Material derivatives of boundary integral operators in electromagnetism and application to inverse scattering problems. (5th July 2016)

• Record Type: Journal Article
• Authors: Yaman, Olha Ivanyshyn; Louër, Frédérique Le
• Is Part Of: Inverse problems. Volume 32:Number 9(2016:Sep.)
• Publication Date: 2016-07-05
• Subjects: electromagnetism -- boundary integral equations -- material derivatives -- inverse obstacle scattering problem; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/9/095003
• Languages: English
• ISSNs: 0266-5611

Abstract

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.