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Coupled Boundary and Volume Integral Equations for Electromagnetic Scattering

by I. Labarca-Figueroa and R. Hiptmair

(Report number 2024-13)

Abstract
We study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle $\Omega \subset \mathbb{R}^3$ . From the Stratton-Chu integral representation, we derive a new representation formula when constant reference coefficients are given for the interior domain. The resulting integral representation contains the usual layer potentials, but also volume potentials on $\Omega$. Then it is possible to follow a single-trace approach to obtain boundary integral equations perturbed by traces of compact volume integral operators with weakly singular kernels. The coupled boundary and volume integral equations are discretized with a Galerkin approach with usual Curl-conforming and Div-conforming finite elements on the boundary and in the volume. Compression techniques and special quadrature rules for singular integrands are required for an efficient and accurate method. Numerical experiments provide evidence that our new formulation enjoys promising properties.

Keywords: boundary integral equations, volume integral equations, transmission problems, electromagnetic scattering

@Techreport{LH24_1095,
  author = {I. Labarca-Figueroa and R. Hiptmair},
  title = {Coupled Boundary and Volume Integral Equations for Electromagnetic Scattering},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2024-13},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2024/2024-13.pdf },
  year = {2024}
}

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