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Second-Kind Boundary Integral Equations for Electromagnetic Scattering at Composite Objects

by X. Claeys and R. Hiptmair and E. Spindler

(Report number 2016-43)

Abstract
We consider electromagnetic scattering of time-harmonic fields in \(\mathbb{R}^3\) at objects composed of several linear, homogeneous, and isotropic materials. Adapting earlier work on acoustic scattering \([\)X. Claeys, R. Hiptmair, and E. Spindler, A second-kind Galerkin boundary element method for scattering at composite objects, BIT 55(1):33-57, 2015\(]\) we develop a novel second-kind direct boundary integral formulation for this scattering problem, extending the so-called Müller formulation for a homogeneous scatterer to composite objects. The new formulation is amenable to Galerkin boundary element discretization by means of discontinuous tangential surface vectorfields. Numerical tests demonstrate competitive accuracy of the new approach compared with a widely used direct Galerkin boundary element method based on a first-kind boundary integral formulation. For piecewise constant approximation our experiments also confirm fast convergence of GMRES iterations independently of mesh resolution.

Keywords: Electromagnetic scattering, second-kind boundary integral equations, Galerkin boundary element methods

@Techreport{CHS16_680,
  author = {X. Claeys and R. Hiptmair and E. Spindler},
  title = {Second-Kind Boundary Integral Equations for Electromagnetic Scattering at Composite Objects},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2016-43},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2016/2016-43.pdf },
  year = {2016}
}

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