Coupled Boundary and Volume Integral Equations for Electromagnetic Scattering
arxiv(2024)
摘要
We study frequency domain electromagnetic scattering at a bounded,
penetrable, and inhomogeneous obstacle Ω⊂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 Ω. 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.
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