A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM formulations either lead to a poorly conditioned system matrix for multiscale problems, or are computationally expensive for objects embedded in layered substrates. This article presents a new BEM formulation which leverages the surface equivalence principle and Buffa-Christiansen basis functions defined on a dual mesh, to obtain a well-conditioned system matrix suitable for multiscale EM modeling. Unlike existing methods involving dual meshes, the proposed formulation avoids the double-layer potential operator for the surrounding medium, which may be a stratified substrate requiring the use of an advanced Green's function. This feature greatly alleviates the computational expense associated with the use of Buffa-Christiansen functions. Numerical examples drawn from several applications, including remote sensing, chip-level EM analysis, and metasurface modeling, demonstrate speed-ups ranging from 3x to 7x compared to state-of-the-art formulations.

翻译：马克斯韦尔方程式表面整体表示法允许通过边界要素法(BEM)对三维结构进行高效的电磁(EM)建模,采用二维分解法(BEM)。然而,现有的BEM配方要么导致多尺度问题系统矩阵条件差,要么对嵌入层层基体的物体计算成本高昂。本条款提出了一个新的BEM配方,利用在双网状下界定的表面等同原则和Buffa-基督教基础功能,以获得适合于多尺度EM建模的完善的系统矩阵。与涉及双层模组的现有方法不同,拟议的配方避免了周围介质的双层潜在操作器,后者可能是需要使用先进的Green函数的分层分层操作器。这极大地降低了与使用Buffa-基督教函数相关的计算费用。从若干应用中提取的数值示例,包括遥感、芯片级EM分析以及元表建模,显示了从3x到7x之间的速度,与状态制式配方相比,从3x到7x不等。