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计算数学教研室--李杰权

李杰权

计算数学教研室,博士生导师

联系方式:010-

电子邮箱:li_jiequan@iapcm.ac.cn

从事专业:

计算流体力学,偏微分方程,数值分析

教育经历

·1991/09—1994/07:北京师范大学数学系攻读硕士学位

·1994/09—1997/03:中国科学院数学所攻读博士学位

工作经历
(长期职位)

2015/08---:北京应用物理与计算数学研究所研究员,博士生导师

2010/12—2015/07:北京师范大学数学学院教授、博士生导师

2013/07—2014/06:美国宾州州立大学数学系,访问教授

2002/08—2010/12:北京市首都师范大学数学学院研究员(2003年始博士生导师)

2004/03—2005/06: 德国马格德堡大学数学系,洪堡学者

2001/08—2002/07:台北中央研究院数学所访问教授

1999/10—2001/08:以色列希伯莱大学爱因斯坦数学所Lady Davis和 Golda Meir 研究员(以色列总理基金资助)

1997/03—1998/12:中国科学院应用数学所博士后

(短期访问)

2017/07—08(1个月):香港科技大学数学系

2017/05:美国内华达大学(拉斯维加斯)数学系

2016/09 (10天):德国美因茨大学数学系

2016/04-05(1个月): 香港科技大学数学系

2015/02:香港科技大学数学系

2014 /06-09:德国美因茨(Mainz)大学数学系(洪堡学者)

2010/11—12(20天):新加坡国立大学

2010/10:香港科技大学理学院

2009/11-12:美国宾州州立大学数学系

2009/08-09:德国马格德堡大学数学系、汉堡科技大学

2008/06-07(3周): 法国巴黎庞卡莱数学研究所

2007/06-07: 美国斯坦福大学数学系

2007/01: 以色列希伯莱大学爱因斯坦数学研究所,特拉维夫大学数学系

2006/09-11: 美国宾州州立大学数学系

2006/01: 以色列希伯莱大学爱因斯坦数学研究所

2004/10-11: 德国汉堡科技大学数学系

2004/09: 法国Metz大学数学系

2003/06-07: 香港中文大学数学研究所

1999/01-1999/10:德国马格德堡大学数学系DFG项目博士后

1998/01-1998/3:以色列希伯莱大学爱因斯坦数学所博士后

研究方向简介
计算流体力学:

面向航天航空、武器物理以及其它工程应用领域,致力发展三高(高置信度、高精度、高效)数值方法。涉及的背景问题有:可压缩流体的普适性问题、爆轰、弹塑性材料、信号传输、多介质流体的界面不稳定性等。目前和成娟、田保林、于明、程军霞研究员等组成联合团队从事多介质大变形流体力学数值方法与应用研究,感兴趣的问题有:

(1)可压缩流体力学的高精度数值方法,包括有限体积、有限差分、间断有限元方法等;

(2)从介观到宏观的多介质流体力学数学建模;

(3)可压缩湍流的形成机理以及大规模数值模拟;

团队成员与美国、德国、瑞士、法国、意大利、以色列、日本、香港等国家和地区有着密切的合作关系。每两年有定期的多介质流体力学国际会议以及每年有小规模的高精度数值方法国际会议,推动着该领域内同行的合作与交流。

数值分析:

数值分析是理解、评价数值方法的重要手段,也是设计高置信度数值方法的基础。本方向致力于:

(1)分析各种新型数值方法的稳定性;

(2)针对复杂物理模型,分析相应数值方法保物理性质;

偏微分方程

基于无粘欧拉方程组和BGK模型,研究可压缩流体的流场结构及其各种非线性波(激波、滑移面、爆轰波、Delta波等)的稳定性。具体有:

(1)可压缩欧拉方程组的两维黎曼问题以及多维非线性波的相互作用;

(2)从稀薄到连续流相关模型的适定性。

美国 Mathematical Reviews评价其所在团队的成果为“中国数学学派”(Chinese School of Mathematics)的工作。

个人荣誉、所获奖项等

·2008国务院政府特殊津贴

·2008年北京市百千万工程人选

·2006年教育部新世纪优秀人才

·2005年第十届霍英东高等学校青年教师奖(研究类)

·2004年德国洪堡研究类奖学金

·2003年北京市科学技术一等奖

·2001,2002年以色列Golda Meir(总理)奖

代表性研究成果列表(请按照参考文献引用格式提供详细信息)

**专著:The Two-dimensional Riemann Problem in Gas Dynamics (第一作者;合作者:Tong Zhang, Shuli Yang), Pitmann Monographs and Surveys in Pure and Applied Mathematics 98, 312页, Longman Scientific & Technical, Harlow.

(美国数学会数学评论MR1697999 (2000d:76106):More recently, the two-dimensional Riemann problem has attracted the attention of many researchers, particularly the Chinese school of mathematics: J. Li, D. Tan, S. Yang, T. Zhang, Y. Zheng, etc.A complete and rigorous study is presented for both the two-dimensional scalar conservation laws and the zero-pressure gas dynamics model. Many important properties of the structure and qualitative behavior of solutions are derived for the two-dimensional compressible Euler system. Precise conjectures are stated, which are carefully tested in numerical experiments.)

代表性研究论文

[1] Jiequan Li and Yue Wang,Thermodynamical Effects and High Resolution Methods for Compressible Fluid Flows, Journal of Computational Physics, 343 (2017),340–354.

[2] Jiequan Li and Zhifang Du, A two-stage fourth order time-accurate discretization for Lax-Wendroff type flow solvers, I. Hyperbolic conservation laws, SIAM J. Sci. Comput..38 (2016), 3045-3069.

[3] Yue Wang and Jiequan Li, Numerical Defects of the HLL Scheme and Dissipation Matrices for the Euler equations, SIAM J. Numerical Analysis, No. 52, Vol. 1(2014), 207-219.

[4] JianzhenQian, Jiequan Li and Shuanghua Wang, The generalized Riemann problems for compressible fluid flows: Towards high order, Journal of Computational Physics, 259 (2014) 358–389.

[5]Jiequan Li and Yongjin Zhang, The adaptive GRP scheme for compressible fluid flows over unstructured meshes, Journal of Computational Physics, 242 (2013), 367--386.

[6] Jiequan Li and Zhicheng Yang, Heuristic modified equation analysis on oscillations in numerical solutions of conservation laws, SIAM Journal on Numerical Analysis, 49, 2386-2406,2011.

[7] Jiequan Li, Qibing Li and Kun Xu, Comparison of the Generalized Riemann Solver and the Gas-Kinetic scheme for Compressible Inviscid Flow Simulations, Journal of Computational Physics, 230, pp. 5080-5099, 2011.

[8] Jiequan Li and YuxiZheng, Interaction of four rarefaction waves in the bi-symmetric class of the two-dimensional Euler equations, Communications in Mathematical Physics, 296, 303—321,2010.

[9] Ee Han, Jiequan Li and Huazhong Tang, An adaptive GRP scheme for compressible fluid flows, Journal of Computational Physics, 229, 1448-1466, 2010.

[10] Jiequan Li and YuxiZheng, Interaction of rarefaction waves of the two-dimensional self-similar Euler equations, Archive Rational Mechanics and Analysis, 193, 623--657, 2009.

[11] Jiequan Li, Huazhong Tang, Gerald Warnecke and Lumei Zhang, Local oscillations in finite difference solutions of hyperbolic conservation laws, Mathematics of Computation, 78, 1997--2018, 2009.

[12] Jiequan Li, Tiegang Liu and Zhongfeng Sun, Implementation of the GRP scheme for computing spherical compressible fluid flows, Journal of Computational Physics, 228, 5867--5887, 2009.

[13] J. Glimm, X. Ji, Jiequan Li, X. Li, T. Zhang, P. Zhang and Y. Zheng, Transonic shock formation in a rarefaction Riemann problem for the 2-D compressible Euler equations, SIAM Journal on Applied Mathematics, Vol. 69, No. 3, 720--742, 2008.

[14] Jiequan Li and Zhongfeng Sun, Remark on the generalized Riemann problem method for compressible fluid flows, Journal of Computational Physics, 222, 796--808, 2007.

[15] M.Ben-Artzi and Jiequan Li, Hyperbolic conservation laws: Riemann invariants and the generalized Riemann problem, NumerischeMathematik, 106, 369--425, 2007.

[16] Jiequan Li and Guoxian Chen, The generalized Riemann problem method for the shallow water equations with bottom topography, International Journal of Numerical Methods in Engineering, Vol. 6, No. 6, 834--862, 2006.

[17] Matania Ben-Artzi, Jiequan Li and Gerald Warnecke, A direct Eulerian GRP scheme for compressible fluid flows, Journal of Computational Physics, 218, 19--43, 2006.

[18] Jiequan Li, Tong Zhang and YuxiZheng, Simple waves and a characteristic decomposition for the two dimensional compressible Euler equations, Communications in Mathematical Physics, 267, 1--12, 2006.

[19] Jiequan Li and Peng Zhang, The transition from ZND to CJ theories for nonconvex scalar combustion model, SIAM Journal on Mathematical Analysis, Vol. 34, No. 3, 675--699, 2003.

[20] Jiequan Li, Global solution of an initial—value problem for two--dimensional compressible Euler equations, Journal of Differential Equations, Vol. 179, No. 1, 178-- 194, 2002.

[21] Jiequan Li, On the two--dimensional gas expansion for compressible Euler equations, SIAM Journal on Applied Mathematics, Vol. 62, No. 3, 831--852, 2001/2002.

[22] Jiequan Li, On the uniqueness and existence problem for a multidimensional reacting and convection system, Journal of the London Mathematical Society, Vol. 62, No. 2, 473-- 488, 2000.


其他期刊论文

[1] Liang Pan, Jiequan Li and Kun Xu, A Few Benchmark Test Cases for Higher-order Euler Solvers,Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), 489-514.

[2] Liang Pan, Kun Xu, QibingLi andJiequan Li, An efficient and accurate two-stage fourth-order gas-kinetic scheme for the Euler and Navier-Stokes equations, Journal of Computational Physics, Vol 326 (2016), 197-221.

[3] Yue Wang and Jiequan Li, Entropy Convergence of a New Two-ValueScheme with Slope Relaxation for Conservation Laws, Applied Mathematics and Mechanics, 37 (11), 1151-1170, 2016.

[4] Jin Qi, BaolinTian and Jiequan Li, A High-order Cell-centered Lagrangian Method with a Vorticity-based Adaptive Nodal Solver for 2-D Compressible Euler Equations, submitted to communications in Computational Physics, in revision, 2017.

[5] Jin Qi and Jiequan Li, A fully discrete high order ALE method over untwisted time-space control volumes, International Journal of Numerical Methods in Fluids, 83 (2017), 625-641.

[6] Jiequan Li,BaolinTian and Shuanghu Wang, Dissipation Matrix and Artificial Heat Conduction for Godunov-type Schemes of Compressible Fluid Flows, International Journal of Numerical Methods in Fluids, 84 (2017), 57-75.

[7] Jiequan Li, Self-similar solutions of 2-D compressible Euler equations and mixed-type problems, Bulletin of the Institute of Mathematics, Academia Sinica, Vol. 10 (2015), 393--421.

[8] Jin Qi, Yue Wang and Jiequan Li, Remapping-free Adaptive GRP Method for Multi-Fluid Flows I: One Dimensional Euler Equations, Communications in Computational Physics, Vol 15(2014), 1029-1044.

[9] Yanbo Hu, Jiequan Li and Wancheng Sheng, Degenerate Goursat-type boundary value problems arising from the study of two-dimensional isothermal Euler equations, Z. Angew. Math. Phys.,63(2012), 1021-1046.

[10]Jiequan Li, Zhicheng Yang and YuxiZheng, Characteristic decompositions and interactions of rarefaction waves of 2-D Euler Equations, Journal of Differential Equations, 250, 782–798, 2011.

[11] Ee Han, Jiequan Li and Huazhong Tang, Accuracy of the adaptive GRP scheme and the simulation of 2-D Riemann problem for compressible Euler equations, Communications in Computational Physics, Vol. 10, No. 3, pp. 577-606, 2011.

[12] Matania Ben-Artzi,Joseph Falcovitz and Jiequan Li, The convergence of the GRP scheme,Discrete and Continuous Dynamical Systems, Vol. 23, 1&2, 1--27, 2009.

[13] Jiequan Li,Wancheng Sheng, Tong Zhang and YuxiZheng, Two-dimensional Riemann problems: From scalar conservation laws to compressible Euler equations,ActaMathematicaScientia, Vol. 29 (4): 777--802, 2009.

[14] M. Ben-Artzi, J. Falcovitz and Jiequan Li, Wave interaction and numerical approximation for two-dimensional scalar conservation laws, Computational Fluid Dynamics Journal, 14(4): 46, 401-418, 2006.

[15] Jiequan Li and Gerald Warnecke, Generalized characteristics and the uniqueness of entropy solutions to zero-pressure gas dynamics, Advances in Differential Equations, Vol. 8, No. 8, 961--1004, 2003.

[16] Jiequan Li, Maria Lukacova—Medvidova and Gerald Warnecke, Evolution Galerkin schemes applied to the two—dimensional Riamann problem for the wave equation system, Discrete and Continuous Dynamical Systems, Vol.9, No. 3, 559--573, 2003.

[17] Shaozhong Chen, Jiequan Li and Tong Zhang, Transition from a deflagration to a detonation in gas dynamic combustion, Chinese Annals of Mathematics 24B, No. 4, 423-432,2003.

[18] Jiequan Li and Wei Li, The Riemann problem for zero-pressure flow in gas dynamics, Progresses in Natural Sciences, Vol. 11, No. 5, 331--344, 2001.

[19] Jiequan Li, Note on the compressible Euler equations with zero temperature, Applied Mathematical Letter, Vol. 14, No. 4, 519--523, 2001.

[20] Jiequan Li and Hanchun Yang, Delta-shocks as limit of solutions of multidimensional zero-pressure gas dynamics, Quarterly of Applied Mathematics, 59, No.2, 315--342, 2001.

[21] Jiequan Li and Shuli Yang, Two-dimensional Riemann problem for Euler equations of gas dynamics in three pieces, Journal of Computational Mathematics, Vol. 17, No. 3, 327--336, 1999.

[22] Peng Zhang, Jiequan Li and Tong Zhang, On Two-dimensional Riemann problem for pressure-gradient equations in gas dynamics, Discrete and Continuous Dynamical Systems, Vol. 4, No. 4, 609--634, 1998.

[23] Shaozhong Cheng, Jiequan Li and Tong Zhang, Explicit construction of measure solutions of Cauchy problem for transportation equations, Science in China (Series A), Vol. 40, 12: 1287--1299, 1997.

(经审稿的)会议论文集论文

[1] Jiequan Li and G. Warnecke, On measure solutions to the zero-pressure gas model and their uniqueness, MathematicaBohemica, Vol. 127, No. 2, 265--273, 2002.

[2] Jiequan Li and Tong Zhang, Two-dimensional Riemann problem for conservation laws in gas dynamics, AMS/IP Studies in Advanced Mathematics, Vol. 20, 461--472, 2001.

[3] Jiequan Li and Tong Zhang, The dominator of compressible Euler equations, Luso-Chinese Symposium on Nonlinear Evolution Equations and Their Application, Macau,7-9 October 1998, Edited by Ta-tsienLi,Long-Wei Lin and Jose Francisco Rodriques, World Scientific, 116--127, 1999.

[4] Jiequan Li and Tong Zhang, On the initial-value problem for zero-pressure gas dynamics, Proceeding of the Seventh Hyperbolic Conference on Theory, Numerics and Computation, International Series of Numerical Mathematics, Edited by M. Fey and R. Jeltsch, Birhauser, Vol. 130, 629--641,1999.

[5] Jiequan Li and Tong Zhang, Generalized Rankine-Hugoniot relations of delta-shocks in solutions of transportation equations, Nonlinear PDE and Related Areas, Edited by Guiqiang Chen, Yanyan Li, Xiping Zhu and Daomin Cao, World Scientific, Singapore, 219--232, 1998.