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Mathematical Problems in Engineering
Volume 2013, Article ID 125909, 7 pages
http://dx.doi.org/10.1155/2013/125909
Research Article

Shape Reconstruction of Thin Electromagnetic Inclusions via Boundary Measurements: Level-Set Method Combined with the Topological Derivative

Department of Mathematics, Kookmin University, Seoul 136-702, Republic of Korea

Received 15 July 2013; Revised 31 October 2013; Accepted 31 October 2013

Academic Editor: Sotiris Ntouyas

Copyright © 2013 Won-Kwang Park. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An inverse problem for reconstructing arbitrary-shaped thin penetrable electromagnetic inclusions concealed in a homogeneous material is considered in this paper. For this purpose, the level-set evolution method is adopted. The topological derivative concept is incorporated in order to evaluate the evolution speed of the level-set functions. The results of the corresponding numerical simulations with and without noise are presented in this paper.