Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616730 | Journal of Mathematical Analysis and Applications | 2013 | 19 Pages |
Abstract
In this paper we present a technique for shape reconstruction based on the topological and shape gradients. The shape in consideration is a solution of an inverse conductivity problem. To solve such a problem numerically, we compute the topological gradient of a Kohn–Vogelius-type cost function when the domain under consideration is perturbed by the introduction of a small inclusion instead of a hole. The reconstruction is done by considering the shape as a superposition of very thin elliptic inclusions to get a first approximation. Then, we use a gradient-type algorithm to perform a good reconstruction. Various numerical experiments of single and multiple inclusions demonstrate the viability of the designed algorithm.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
S. Chaabane, M. Masmoudi, H. Meftahi,