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：本文研究有界、可穿透且非均匀障碍物$ \Omega \subset \mathbb{R}^3 $的频域电磁散射问题。基于Stratton-Chu积分表示，在给定内部区域常系数参考值的情况下，我们推导出新的表示公式。所得积分表示不仅包含常规层势，还包含$\Omega$上的体积势。随后采用单迹方法，得到由弱奇异核紧体积积分算子迹扰动的边界积分方程。通过Galerkin方法对耦合边界-体积积分方程进行离散化，在边界和体积区域分别采用常规的Curl相容与Div相容有限元。为实现高效精确的计算，需采用压缩技术及针对奇异被积函数的特殊求积规则。数值实验表明，新构建的方程体系具有优越的数值特性。