Topological and shape gradient strategy for solving geometrical inverse problems
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...
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| Veröffentlicht in: | Journal of mathematical analysis and applications 2013-04, Vol.400 (2), p.724-742 |
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| container_title | Journal of mathematical analysis and applications |
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| creator | Chaabane, S. Masmoudi, M. Meftahi, H. |
| description | 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. |
| doi_str_mv | 10.1016/j.jmaa.2012.11.044 |
| format | Article |
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| issn | 0022-247X 1096-0813 |
| language | eng |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Inverse problem Shape gradient Topological asymptotic expansion Topological gradient |
| title | Topological and shape gradient strategy for solving geometrical inverse problems |
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