This paper introduces a time-domain combined field integral equation for electromagnetic scattering by a perfect electric conductor. The new equation is obtained by leveraging the quasi-Helmholtz projectors, which separate both the unknown and the source fields into solenoidal and irrotational components. These two components are then appropriately rescaled to cure the solution from a loss of accuracy occurring when the time step is large. Yukawa-type integral operators of a purely imaginary wave number are also used as a Calderon preconditioner to eliminate the ill-conditioning of matrix systems. The stabilized time-domain electric and magnetic field integral equations are linearly combined in a Calderon-like fashion, then temporally discretized using an appropriate pair of trial functions, resulting in a marching-on-in-time linear system. The novel formulation is immune to spurious resonances, dense discretization breakdown, large-time step breakdown and dc instabilities stemming from non-trivial kernels. Numerical results for both simply-connected and multiply-connected scatterers corroborate the theoretical analysis.

翻译：本文针对理想电导体电磁散射问题提出了一种时域组合场积分方程。该新方程通过利用准亥姆霍兹投影算子构建，该算子将未知场与源场同时分解为螺线分量与无旋分量。随后对这两个分量进行适当的重新标度，以修正时间步长较大时出现的精度损失问题。采用纯虚波数的汤川型积分算子作为Calderon预条件子，以消除矩阵系统的病态性。稳定化的时域电场与磁场积分方程以类Calderon形式进行线性组合，随后采用适当的试验函数对进行时间离散，最终形成推进求解的时域线性系统。该新颖公式能够避免伪谐振、密集离散化失效、大时间步长失效以及非平凡核引起的直流不稳定性等问题。针对单连通与多连通散射体的数值结果验证了理论分析的有效性。