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$\Omega \subset \mathbb{R}^3$的频域电磁散射问题。基于Stratton-Chu积分表示，当给定内部区域的恒定参考系数时，我们推导出一种新的表示公式。所得积分表示不仅包含通常的层势，还包含$\Omega$上的体积势。随后可采用单迹线方法，通过弱奇异核的紧致体积积分算子迹线扰动，得到边界积分方程。通过Galerkin方法对耦合边界与体积积分方程进行离散化，在边界和体积上分别使用标准旋度相容与散度相容有限元。为实现高效精确的计算，需采用压缩技术和针对奇异被积函数的特殊求积法则。数值实验表明，我们提出的新公式具有良好的性质。