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arXiv · 2309.02289

An operator preconditioned combined field integral equation for electromagnetic scattering

Van Chien Le·Kristof Cools
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Abstract

This paper aims to address two issues of integral equations for the scattering of time-harmonic electromagnetic waves by a perfect electric conductor with Lipschitz continuous boundary: ill-conditioned {boundary element Galerkin matrices} on fine meshes and instability at spurious resonant frequencies. The remedy to ill-conditioned matrices is operator preconditioning, and resonant instability is eliminated by means of a combined field integral equation. Exterior traces of single and double layer potentials are complemented by their interior counterparts for a purely imaginary wave number. We derive the corresponding variational formulation in the natural trace space for electromagnetic fields and establish its well-posedness for all wave numbers. A Galerkin discretization scheme is employed using conforming edge boundary elements on dual meshes, which produces well-conditioned discrete linear systems of the variational formulation. Some numerical results are also provided to support the numerical analysis.

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Van Chien Le, Kristof Cools. 2023-09-05. An operator preconditioned combined field integral equation for electromagnetic scattering. https://doi.org/10.1137/23m1581674

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