We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission conditions to reduce the number of unknown densities and to formulate a system of coupled boundary integral equations describing the scattered and transmitted waves. The system is transformed into the Laplace domain where it is proven to be stable and uniquely solvable. The Laplace domain stability estimates are then used to establish the stability and unique solvability of the original time domain problem. Finally, we show how the bounds obtained in both Laplace and time domains can be used to derive error estimates for semi discrete Galerkin discretizations in space and for fully discrete numerical schemes that use Convolution Quadrature for time discretization and a conforming Galerkin method for discretization of the space variables.

翻译：本文针对均匀介质障碍物的电磁散射与透射动态问题，提出了一种边界积分方程表述。遵循 Costabel 和 Stephan 的思想，我们利用透射条件减少未知密度函数的数量，并构建了一个描述散射波与透射波的耦合边界积分方程组。该方程组被转换至 Laplace 域，并在该域中证明了其稳定性和唯一可解性。随后，利用 Laplace 域的稳定性估计，确立了原始时域问题的稳定性与唯一可解性。最后，我们展示了如何利用在 Laplace 域和时域中获得的界，推导出空间上半离散 Galerkin 离散化以及全离散数值格式的误差估计，其中全离散格式采用卷积求积法进行时间离散，并采用协调 Galerkin 方法对空间变量进行离散。