Yongyong Cai

Publication Activity (10 Years)

Years Active: 2010-2024
Publications (10 Years): 32

Top Topics

Finite Difference

Error Estimates

Top Venues

J. Comput. Phys.

SIAM J. Numer. Anal.

Publications

Fenghua Tong, Yongyong Cai
Positivity preserving and mass conservative projection method for the Poisson-Nernst-Planck equation. CoRR (2024)
Xuanxuan Zhou, Tingchun Wang, Yong Wu, Yongyong Cai
Error estimates of a regularized finite difference method for the Logarithmic Schr\"{o}dinger equation with Dirac delta potential. CoRR (2024)
Jingwei Li, Rihui Lan, Yongyong Cai, Lili Ju, Xiaoqiang Wang
Second-Order Semi-Lagrangian Exponential Time Differencing Method with Enhanced Error Estimate for the Convective Allen-Cahn Equation. J. Sci. Comput. 97 (1) (2023)
Yongyong Cai, Xuanxuan Zhou
Uniformly accurate nested Picard iterative integrators for the Klein-Gordon-Schrödinger equation in the nonrelativistic regime. Numer. Algorithms 94 (1) (2023)
Rihui Lan, Jingwei Li, Yongyong Cai, Lili Ju
Operator splitting based structure-preserving numerical schemes for the mass-conserving convective Allen-Cahn equation. J. Comput. Phys. 472 (2023)
Yongyong Cai, Wenfan Yi
A uniformly accurate method for the Klein-Gordon-Dirac system in the nonrelativistic regime. J. Comput. Phys. 486 (2023)
Yongyong Cai, Xuanxuan Zhou
Uniformly Accurate Nested Picard Iterative Integrators for the Klein-Gordon Equation in the Nonrelativistic Regime. J. Sci. Comput. 92 (2) (2022)
Weizhu Bao, Yongyong Cai, Yue Feng
Improved Uniform Error Bounds on Time-Splitting Methods for Long-Time Dynamics of the Nonlinear Klein-Gordon Equation with Weak Nonlinearity. SIAM J. Numer. Anal. 60 (4) (2022)
Yongyong Cai, Yan Wang
Uniformly Accurate Nested Picard Iterative Integrators for the Nonlinear Dirac Equation in the Nonrelativistic Regime. Multiscale Model. Simul. 20 (1) (2022)
Weizhu Bao, Yongyong Cai, Yue Feng
Improved uniform error bounds on time-splitting methods for the long-time dynamics of the weakly nonlinear Dirac equation. CoRR (2022)
Yongyong Cai, Jingrun Chen, Cheng Wang, Changjian Xie
A second-order numerical method for Landau-Lifshitz-Gilbert equation with large damping parameters. J. Comput. Phys. 451 (2022)
Weizhu Bao, Yongyong Cai, Yue Feng
Improved uniform error bounds of the time-splitting methods for the long-time (nonlinear) Schrödinger equation. Math. Comput. 92 (341) (2022)
Yongyong Cai, Lili Ju, Rihui Lan, Jingwei Li
Stabilized exponential time differencing schemes for the convective Allen-Cahn equation. CoRR (2022)
Weizhu Bao, Yongyong Cai, Jia Yin
Uniform Error Bounds of Time-Splitting Methods for the Nonlinear Dirac Equation in the Nonrelativistic Regime without Magnetic Potential. SIAM J. Numer. Anal. 59 (2) (2021)
Weizhu Bao, Yongyong Cai, Yue Feng
Improved uniform error bounds for the time-splitting methods for the long-time dynamics of the Schrödinger/nonlinear Schrödinger equation. CoRR (2021)
Jingwei Li, Lili Ju, Yongyong Cai, Xinlong Feng
Unconditionally Maximum Bound Principle Preserving Linear Schemes for the Conservative Allen-Cahn Equation with Nonlocal Constraint. J. Sci. Comput. 87 (3) (2021)
Wei Liu, Yongyong Cai
Normalized Gradient Flow with Lagrange Multiplier for Computing Ground States of Bose-Einstein Condensates. SIAM J. Sci. Comput. 43 (1) (2021)
Yongyong Cai, Jingrun Chen, Cheng Wang, Changjian Xie
Convergence Analysis of A Second-order Accurate, Linear Numerical Scheme for The Landau-Lifshitz Equation with Large Damping Parameters. CoRR (2021)
Weizhu Bao, Yongyong Cai, Yue Feng
Improved uniform error bounds on time-splitting methods for long-time dynamics of the nonlinear Klein-Gordon equation with weak nonlinearity. CoRR (2021)
Yongyong Cai, Wei Liu
Efficient and accurate gradient flow methods for computing ground states of spinor Bose-Einstein condensates. J. Comput. Phys. 433 (2021)
Tonghua Tian, Yongyong Cai, Xinming Wu, Zaiwen Wen
Ground States of Spin-F Bose-Einstein Condensates. SIAM J. Sci. Comput. 42 (4) (2020)
Yali Gao, Yongyong Cai
Numerical methods for Bogoliubov-de Gennes excitations of Bose-Einstein condensates. J. Comput. Phys. 403 (2020)
Weizhu Bao, Yongyong Cai, Jia Yin
Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime. Math. Comput. 89 (325) (2020)
Yongyong Cai, Emmanuel Lorin
Stationary state computation for nonlinear Dirac operators. J. Comput. Phys. 420 (2020)
Tonghua Tian, Yongyong Cai, Xinming Wu, Zaiwen Wen
Ground states and their characterization of spin-F Bose-Einstein condensates. CoRR (2019)
Yongyong Cai, Yan Wang
Uniformly Accurate Nested Picard Iterative Integrators for the Dirac Equation in the Nonrelativistic Limit Regime. SIAM J. Numer. Anal. 57 (4) (2019)
Weizhu Bao, Yongyong Cai, Jia Yin
Uniform error bounds of time-splitting methods for the nonlinear Dirac equation in the nonrelativistic limit regime. CoRR (2019)
Yongyong Cai, Yongjun Yuan
Uniform error estimates of the conservative finite difference method for the Zakharov system in the subsonic limit regime. Math. Comput. 87 (311) (2018)
Yongyong Cai, Jie Shen
Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field model for two-phase incompressible flows. Math. Comput. 87 (313) (2018)
Yongyong Cai, Heejun Choi, Jie Shen
Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows. Numerische Mathematik 137 (2) (2017)
Weizhu Bao, Yongyong Cai, Xiaowei Jia, Qinglin Tang
Numerical Methods and Comparison for the Dirac Equation in the Nonrelativistic Limit Regime. J. Sci. Comput. 71 (3) (2017)
Weizhu Bao, Yongyong Cai, Xiaowei Jia, Qinglin Tang
A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Dirac Equation in the Nonrelativistic Limit Regime. SIAM J. Numer. Anal. 54 (3) (2016)
Weizhu Bao, Yongyong Cai
Ground States and Dynamics of Spin-Orbit-Coupled Bose-Einstein Condensates. SIAM J. Appl. Math. 75 (2) (2015)
Weizhu Bao, Yongyong Cai
Uniform and Optimal Error Estimates of an Exponential Wave Integrator Sine Pseudospectral Method for the Nonlinear Schrödinger Equation with Wave Operator. SIAM J. Numer. Anal. 52 (3) (2014)
Weizhu Bao, Yongyong Cai, Xiaofei Zhao
A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Klein-Gordon Equation in the Nonrelativistic Limit Regime. SIAM J. Numer. Anal. 52 (5) (2014)
Weizhu Bao, Yongyong Cai
Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation. Math. Comput. 82 (281) (2013)
Yongyong Cai, Hanquan Wang
Analysis and Computation for Ground State Solutions of Bose-Fermi Mixtures at Zero Temperature. SIAM J. Appl. Math. 73 (2) (2013)
Weizhu Bao, Naoufel Ben Abdallah, Yongyong Cai
Gross-Pitaevskii-Poisson Equations for Dipolar Bose-Einstein Condensate with Anisotropic Confinement. SIAM J. Math. Anal. 44 (3) (2012)
Weizhu Bao, Yongyong Cai
Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator. SIAM J. Numer. Anal. 50 (2) (2012)
Weizhu Bao, Yongyong Cai, Hanquan Wang
Efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates. J. Comput. Phys. 229 (20) (2010)