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: resonant instability and dense discretization breakdown. The remedy to resonant instability is a combined field integral equation, and dense discretization breakdown is eliminated by means of operator preconditioning. The exterior traces of single and double layer potentials are complemented by their interior counterparts of a pure 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Lipschitz连续边界完美电导体对时谐电磁波散射积分方程的两个问题：共振不稳定性和密集离散化崩溃。针对共振不稳定性的解决方案是组合场积分方程，而密集离散化崩溃则通过算子预处理消除。通过引入纯虚数波数的内部对应量，对单层和双层势的外迹进行了补充。我们在电磁场的自然迹空间中推导了相应的变分公式，并建立了其对所有波数的适定性。采用基于对偶网格的协调边元进行Galerkin离散化方案，从而生成变分公式的良态离散线性系统。文中还提供了部分数值结果以支持数值分析。