SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2484-2505, December 2024.
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 discretization 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.

中文翻译：

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用于电磁散射的算子预设组合场积分方程


SIAM 数值分析杂志，第 62 卷，第 6 期，第 2484-2505 页，2024 年 12 月。

抽象。本文旨在解决具有 Lipschitz 连续边界的完美电导体散射时谐电磁波的积分方程的两个问题：细网格上的病态边界元 Galerkin 离散矩阵和杂散谐振频率下的不稳定性。对病态矩阵的补救措施是算子预处理，并通过组合场积分方程消除共振不稳定性。单层和双层电势的外部迹线与它们的内部对应物相辅相成，得到一个纯虚数的波数。我们在电磁场的自然轨迹空间中推导出相应的变分公式，并建立其对所有波数的适定性。采用 Galerkin 离散化方案，在双网格上使用符合标准的边缘边界元，从而产生变分公式的条件良好的离散线性系统。还提供了一些数值结果来支持数值分析。