Semester
Spring
Date of Graduation
2009
Document Type
Dissertation
Degree Type
PhD
College
Eberly College of Arts and Sciences
Department
Mathematics
Committee Chair
Mary Ann Clarke
Abstract
In this dissertation, we study boundary inverse problems for some elliptic partial differential equations. These are problems arising from quantitative analysis of various non-destructive testing techniques in applications. In such a problem, we are interested in using boundary measurements of the solution to recover either an unknown coefficient function in the boundary condition, or a portion of the boundary, or an unknown interior interface. We first introduce formulations of the boundary value problems into integral equations, then design numerical algorithms for solving each of these inverse problems. Numerical implementation and examples are presented to illustrate the feasibility and effectiveness of the numerical methods.;Keywords. Robin inverse problem, inverse linear source problem, boundary integral equation, Tikhonov regularization, Nystrom method.
Recommended Citation
Zeng, Suxing, "Numerical solutions of boundary inverse problems for some elliptic partial differential equations" (2009). Graduate Theses, Dissertations, and Problem Reports. 4555.
https://researchrepository.wvu.edu/etd/4555