School of Mathematics
China University of Mining and Technology
Xuzhou, Jiangsu 221116, China
email: liujichuan2003@126.com
Ji-Chuan Liu
Abstract:
In this article, we study an inverse source problem of the
Poisson equation with Cauchy data. We want to find iterative algorithms
to detect the hidden source within a body from measurements on the boundary.
Our goal is to reconstruct the location, the size and the shape of the hidden
source. This problem is ill-posed, regularization techniques should be employed
to obtain the regularized solution. Numerical examples show that our proposed
algorithms are valid and effective.
Submitted October 26, 2016. Published May 4, 2017.
Math Subject Classifications: 65N20, 65N21.
Key Words: Inverse source problem; gradient descent method;
trust-region-reflective algorithm; Poisson equation;
ill-posed problem.
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Ji-Chuan Liu School of Mathematics China University of Mining and Technology Xuzhou, Jiangsu 221116, China email: liujichuan2003@126.com |
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