程晓良 - 浙江大学 - 数学科学学院

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。教学工作本学年教学工作： 1.科学计算，2017-18春夏学期,本科生 2.微分方程数值解,2017-18春夏学期,研究生; 3.科学计算，2017-18秋冬学期,求是班及其它，本科生; 4.离散数学，2017-2018秋冬学期，本科生. 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。 4.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。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.

研究领域

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。

近期论文

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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.