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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 816134, 20 pages
http://dx.doi.org/10.1155/2013/816134
Research Article

Hybrid Topological Derivative-Gradient Based Methods for Nondestructive Testing

1Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain
2Departamento de Fundamentos Matematicos, Universidad Politécnica de Madrid, 28040 Madrid, Spain

Received 26 December 2012; Accepted 9 June 2013

Academic Editor: Ağacik Zafer

Copyright © 2013 A. Carpio and M.-L. Rapún. 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

This paper is devoted to the reconstruction of objects buried in a medium and their material properties by hybrid topological derivative-gradient based methods. After illustrating the techniques in time-harmonic acoustic problems with different boundary conditions and in electrical impedance tomography problems with continuous Neumann conditions, we extend the hybrid method for a realistic model in tomography where the boundary conditions are given at a discrete set of electrodes.