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Title: Material derivatives of boundary integral operators in electromagnetism and application to inverse scattering problems
Authors: Ivanyshyn Yaman, Olha
Louër, Frederique Le
Keywords: Boundary integral equations
Material derivatives
Obstacle scattering
Inverse problems
Issue Date: 5-Jul-2016
Publisher: IOP Publishing Ltd.
Source: Ivanyshyn Yaman, O., and Louër, F. L. (2016). Material derivatives of boundary integral operators in electromagnetism and application to inverse scattering problems. Inverse Problems, 32(9). doi:10.1088/0266-5611/32/9/095003
Abstract: This paper deals with the material derivative analysis of the boundary integral operators arising from the scattering theory of time-harmonic electromagnetic waves and its application to inverse problems. We present new results using the Piola transform of the boundary parametrisation to transport the integral operators on a fixed reference boundary. The transported integral operators are infinitely differentiable with respect to the parametrisations and simplified expressions of the material derivatives are obtained. Using these results, we extend a nonlinear integral equations approach developed for solving acoustic inverse obstacle scattering problems to electromagnetism. The inverse problem is formulated as a pair of nonlinear and ill-posed integral equations for the unknown boundary representing the boundary condition and the measurements, for which the iteratively regularized Gauss-Newton method can be applied. The algorithm has the interesting feature that it avoids the numerous numerical solution of boundary value problems at each iteration step. Numerical experiments are presented in the special case of star-shaped obstacles.
ISSN: 0266-5611
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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