applied Sciences 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Proceedings of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Discrete Dynamics in Nature and Society 2 Journal of Evolution Equations 1 Communications in Mathematical Physics 1 Nonlinearity 1 Physics Letters. A 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Calcolo 1 Manuscripta Mathematica 1 Quarterly of Applied Mathematics 1 Siberian Mathematical Journal 1 Studies in Applied Mathematics 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Stochastic Analysis and Applications 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Asymptotic Analysis 1 SIAM Journal on Matrix Analysis and Applications 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Japan Journal of Industrial and Applied Mathematics 1 Applied Mathematical Modelling 1 International Journal of Computer Mathematics 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Applied Mathematics 1 Computational and Applied Mathematics 1 NoDEA. Nonlinear Differential Equations and Applications 1 Nonlinear Dynamics 1 International Journal of Applied Mathematics and Computer Science 1 Annales Henri Poincaré 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 The ANZIAM Journal 1 Advanced Nonlinear Studies 1 Communications on Pure and Applied Analysis 1 Journal of Hyperbolic Differential Equations 1 Journal of Physics A: Mathematical and Theoretical 1 Discrete and Continuous Dynamical Systems. Series S 1 Advances in Mathematical Physics 1 International Journal of Differential Equations 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Carpathian Mathematical Publications 1 Research in the Mathematical Sciences 1 AMM. Applied Mathematics and Mechanics. (English Edition) 1 SMAI Journal of Computational Mathematics
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#### Cited in 31 Fields

 244 Partial differential equations (35-XX) 196 Numerical analysis (65-XX) 59 Statistical mechanics, structure of matter (82-XX) 57 Quantum theory (81-XX) 21 Fluid mechanics (76-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 9 Optics, electromagnetic theory (78-XX) 7 Ordinary differential equations (34-XX) 7 Dynamical systems and ergodic theory (37-XX) 6 Functional analysis (46-XX) 4 Difference and functional equations (39-XX) 4 Probability theory and stochastic processes (60-XX) 4 Operations research, mathematical programming (90-XX) 3 Real functions (26-XX) 3 Operator theory (47-XX) 3 Mechanics of deformable solids (74-XX) 3 Astronomy and astrophysics (85-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of particles and systems (70-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Nonassociative rings and algebras (17-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX)