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A spectrally accurate method for the dielectric obstacle scattering problem and applications to the inverse problem
- Publication Year :
- 2020
- Publisher :
- arXiv, 2020.
-
Abstract
- 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 Fr��chet 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.<br />22 pages
- Subjects :
- FOS: Mathematics
65R20, 35R30
Numerical Analysis (math.NA)
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi...........e9a89cdcf3c6cf83954dc22742df5816
- Full Text :
- https://doi.org/10.48550/arxiv.2006.10830