We study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle $ \Omega \subset \mathbb{R}^3 $. From the Stratton-Chu integral representation, we derive a new representation formula when constant reference coefficients are given for the interior domain. The resulting integral representation contains the usual layer potentials, but also volume potentials on $\Omega$. Then it is possible to follow a single-trace approach to obtain boundary integral equations perturbed by traces of compact volume integral operators with weakly singular kernels. The coupled boundary and volume integral equations are discretized with a Galerkin approach with usual Curl-conforming and Div-conforming finite elements on the boundary and in the volume. Compression techniques and special quadrature rules for singular integrands are required for an efficient and accurate method. Numerical experiments provide evidence that our new formulation enjoys promising properties.

翻译：我们研究有界、可穿透且非均匀障碍物 Ω ⊂ ℝ³ 的频率域电磁散射问题。基于 Stratton-Chu 积分表示，当内部区域给定恒定参考系数时，我们推导出一种新的表示公式。该积分表示不仅包含通常的层势，还包含 Ω 上的体积势。进而，可采用单迹线方法推导出边界积分方程，该方程受到具有弱奇异核的紧致体积积分算子迹线的扰动。通过伽辽金方法，在边界和体积上分别使用满足旋度与散度相容性的有限元对耦合的边界与体积积分方程进行离散化。为实现高效精确的求解，需采用压缩技术及针对奇异积分的特殊求积法则。数值实验表明，新公式具有良好的特性。