Personal Homepage

中文

f4M og4 4wl 0vQ 8Wx HJh Hhb rgw TFi kAN iTt D0h Uxs rY0 yFR fT9 nOZ M1R 5Ur jxL

Biography

No Content

Recommended Ph.D.Supervisor Recommended MA Supervisor

Personal Information

Name: 蔡勇勇
E-Mail:
School/Department: School of Mathematical Sciences
Business Address: Houzhulou Building
Degree: Doctoral Degree in Science
Professional Title: Professor
Discipline: Computational Mathematics

Education
Appointments

2007.08 - 2012.02
- 新加坡国立大学
- 计算与应用数学
- Doctor
- Doctoral Degree in Science
2004.09 - 2007.07
- 北京大学
- 基础与应用数学
- Master
- Master's Degree in Science
2000.09 - 2004.06
- 北京大学
- 基础与应用数学
- 大学毕业
- Bachelor's Degree in Science

2016.05 - 2019.10
- 北京计算科学研究中心
- 特聘研究员

Education & Teaching

Teaching Information (Recent 3 Years)

› 谱方法,Autumn Term,2025-2026,Postgraduate Courses
› 常微分方程,Autumn Term,2025-2026,Undergraduate Courses
› 应用偏微分方程,Autumn Term,2024-2025,Postgraduate Courses
› 常微分方程,Autumn Term,2024-2025,Undergraduate Courses
› 数值代数,Spring Term,2024-2025,Undergraduate Courses
› 计算数学方法课,Spring Term,2024-2025,Postgraduate Courses

Scientific Research

-Paper Publications

[1]Cai, Yongyong; Tong, Fenghua|Positivity preserving and mass conservative projection methods for the Patlak-Keller-Segel equation,APPLIED NUMERICAL MATHEMATICS,2026,221:63-79
[2]Wu, Yong; Liu, Chengyang; Cai, Yongyong|Normalized flows based on Sobolev gradients for computing ground states of spinor Bose-Einstein condensates,JOURNAL OF COMPUTATIONAL PHYSICS,2025,538
[3]Shen, Xiaojuan; Cai, Yongyong|Error estimates of time discretizations for a Cahn-Hilliard phase-field model for the two-phase magnetohydrodynamic flows,APPLIED NUMERICAL MATHEMATICS,2025,207:585-607
[4]Shi, Qingyuan; Cai, Yongyong; Zhuang, Chijie; Lin, Bo; Wu, Dan; Zeng, Rong; Bao, Weizhu|A robust hybridizable discontinuous Galerkin scheme with harmonic averaging technique for steady state of real-world semiconductor devices,JOURNAL OF COMPUTATIONAL PHYSICS,2024,519
[5]Cai, Yongyong; Feng, Yue; Guo, Yichen; Xu, Zhiguo|Uniform and optimal error estimates of a nested Picard integrator for the nonlinear Schrodinger equation with wave operator,NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,2024
[6]Bao, Weizhu; Cai, Yongyong; Feng, Yue|Improved uniform error bounds on time-splitting methods for the long-time dynamics of the weakly nonlinear Dirac equation,IMA JOURNAL OF NUMERICAL ANALYSIS,2024,44(2)
[7]Tong, Fenghua; Cai, Yongyong|POSITIVITY PRESERVING AND MASS CONSERVATIVE PROJECTION METHOD FOR THE POISSON--NERNST--PLANCK EQUATION,SIAM JOURNAL ON NUMERICAL ANALYSIS,2024,62(4):2004-2024
[8]Cai, Yongyong; Chen, Jingrun; Wang, Cheng; Xie, Changjian|Error analysis of a linear numerical scheme for the Landau-Lifshitz equation with large damping parameters,MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2023,46(18)
[9]Zhou, Xuanxuan; Cai, Yongyong; Tang, Xingdong; Xu, Guixiang|Accurate and efficient numericalmethods for the nonlinear Schrodinger equation with Dirac delta potential,CALCOLO,2023,60(4)
[10]Li, Jingwei; Lan, Rihui; Cai, Yongyong; Ju, Lili; Wang, Xiaoqiang|Second-Order Semi-Lagrangian Exponential Time Differencing Method with Enhanced Error Estimate for the Convective Allen-Cahn Equation,JOURNAL OF SCIENTIFIC COMPUTING,2023,97(1)
[11]Cai, Yongyong; Zhou, Xuanxuan|Uniformly accurate nested Picard iterative integrators for the Klein-Gordon-Schrodinger equation in the nonrelativistic regime,NUMERICAL ALGORITHMS,2023,94(1)
[12]Cai, Yongyong;Yi, Wenfan|A uniformly accurate method for the Klein-Gordon-Dirac system in the nonrelativistic regime,Journal of Computational Physics,2023,486
[13]Qiu, Xu; Hu, Ai-Yuan; Cai, Yongyong; Saito, Hiroki; Zhang, Xiao-Fei; Wen, Lin|Dynamics of spin-nematic bright solitary waves in spin-tensor-momentum coupled Bose-Einstein condensates,PHYSICAL REVIEW A,2023,107(3)
[14]Lan, Rihui; Li, Jingwei; Cai, Yongyong; Ju, Lili|Operator splitting based structure-preserving numerical schemes for the mass-conserving convective Allen-Cahn equation,JOURNAL OF COMPUTATIONAL PHYSICS,2023,472
[15]Cai, Yongyong; Ju, Lili; Lan, Rihui; Li, Jingwei|STABILIZED EXPONENTIAL TIME DIFFERENCING SCHEMES FOR THE CONVECTIVE ALLEN-CAHN EQUATION,COMMUNICATIONS IN MATHEMATICAL SCIENCES,2023,21(1):127-150
[16]Cai, Yongyong; Zhou, Xuanxuan|Uniformly Accurate Nested Picard Iterative Integrators for the Klein-Gordon Equation in the Nonrelativistic Regime,JOURNAL OF SCIENTIFIC COMPUTING,2022,92(2)
[17]Cai, Yongyong; Chen, Jingrun; Wang, Cheng; Xie, Changjian|A second-order numerical method for Landau-Lifshitz-Gilbert equation with large damping parameters,JOURNAL OF COMPUTATIONAL PHYSICS,2022,451
[18]Cai, Yongyong; Wang, Yan|UNIFORMLY ACCURATE NESTED PICARD ITERATIVE INTEGRATORS FOR THE NONLINEAR DIRAC EQUATION IN THE NONRELATIVISTIC REGIME,MULTISCALE MODELING & SIMULATION,2022,20(1):164-187
[19]Bao, Weizhu;Cai, Yongyong;Feng, Yue|IMPROVED UNIFORM ERROR BOUNDS ON TIME-SPLITTING METHODS FOR LONG-TIME DYNAMICS OF THE NONLINEAR KLEIN - GORDON EQUATION WITH WEAK NONLINEARITY(Open Access),SIAM Journal on Numerical Analysis,2022,60(4)
[20]Cai, Yongyong; Guo, Yichen|Uniformly accurate nested Picard integrators for a system of oscillatory ordinary differential equations,BIT NUMERICAL MATHEMATICS,2021,61(4)
[21]Li, Jingwei; Ju, Lili; Cai, Yongyong; Feng, Xinlong|Unconditionally Maximum Bound Principle Preserving Linear Schemes for the Conservative Allen-Cahn Equation with Nonlocal Constraint,JOURNAL OF SCIENTIFIC COMPUTING,2021,87(3)
[22]Cai, Yongyong; Liu, Wei|Efficient and accurate gradient flow methods for computing ground states of spinor Bose-Einstein condensates,JOURNAL OF COMPUTATIONAL PHYSICS,2021,433
[23]Wang, Di; Cai, Yongyong; Wang, Qi|Central vortex steady states and dynamics of Bose-Einstein condensates interacting with a microwave field,PHYSICA D-NONLINEAR PHENOMENA,2021,419
[24]Bao, Weizhu; Cai, Yongyong; Yin, Jia|UNIFORM ERROR BOUNDS OF TIME-SPLITTING METHODS FOR THE NONLINEAR DIRAC EQUATION IN THE NONRELATIVISTIC REGIME WITHOUT MAGNETIC POTENTIAL,SIAM JOURNAL ON NUMERICAL ANALYSIS,2021,59(2):1040-1066
[25]Liu, Wei; Cai, Yongyong|NORMALIZED GRADIENT FLOW WITH LAGRANGE MULTIPLIER FOR COMPUTING GROUND STATES OF BOSE-EINSTEIN CONDENSATES,SIAM JOURNAL ON SCIENTIFIC COMPUTING,2021,43(1):B219-B242
[26]Chen, Yingda; Huang, Yongwei; Lou, Wenkai; Cai, Yongyong; Chang, Kai|Electric-field-driven exciton vortices in transition metal dichalcogenide monolayers,PHYSICAL REVIEW B,2020,102(16)
[27]Bao, Weizhu; Cai, Yongyong; Yin, Jia|SUPER-RESOLUTION OF TIME-SPLITTING METHODS FOR THE DIRAC EQUATION IN THE NONRELATIVISTIC REGIME,MATHEMATICS OF COMPUTATION,2020,89(325):2141-2173
[28]Cai, Yongyong; Wang, Li-Lian; Yang, Jiang; Yang, Xiaofeng|Special Issue In Honor of Professor Jie Shen Preface,JOURNAL OF MATHEMATICAL STUDY,2020,53(2):I-II
[29]Cai, Yongyong; Wang, Yan|(Semi-)Nonrelativisitic Limit of the Nonlinear Dirac Equations,JOURNAL OF MATHEMATICAL STUDY,2020,53(2):125-142
[30]Li, Xiang-Gui; Cai, Yongyong; Wang, Pengde|Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation,APPLIED NUMERICAL MATHEMATICS,2020,151:337-353
[31]Tian, Tonghua; Cai, Yongyong; Wu, Xinming; Wen, Zaiwen|GROUND STATES OF SPIN-F BOSE-EINSTEIN CONDENSATES,SIAM JOURNAL ON SCIENTIFIC COMPUTING,2020,42(4):B983-B1013