2023-06-13
蔡晓峰，数学研究中心特聘副研究员
Email：xfcai@bnu.edu.cn
基本情况
蔡晓峰博士是北京师范大学珠海校区特聘副研究员，也是北师港浸大（UIC）应用数学专业助理教授。研究领域是计算流体力学、微分方程数值解，主要从事针对对流占优问题的高效稳健可靠的数值方法研究及其在空气动力学、等离子体物理模拟等领域中的应用。在Journal of Computational Physics(7篇)、SIAM Journal on Scientific Computing(2篇)、Mathematics of Computation、Computer Methods in Applied Mechanics and Engineering等权威期刊发表20篇学术论文。
欢迎高年级本科生联系暑期科研项目，并欢迎联系报考计算数学方向的研究生。
研究领域
计算流体力学
· 高分辨率高精度计算方法，包括：间断有限元、加权本质无振荡格式
· 半拉格朗日算法
· Eulerian-Lagrangian 间断Galerkin有限元方法、自适应移动网格方法、Arbitrary Lagrangian-Eulerian 方法
· 等离子物理模拟的高效高精度保结构数值算法
· 应用，包括：数值天气预报、环境流体力学等
最优控制问题
学习经历
2011/09-2016/07厦门大学 计算数学博士
2015/01-2016/07休斯敦大学 联合培养博士生
工作经历
2016/07-2017/08 休斯敦大学 博士后
2017/09-2020/01 特拉华大学 博士后
2020/01-2021/07 特拉华大学 研究员
2021/08-现在，北京师范大学珠海校区，自然科学高等研究院，数学研究中心，特聘副研究员（青年英才）
代表论文（*，代表通讯作者）
1. Xiaofeng Cai, Sebastiano Boscarino and 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.
2. Xiaofeng Cai, Jing-Mei Qiu and Yang Yang, An Eulerian-Lagrangian discontinuous Galerkin method for transport problems and its application to nonlinear dynamics, Journal of Computational Physics, 439, 110392, 2021.
3. Yang Yang, Xiaofeng Cai and 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.
4. Xiaofeng Cai, Wei Guo and Jing-Mei Qiu, A high order semi-Lagrangian discontinuous Galerkin method for Vlasov-Poisson simulations without operator splitting, Journal of Computational Physics, 354 (2018): 529-551.
5. Xiaofeng Cai, Wei Guo and 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 (2019): 1111-1134.
6. 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.
7. Nanyi Zheng, Xiaofeng Cai, Jing-Mei Qiu and 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 (2022): 114973.
8. Xiaofeng Cai, Jing-Mei Qiu, Eulerian-Lagrangian Runge-Kutta Discontinuous Galerkin Method for Transport Simulations on Unstructured Meshes. SIAM Journal on Scientific Computing. 2022.
9. Xiaofeng Cai, Wei Guo and Jing-Mei Qiu, A high order conservative semi-Lagrangian discontinuous Galerkin method for two-dimensional transport simulations, Journal of Scientific Computing, 73.2-3, (2017): 514-542.
10. Xiaofeng Cai, Jianxian Qiu and Jing-Mei Qiu, A conservative semi-Lagrangian HWENO method for the Vlasov equation, Journal of Computational Physics, 323 (2016): 95-114.
11. Xiaofeng Cai, Xiangxiong Zhang and Jianxian Qiu, Positivity-preserving high order finite volume HWENO schemes for compressible Euler equations, Journal of Scientific Computing, 68 (2016): 464-483.
12. Xiaofeng Cai, Jianxian Qiu and Jing-Mei Qiu, Finite volume HWENO schemes for nonconvex conservation laws, Journal of Scientific Computing, 75.1 (2018): 65-82.
13. Xiaofeng Cai, Jun Zhu and Jianxian Qiu, Hermite WENO schemes with strong stability preserving multi-step temporal discretization methods for conservation laws, Journal of Computational Mathematics, 35 (2017): 19-40.
14. Xiaofeng Cai, Wei Guo and Jing-Mei Qiu, Comparison of semi-Lagrangian discontinuous Galerkin schemes for linear and nonlinear transport simulations, Communications on Applied Mathematics and Computation, to appear, https://doi.org/10.1007/s42967-020-00088-0.
15. Nanyi Zheng, Xiaofeng Cai, Jing-Mei Qiu and 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.
16. Jiajie Chen, Xiaofeng Cai, Jianxian Qiu and Jing-Mei Qiu, Adaptive Order WENO Reconstructions for the Semi-Lagrangian Finite Difference Scheme for advection problem, Communications in Computational Physics, 30: 67-96, 2021.
17. Mingchang Ding, Xiaofeng Cai, Wei Guo and Jing-Mei Qiu, A semi-Lagrangian discontinuous Galerkin (DG) - local DG method for solving convection-diffusion equations, Journal of Computational Physics, 409 (2020): 109295.
18. Hongtao Liu, Xiaofeng Cai, Giovanni Lapenta, Yong Cao, Conservative semi-Lagrangian kinetic scheme coupled with implicit finite element field solver for multidimensional Vlasov Maxwell system, Communications in Nonlinear Science and Numerical Simulation, 102, 105941, 2021.
19. Leitao Chen, Sauro Succi, Xiaofeng Cai, and Laura Schaefer, Semi-Lagrangian implicit BhatnagarGross-Krook collision model for the finite-volume discrete Boltzmann method, Physical Review E, 101.6 (2020): 063301.
20. 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, 2023
主持、参与的科研项目
1. A research on high order Eulerian-Lagrangian Runge-Kutta discontinuous Galerkin method，UIC 校内基金科研启动经费, 2022-2025, 主持
2. 非结构网格的高阶守恒欧拉拉格朗日型间断伽辽金方法的研究与应用，国家自然科学青年基金，12201052，2023-2025，主持
3. 高维输运问题的特征线间断有限元方法的设计及应用，北京师范大学青年英才科研启动基金，310432105，2021-2024，主持
获奖情况
Travel award: Advances in PDEs: Theory, Computation and Application to CFD, ICERM, Brown University, Providence, RI, USA, August 20-24, 2018.
学术兼职
中国数学会会员、美国《数学评论》评论员
Journal of Computational Physics, Computer Physics Communications, Journal of Scientific Computing, Communications in Computational Physics, International Journal for Numerical Methods in Fluids, Advances in Applied Mathematics and Mechanics, Results in Applied Mathematics, Computers and Mathematics with Applications等期刊审稿人
学术交流
1. 数值方法青年研讨会，40mins, 国家天元中心东南中心, 厦门大学, 5月13 - 14日，2022年20 - 21日.
2. 组织者，科学计算进展研讨会, 北京师范大学珠海校区, 2023年2月9- 11日.
3. 科学计算及其应用，汕头大学数学系, 2023年5月13-14日.
4. 北京师范大学珠海校区交叉学科前沿论坛，2021年11月23-25日.
5. 数学和难题挑战研讨会，华为，松山湖，2022年6月2日.
6. BNU-UIC数学研究中心与南方科技大学数学系学术交流会，南科大，2021年11月12日-14日.
7. The 5th Annual Meeting of SIAM Central States Section, Ames, IA, October 19-20, 2019.
8. DelMar Numeric Day 2019, Annual Workshop on Computational Mathematics, In Honor of the 50th Birthday of FRANCISCO-JAVIER SAYAS, The University of Maryland, College Park, Maryland, USA, May 11, 2019.
9. Fall Central Sectional Meeting of the AMS, University of Michigan, Ann Arbor, Michigan, USA, October 20-21, 2018.
10. The fifteenth International Conference on Mesoscopic Methods in Engineering and Science (ICMMES), Newark, Delaware, USA, July 09-13, 2018.
11. Mid Atlantic Numerical Analysis Day 2017, Temple University, Philadelphia, PA, USA, November 3, 2017.
12. 45-min Talk, IMAGe 2017 Theme of the Year: Workshop on Multiscale Geoscience Numerics, NCAR, Boulder, Colorado, May 16 - 19, 2017.
13. 2017 Finite Element Rodeo, Houston, TX, USA, March 3-4, 2017.
14. SIAM conference on Computational Science and Engineering, Atlanta, GA, USA, February 27-March 3, 2017.
15. Two 30-min Talks, 2016 SIAM Annual Meeting, Boston, MA, USA, July 11-15, 2016.
16. Mid Atlantic Numerical Analysis Day 2015, Temple University, Philadelphia, PA, Nov. 13, 2015.
17. International Symposium of High-order Methods for Computational Fluid Dynamics, 13th U.S. National Congress on Computational Mechanics, San Diego, CA, USA, July 26-30, 2015.
邀请讲座
1. 华东师范大学，2023年6月30日
2. 东南大学数学学院, 2023年3月30日.
3. 中山大学，海洋工程与技术学院，珠海，2023年4月14日.
4. 北京应用物理与计算数学研究所, 北京, 2023年 3月9日.
5. 北京应用物理与计算数学研究所, 北京，2023年4月14日.
6. 国家天元中心东南中心, 厦门大学, 2023年3月2日.
7. 四川大学数学学院, 2022年4月28日.
8. 国家应用数学中心, 湘潭大学, 2022年7月21日.
9. 中山大学大气科学学院，2021年12月25日.
10. School of Civil and Environmental Engineering, Cornell University, USA, August 13, 2021.
11. 哈尔滨工业大学(深圳)，2018年7月2日.
12. 厦门大学数学科学学院, 2018年6月12日.
