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Analysis of Some Qualitative Methods for Inverse Electromagnetic Scattering Problems

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Computational Electromagnetism

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2148))

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Abstract

This chapter provides an a comprehensive presentation of some qualitative methods associated with inverse 3D electromagnetic scattering problem from inhomogeneous and anisotropic media. We first discuss the problem in the framework of so-called Born approximation, that leads to a linearisation of the inverse problem. We second present and analyze the application of the Linear Sampling Method to the full non linear problem using multistatic data at a given frequency. We especially focus on a generalization of this method based on an exact characterization of the inclusion shape in terms of the available data. We then discuss the closely related interior transmission problem and associated transmission eigenvalues. We complements each chapter with some open challenging questions as well as references for further readings.

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Authors and Affiliations

  1. INRIA, Saclay - Ile de France and CMAP, Ecole Polytechnique, Route de Saclay, 91128, Palaiseau Cedex, France

    Houssem Haddar

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  1. Houssem Haddar
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Correspondence to Houssem Haddar .

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Editors and Affiliations

  1. Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, Santiago de Compostela, Spain

    Alfredo Bermúdez de Castro

  2. Dipartimento di Matematica, Università di Trento, Povo (Trento), Italy

    Alberto Valli

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Haddar, H. (2015). Analysis of Some Qualitative Methods for Inverse Electromagnetic Scattering Problems. In: Bermúdez de Castro, A., Valli, A. (eds) Computational Electromagnetism. Lecture Notes in Mathematics(), vol 2148. Springer, Cham. https://doi.org/10.1007/978-3-319-19306-9_4

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