蔡曉峰檢視原始碼討論檢視歷史
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蔡曉峰，男，北京師範大學-香港浸會大學聯合國際學院助理教授。
人物簡歷
蔡曉峰博士是北京師範大學珠海校區和 北師港浸大 助理教授。研究領域是計算流體力學，研究工作主要面向等離子體物理模擬、數值天氣預報等領域，從事針對對流占優問題的高效穩健可靠的高階數值方法研究。發展了一套求解多維輸運問題的守恆型半拉格朗日算法。
研究領域
高分辨率高精度計算方法，包括：間斷有限元、加權本質無振盪格式
Eulerian-Lagrangian 間斷Galerkin有限元方法、自適應移動網格方法、Arbitrary Lagrangian-Eulerian 方法
應用，包括：數值天氣預報、等離子體物理、環境流體力學等
學術成果
著作文章
Eulerian-Lagrangian high order Runge-Kutta discontinuous Galerkin method
1. 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.
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.
high order semi-Lagrangian discontinuous Galerkin method
3. 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, 2017, 73(2): 514-542.
4. 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. 5. 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.
6. 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.
7. 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.
10. 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
Volume 395 , 15 May 2022, 114973
Hermite WENO schemes
11. 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. 12. 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, to appear.
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, Jianxian Qiu and Jing-Mei Qiu, Finite volume HWENO schemes for nonconvex conservation laws, Journal of Scientific Computing, 75.1 (2018): 65-82. 15. 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. Applications
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.
Leitao Chen, Sauro Succi, Xiaofeng Cai, and Laura Schaefer, Semi-Lagrangian implicit Bhatnagar- Gross-Krook collision model for the finite-volume discrete Boltzmann method, Physical Review E, 101.6 (2020): 063301.
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, Laura Schaefer and Xiaofeng Cai, An Accurate Unstructured Finite Volume Discrete Boltzmann Method, ASME 2018 International Mechanical Engineering Congress and Exposition, Volume 7: Fluids Engineering: pp. V007T09A010. Preprints
20. Nanyi Zheng, Xiaofeng Cai, Jing-Mei Qiu, Jianxian Qiu, Fourth-order conservative non-splitting semi-Lagrangian Hermite WENO schemes for kinetic and fluid simulations
21. Hongtao Liu, Xiaofeng Cai, Giovanni Lapenta, Yong Cao, Discrete unified gas kinetic scheme for the plasma flow in all electromagnetic plasma regimes.
22. Hongtao Liu, Mengyu Chen, Xiaofeng Cai, Yong Cao, Giovanni Lapenta, A combined immersed finite element and conservative semi-Lagrangian scheme for plasma-material interactions.
教學
At UIC
Numerical Method I (Applied Mathematics), 2022年秋季
Fundamental Mathematics (DBM), 2022年秋季
Calculus, 2022春季
Calculus for Science and Engineering, 2021年秋季
Linear Algebra, 2021年秋季
At Udel
Engineering Mathematics III, Spring 2018 to Fall 2019
Engineering Mathematics III, Fall 2020, Spring 2021 (online)[1]