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Topological Derivative for the Inverse Conductivity Problem: A Bayesian Approach

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Abstract

The employment of topological derivative concept is considered to propose a new optimization algorithm for the inverse conductivity problem. Since this inverse problem is nonlinear and ill-posed it is necessary to incorporate a prior knowledge about the unknown conductivity. In particular, we apply the Bayes theorem to add the assumption that we have just one small ball-shaped inclusion, which must be at a certain distance from the boundary of the domain. As the main emphasis of this paper is to investigate numerically the proposed approach, we shall use the meshless method of fundamental solutions to present some numerical results.

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Acknowledgments

The first author would like to thank CNPq-Science without Borders program for the financial support in this research. The hospitality shown by the University of Leeds is also gratefully acknowledged. The comments made by the referee are gratefully acknowledged.

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Authors and Affiliations

  1. Departamento de Computação Científica, Universidade Federal da Paraíba, João Pessoa, Brazil

    J. Rocha de Faria

  2. Department of Applied Mathematics, University of Leeds, Leeds , LS2 9JT, UK

    D. Lesnic

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  1. J. Rocha de Faria
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  2. D. Lesnic
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Correspondence to J. Rocha de Faria.

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de Faria, J.R., Lesnic, D. Topological Derivative for the Inverse Conductivity Problem: A Bayesian Approach. J Sci Comput 63, 256–278 (2015). https://doi.org/10.1007/s10915-014-9891-4

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  • DOI: https://doi.org/10.1007/s10915-014-9891-4

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