A spectrally accurate method for the dielectric obstacle scattering problem and applications to the inverse problem

06/18/2020 ∙ by Thorsten Hohage, et al. ∙ 0

We analyze the inverse problem to reconstruct the shape of a three dimensional homogeneous dielectric obstacle from the knowledge of noisy far field data. The forward problem is solved by a system of second kind boundary integral equations. For the numerical solution of these coupled integral equations we propose a fast spectral algorithm by transporting these equations onto the unit sphere. We review the differentiability properties of the boundary to far field operator and give a characterization of the adjoint operator of the first Fréchet derivative. Using these results we discuss the implementation of the iteratively regularized Gauss-Newton method for the numerical solution of the inverse problem and give numerical results for star-shaped obstacles.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.