北京师范大学文理学院副教授，博士生导师。研究方向是双曲方程和动理学模型的高效计算方法设计及其在等离子体物理模拟等领域的应用。在Journal of Computational Physics、SIAM Journal on Scientific Computing、Mathematics of Computation等权威期刊发表20余篇学术论文。主页：math-cai.github.io（招收研究生中，感兴趣的同学联系xfcai@bnu.edu.cn ）

教育背景

2013.09-2016.06    厦门大学 计算数学 理学博士

工作经历

2023.07-至今 北京师范大学 数学研究中心 长聘副教授

2021.08-2023.06 北京师范大学 数学研究中心 特聘副研究员（青年英才）

2021.08-2026.06 北师香港浸会大学 数学科学系 助理教授、副教授

2017.09-2021.06 特拉华大学 数学科学系 博士后、讲师                                                                                     

2015.01-2017.08 休斯敦大学 数学系 研究助理、博士后 

研究方向

科学计算，尤其是计算流体力学和等离子体物理模拟:

• 双曲型守恒律的高阶数值方法：有限差分/有限体积 WENO 方法、间断伽辽金方法、任意拉格朗日欧拉方法

• 动理学模型的高效数值方法，应用于等离子体物理模拟和数值天气预报

代表论文

1. Xiaofeng Cai, Yibing Chen, Kunkai Fu, Liujun Pan. A third-order conservative semi-Lagrangian discontinuous Galerkin scheme for the transport equation on curvilinear unstructured meshes. SIAM Journal on Scientific Computing, 2026.

2. Xiaofeng Cai, Qingtao Li, Hongtao Liu, Haibiao Zheng. A high-order energy-conserving semi-Lagrangian discontinuous Galerkin method for the Vlasov-Ampère system. Acta Mechanica Sinica, Vol. 42, 725364, 2026.

3. Wenyong Gan, Qi Ye, Xiaofeng Cai. Kernel-based WENO schemes for hyperbolic conservation laws. (special issue in honor of the 80th birthday of Robert Schaback). Engineering Analysis with Boundary Elements, Volume 190, 106870, 2026.

4. Nanyi Zheng, Xiaofeng Cai, Jing-Mei Qiu, Jianxian Qiu. Non-splitting Eulerian-Lagrangian WENO schemes for two-dimensional nonlinear convection-diffusion equations. Journal of Computational Physics, 529, 113890, 2025.

5. Hongtao Liu, Xiaofeng Cai, Yong Cao, Giovanni Lapenta. An asymptotic-preserving conservative semi-Lagrangian scheme for the Vlasov-Maxwell system in the quasi-neutral limit. Journal of Computational Physics, 528, 113840, 2025.

6. Hongtao Liu, Xiaofeng Cai, Yong Cao, Giovanni Lapenta. An efficient energy conserving semi-Lagrangian kinetic scheme for the Vlasov-Ampère system. Journal of Computational Physics, 492, 112412, 2023.

7. Hongtao Liu, Mengyu Chen, Xiaofeng Cai, Yong Cao, Giovanni Lapenta. A combined immersed finite element and conservative semi-Lagrangian scheme for plasma-material interactions. Journal of Computational Physics, 488, 112232, 2023.

8. Nanyi Zheng, Xiaofeng Cai, Jing-Mei Qiu, Jianxian Qiu. A fourth-order conservative semi-Lagrangian finite volume WENO scheme without operator splitting for kinetic and fluid simulations. Computer Methods in Applied Mechanics and Engineering, 395, 114973, 2022.

9. Xiaofeng Cai, Jing-Mei Qiu. Eulerian-Lagrangian Runge-Kutta Discontinuous Galerkin Method for Transport Simulations on Unstructured Meshes. SIAM Journal on Scientific Computing, 44(4): A2037–A2060, 2022. 

10. Xiaofeng Cai, Jing-Mei Qiu, Yang Yang. An Eulerian-Lagrangian discontinuous Galerkin method for transport problems and its application to nonlinear dynamics. Journal of Computational Physics, 439, 110392, 2021.

11. Xiaofeng Cai, Sebastiano Boscarino, Jing-Mei Qiu. High Order Semi-Lagrangian Discontinuous Galerkin Method Coupled with Runge-Kutta Exponential Integrators for Nonlinear Vlasov Dynamics. Journal of Computational Physics, 427, 110036, 2021.

12. Nanyi Zheng, Xiaofeng Cai, Jing-Mei Qiu, Jianxian Qiu. A conservative semi-Lagrangian hybrid Hermite WENO scheme for linear transport equations and the nonlinear Vlasov-Poisson system. SIAM Journal on Scientific Computing, 43(5), A3580–A3606, 2021.

13. Yang Yang, Xiaofeng Cai, Jing-Mei Qiu. Optimal convergence and superconvergence of semi-Lagrangian discontinuous Galerkin methods for linear convection equations in one space dimension. Mathematics of Computation, 89(325): 2113–2139, 2020.

14. Mingchang Ding, Xiaofeng Cai, Wei Guo, Jing-Mei Qiu. A semi-Lagrangian discontinuous Galerkin (DG) – local DG method for solving convection-diffusion equations. Journal of Computational Physics, 409, 109295, 2020.

15. Xiaofeng Cai, Wei Guo, Jing-Mei Qiu. A high order semi-Lagrangian discontinuous Galerkin method for the two-dimensional incompressible Euler equations and the guiding center Vlasov model without operator splitting. Journal of Scientific Computing, 79.2: 1111–1134, 2019.

16. Xiaofeng Cai, Wei Guo, Jing-Mei Qiu. A high order semi-Lagrangian discontinuous Galerkin method for Vlasov-Poisson simulations without operator splitting. Journal of Computational Physics, 354: 529–551, 2018.

17. Xiaofeng Cai, Jianxian Qiu, Jing-Mei Qiu. Finite volume HWENO schemes for nonconvex conservation laws. Journal of Scientific Computing, 75.1: 65–82, 2018.

18. Xiaofeng Cai, Wei Guo, Jing-Mei Qiu. A high order conservative semi-Lagrangian discontinuous Galerkin method for two-dimensional transport simulations. Journal of Scientific Computing, 73.2-3: 514–542, 2017 (special issue in honor of the 60th birthday of Chi-Wang Shu)

19. Xiaofeng Cai, Jianxian Qiu, Jing-Mei Qiu. A conservative semi-Lagrangian HWENO method for the Vlasov equation. Journal of Computational Physics, 323: 95–114, 2016.

20. Xiaofeng Cai, Xiangxiong Zhang, Jianxian Qiu. Positivity-preserving high order finite volume HWENO schemes for compressible Euler equations. Journal of Scientific Computing, 68: 464–483, 2016.

荣誉获奖

1. 广东省“珠江人才”青年拔尖人才

2. 2024年 北京师范大学本科优秀毕业论文指导老师

3. 2025年 北京师范大学本科优秀毕业论文指导老师

4. 2026年 北师香港浸会大学本科优秀毕业论文指导老师