Efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates. - Weizhu Bao; Yongyong Cai; Hanquan Wang (J. Comput. Phys., 2010)

Gross-Pitaevskii-Poisson Equations for Dipolar Bose-Einstein Condensate with Anisotropic Confinement. - Weizhu Bao; Naoufel Ben Abdallah; Yongyong Cai (SIAM J. Math. Anal., 2012)

Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator. - Weizhu Bao; Yongyong Cai (SIAM J. Numer. Anal., 2012)

Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation. - Weizhu Bao; Yongyong Cai (Math. Comput., 2013)

Analysis and Computation for Ground State Solutions of Bose-Fermi Mixtures at Zero Temperature. - Yongyong Cai; Hanquan Wang (SIAM J. Appl. Math., 2013)

Uniform and Optimal Error Estimates of an Exponential Wave Integrator Sine Pseudospectral Method for the Nonlinear Schrödinger Equation with Wave Operator. - Weizhu Bao; Yongyong Cai (SIAM J. Numer. Anal., 2014)

A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Klein-Gordon Equation in the Nonrelativistic Limit Regime. - Weizhu Bao; Yongyong Cai; Xiaofei Zhao (SIAM J. Numer. Anal., 2014)

Ground States and Dynamics of Spin-Orbit-Coupled Bose-Einstein Condensates. - Weizhu Bao; Yongyong Cai (SIAM J. Appl. Math., 2015)

A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Dirac Equation in the Nonrelativistic Limit Regime. - Weizhu Bao; Yongyong Cai; Xiaowei Jia; Qinglin Tang (SIAM J. Numer. Anal., 2016)

Numerical Methods and Comparison for the Dirac Equation in the Nonrelativistic Limit Regime. - Weizhu Bao; Yongyong Cai; Xiaowei Jia; Qinglin Tang (J. Sci. Comput., 2017)

Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows. - Yongyong Cai; Heejun Choi; Jie Shen 001 (Numerische Mathematik, 2017)

Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field model for two-phase incompressible flows. - Yongyong Cai; Jie Shen 001 (Math. Comput., 2018)

Uniform error estimates of the conservative finite difference method for the Zakharov system in the subsonic limit regime. - Yongyong Cai; Yongjun Yuan (Math. Comput., 2018)

Uniform error bounds of time-splitting methods for the nonlinear Dirac equation in the nonrelativistic limit regime. - Weizhu Bao; Yongyong Cai; Jia Yin (CoRR, 2019)

Ground states and their characterization of spin-F Bose-Einstein condensates. - Tonghua Tian; Yongyong Cai; Xinming Wu; Zaiwen Wen (CoRR, 2019)

Uniformly Accurate Nested Picard Iterative Integrators for the Dirac Equation in the Nonrelativistic Limit Regime. - Yongyong Cai; Yan Wang (SIAM J. Numer. Anal., 2019)

Stationary state computation for nonlinear Dirac operators. - Yongyong Cai; Emmanuel Lorin (J. Comput. Phys., 2020)

Numerical methods for Bogoliubov-de Gennes excitations of Bose-Einstein condensates. - Yali Gao; Yongyong Cai (J. Comput. Phys., 2020)

Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime. - Weizhu Bao; Yongyong Cai; Jia Yin (Math. Comput., 2020)

Ground States of Spin-F Bose-Einstein Condensates. - Tonghua Tian; Yongyong Cai; Xinming Wu; Zaiwen Wen (SIAM J. Sci. Comput., 2020)

Improved uniform error bounds for the time-splitting methods for the long-time dynamics of the Schrödinger/nonlinear Schrödinger equation. - Weizhu Bao; Yongyong Cai; Yue Feng 006 (CoRR, 2021)

Convergence Analysis of A Second-order Accurate, Linear Numerical Scheme for The Landau-Lifshitz Equation with Large Damping Parameters. - Yongyong Cai; Jingrun Chen; Cheng Wang 015; Changjian Xie (CoRR, 2021)

Efficient and accurate gradient flow methods for computing ground states of spinor Bose-Einstein condensates. - Yongyong Cai; Wei Liu 136 (J. Comput. Phys., 2021)

Unconditionally Maximum Bound Principle Preserving Linear Schemes for the Conservative Allen-Cahn Equation with Nonlocal Constraint. - Jingwei Li; Lili Ju; Yongyong Cai; Xinlong Feng (J. Sci. Comput., 2021)

Uniform Error Bounds of Time-Splitting Methods for the Nonlinear Dirac Equation in the Nonrelativistic Regime without Magnetic Potential. - Weizhu Bao; Yongyong Cai; Jia Yin (SIAM J. Numer. Anal., 2021)

Normalized Gradient Flow with Lagrange Multiplier for Computing Ground States of Bose-Einstein Condensates. - Wei Liu 136; Yongyong Cai (SIAM J. Sci. Comput., 2021)

Improved uniform error bounds on time-splitting methods for the long-time dynamics of the weakly nonlinear Dirac equation. - Weizhu Bao; Yongyong Cai; Yue Feng 006 (CoRR, 2022)

Stabilized exponential time differencing schemes for the convective Allen-Cahn equation. - Yongyong Cai; Lili Ju; Rihui Lan; Jingwei Li (CoRR, 2022)

A second-order numerical method for Landau-Lifshitz-Gilbert equation with large damping parameters. - Yongyong Cai; Jingrun Chen; Cheng Wang 015; Changjian Xie (J. Comput. Phys., 2022)

Uniformly Accurate Nested Picard Iterative Integrators for the Klein-Gordon Equation in the Nonrelativistic Regime. - Yongyong Cai; Xuanxuan Zhou (J. Sci. Comput., 2022)

Uniformly Accurate Nested Picard Iterative Integrators for the Nonlinear Dirac Equation in the Nonrelativistic Regime. - Yongyong Cai; Yan Wang 094 (Multiscale Model. Simul., 2022)

Improved Uniform Error Bounds on Time-Splitting Methods for Long-Time Dynamics of the Nonlinear Klein-Gordon Equation with Weak Nonlinearity. - Weizhu Bao; Yongyong Cai; Yue Feng 006 (SIAM J. Numer. Anal., 2022)

Improved uniform error bounds of the time-splitting methods for the long-time (nonlinear) Schrödinger equation. - Weizhu Bao; Yongyong Cai; Yue Feng 006 (Math. Comput., 2022)

A uniformly accurate method for the Klein-Gordon-Dirac system in the nonrelativistic regime. - Yongyong Cai; Wenfan Yi (J. Comput. Phys., 2023)

Operator splitting based structure-preserving numerical schemes for the mass-conserving convective Allen-Cahn equation. - Rihui Lan; Jingwei Li; Yongyong Cai; Lili Ju (J. Comput. Phys., 2023)

Uniformly accurate nested Picard iterative integrators for the Klein-Gordon-Schrödinger equation in the nonrelativistic regime. - Yongyong Cai; Xuanxuan Zhou (Numer. Algorithms, 2023)

Second-Order Semi-Lagrangian Exponential Time Differencing Method with Enhanced Error Estimate for the Convective Allen-Cahn Equation. - Jingwei Li; Rihui Lan; Yongyong Cai; Lili Ju; Xiaoqiang Wang (J. Sci. Comput., 2023)

Error estimates of a regularized finite difference method for the Logarithmic Schr "{o}dinger equation with Dirac delta potential. - Xuanxuan Zhou; Tingchun Wang; Yong Wu; Yongyong Cai (CoRR, 2024)

A robust hybridizable discontinuous Galerkin scheme with harmonic averaging technique for steady state of real-world semiconductor devices. - Qingyuan Shi; Yongyong Cai; Chijie Zhuang; Bo Lin; Dan Wu; Rong Zeng 001; Weizhu Bao (J. Comput. Phys., 2024)

Positivity Preserving and Mass Conservative Projection Method for the Poisson-Nernst-Planck Equation. - Fenghua Tong; Yongyong Cai (SIAM J. Numer. Anal., 2024)

Conservative Crank-Nicolson-type and compact finite difference schemes for modeling the Schrödinger equation with point nonlinearity. - Yong Wu; Fenghua Tong; Xuanxuan Zhou; Yongyong Cai (Appl. Math. Lett., 2025)

Normalized flows based on Sobolev gradients for computing ground states of spinor Bose-Einstein condensates. - Yong Wu; Chengyang Liu; Yongyong Cai (J. Comput. Phys., 2025)

Efficient and stable diffusion generated methods for ground state computation in Bose-Einstein condensates. - Jing Guo; Yongyong Cai; Dong Wang (CoRR, 2025)