I.The Basic Information of the Course
Course Number:202012420027
The EnglishName of theCourse：MathematicalPhysics Inverse Problem
The ChineseName of theCourse：数学物理反问题
In-classHours andAllocation(total class hours:32, classroom teaching:32classhours.)
Credit(s):2
Semester:2
AppliedDiscipline(ProfessionalDegreeCategory)：Mechanics, mathematics
CourseObjectOriented：Masteranddoctoral student
EvaluationMode:Closed-bookExamination
TeachingMethod:MixedTeaching
CourseOpening Department:Collegeof Mathematical Sciences
II.Prerequisite Course
Mathematical physical equations,Numerical calculations,Functional analysis,Optimization theory,Numerical solution of partial differential equations
III. The Objectives and Requirements of the Course
Through the study of this course, students can understand and master how to apply various methods of basic mathematics and computational mathematics to practical problems, research methods and derivation skills in application, as well as current hot issues and technical difficulties. To cultivate students' theoretical thinking ability and practical ability, to develop students' research ideas, and to lay a solid foundation for further applying mathematical knowledge to practical problems and engaging in mathematical applied research.
IV. The Content of the Course
1.Introduction: some examples of the inverse problem, the mathematical structure of the inverse problem, its classification and the concept ofill-posedness.
2. Preparatory Theory:Normed Spaces, bounded operators and compact operators, Riesz theory and Fredholm theory, linear integral operators, spectral theory of compact operators
3.The regularization method of the solution of the linear problem:General regularization theory, method of allowable regularization parameters, method of model function, Tikhonov regularization method, fitting solution and compatibility principle, Landweber iterative regularization method
4. Discretization regularization method:Projection method, Galerkin method, configuration method.
5.Newton type numerical solution of nonlinear inverse problem.The model and basic concept of the problem, Tikhonov regularization method, regular-Gauss-Newton method, Levenberg-Marquardt method, trust region method.
6. Gradient numerical solution of nonlinear inverse problems:Landweb-fridman iteration method, fastest descent method, Newton-CG method, truncated conjugate gradient method, gradient operator method.
V. Reference Books, Reference Literatures, and Reference Materials
1. Liu Jijun et al. Regularization method and application of the ill-posed problem. Science Press, 2003.
2.Xiao Tingyan, YU Shengen, Wang Yanfei. Numerical solution of inverse problem. Science Press, 2002.
3. Wang Yanfei. Calculation method and application of inversion problem. Higher Education Press, 2007.
4.Victor Isakov. Inverse problems for Partial differential equations.Springer, 1998.
5. Andreas Kirsch. An Introduction to the Mathematical Theory of Inverse Problems. Springer, 1996.
Outline Writer (Signature):冯国峰
Leader in charge of teaching at the College (Signature)：
Date：
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