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.

翻译：本文旨在解决具有Lipschitz连续边界的理想电导体在时谐电磁波散射问题中的两个积分方程难题：精细网格上边界元伽辽金矩阵的病态性以及伪谐振频率处的不稳定性。针对矩阵病态问题采用算子预条件技术，而谐振不稳定性则通过组合场积分方程予以消除。通过引入纯虚波数下的内部对应项，对外部单层与双层势的迹进行补充。我们在电磁场的自然迹空间中推导了相应的变分形式，并证明了其对所有波数的适定性。采用对偶网格上的协调边缘边界元实施伽辽金离散化方案，该方案为变分形式生成了良态离散线性系统。同时提供若干数值结果以支持数值分析。