程晓良
时间:2020-11-18 15:10来源:点击:3945次
程晓良 博士
教授 | 博士生导师
学科 数学
单位 数学科学学院
电话 87953671
邮箱 xiaoliangcheng@zju.edu.cn
地址 玉泉校区工商管理楼
研究方向 计算数学
个人简介
1981年北京大学数学系本科学习，2000年升职浙江大学教授。
工作研究项目
- 由边界测量数据的反演计算问题，国家自然科学基金项目(11571311)，45万， 2016-1-1, 2019-12-31.
- 复杂介质中波传播反问题的理论分析、计算方法及应用, 国家自然科学基金“高性能科学计算的基础算法与可计算建模”重大研究计划(91130004), 子项目, 2012-01-01, 2015-12-31.
教学与课程
1. 科学计算，为数学学院除信息与计算科学专业外的本科生开设. 主要内容包括插值，数值逼近与拟合，线性方程组求解，非线性方程求根，数值积分，微分方程数值解等内容.
2. 微分方程数值解, 为1-2年级硕士，直博研究生开设。主要内容椭圆形方程，抛物型方程及双曲型方程的差分方法；有限元方法初步。
3. 离散数学，为数学科学学院本科生开设，主要针对信息与计算科学专业的学生。主要内容包括集合论，代数结构，图论，数理逻辑，组合数学初步等。
研究与成果
主要研究方向：
1. 有限元的理论与算法；
2. 微分方程数值解；
3. 反问题的建模与计算。
发表论文
发表的主要论文:
1. G. Lin, X.L. Cheng and Y. Zhang, A parametric level set based collage method for an inverse problem in elliptic partial differential equations, J. Comput. Appl. Math., 340(1)(2018), 101-121.
2. X.L. Cheng, G.L. Lin, Y. Zhang, R.F. Gong and M. Gulliksson, A modified coupled complex boundary method for an inverse chromatography problem, J. Ill-Posed Probl., 26(1)(2018), 33-49.
3. R.F. Gong, X.L. Cheng and W. Han, A coupled complex boundary method for an inverse conductivity problem with one measurement. Appl. Anal. 96 (2017), no. 5, 869–885.
4. Y.J. Yu and X.L. Cheng, Numerical identification of Robin coefficient by a Kohn-Vogelius type regularization method. Inverse Probl. Sci. Eng. 25 (2017), no. 7, 1014–1041.
5. X.L. Cheng, R.F. Gong and W. Han, A coupled complex boundary method for the Cauchy problem, Inverse Probl. Sci. Eng.，24(2016), 1520-1527.
6. C. Zheng, X.L. Cheng and K.W. Liang, Numerical Analysis of Inverse Elasticity Problem with Signorini’s Condition, Commun. Comput. Phys., 20(2016), 1045-1070.
7. X.L. Cheng, R.F. Gong and W. Han, A new Kohn-Vogelius Type Formulation for inverse source problems, Inverse Problems and Imaging，9(2015), 1051-1067.
8. X.L. Cheng and J. Yang, A computational method for transmission eigenvalues for spherically stratified medium, J. Opt. Soc. Am. A , 32(7), 1243-1246, (2015).
9. Krzysztof Bartosz, Xiaoliang Cheng, Piotr Kalita, Yuanjie Yu and Cong Zheng, Rothe method for parabolic variational–hemivariational inequalities, J. Math. Anal. Appl., 423 (2015) 841–862.
10. R.F. Gong and X.L. Cheng, An optimal finite element error estimate for an inverse problem in multispectral bioluminescence tomography, IMA J. Appl. Math., 80(1)( 2015), 115-134.
12. X.L. Cheng, S. Migorski, A. Ochal and M. Sofonea, Analysis of two quasistatic history-dependent contact models, Discrete Contin. Dyn. Syst. Ser. B, 19(2014), 2425-2445.
13. M. Barboteu, X.L. Cheng and M. Sofonea, Analysis of a contact problem with unilateral constraint and slip-dependent friction, Mathematics and Mechanics of Solids, 19(2014), 1-24. Doi: 10.1177/1081286514537289.
14. X.L. Cheng, R.F. Gong, W. Han and X. Zheng, A novel coupled complex boundary method for inverse source problems, Inverse Problems, 30(2014) 055002.
15. Y.G. Gu and X.L. Cheng, A Numerical approach for defect models localization in an inhomogeneous medium, SIAM J. Appl. Math., 73(2013), 2188-2202.
16. X.L. Cheng and J. Yang, Maximizing band gaps in two-dimensional photonic crystals in square lattices, J. Opt. Soc. Am. A , 30(2013), 2314-2319.
17. X.L. Cheng, R.F. Gong and W. Han, A new general mathematical framework for bioluminescence tomography, Comput. Methods Appl. Mech. Engrg., 197(2008), 524-535.
18. X.L. Cheng and J. Sun, Iterative methods for the forward-backward heat equation, J. Comput. Math., 23(2005), 419-424.
19. X.L. Cheng, A discontinuous quadratic finite element method for one-dimensional diffusion problem, Computers and Mathematics with applications, 40(2000), 921--925.
20. X.L. Cheng, On the nonlinear inexact Uzawa algorithm for saddle point problems, SIAM Journal on Numerical Analysis, 37(6)(2000), 1930--1934.
21. X.L. Cheng, H.C. Huang and J.Zou, Quadrilateral finite elements for planar linear elasticity problem with large Lame constant, Journal of Computational Mathematics, 16(4), 1998, 357-366.
22. X.L. Cheng, W. Han and H.C. Huang, Finite element methods for Timoshenko beam, circular arch and Reissner-Mindlin plate problems, Journal of Computational And Applied Mathematics, 79(1997), 215--234.
23. X.L. Cheng, W. Han and H.C. Huang, Analysis of some mixed elements for the Stokes problem, Journal of Computational And Applied Mathematics, 85(1997), 19--35.
24. J.S. Jiang and X.L. Cheng, On the stability of biquadratic-bilinear velocity-pressure finite elements, Journal of Computational Mathematics, 10(2), 1992, 167--170.
25. X.L. Cheng, An answer to the conjecture of I. Babuska and T. Janik，Journal of Computational Mathematics, 9(2), 1991, 105-110.
出版著作
韩渭敏，程晓良；变分不等式简介--基本理论、数值分析及应用，高等教育出版社，2007.
