基于势的边界元法的有耗材料电磁建模
Electromagnetic Modeling of Lossy Materials with a Potential-Based Boundary Element Method
摘要：
边界元方法（BEM）能够使用二维表面网格来求解三维电磁问题，使得其在从电互连分析到元表面设计的应用范围内具有吸引力。边界元法通常将电场和磁场作为未知量。基于电磁势而不是场的公式最近引起了人们的兴趣，主要有两个原因：（a）它们在低频下本质上是稳定的，不像许多基于场的方法，（b）势为量子物理现象提供了更直接的接口。现有的基于势的电磁散射公式主要是针对理想导体提出的。我们开发了一种基于势的BEM公式，可以捕获介电和导电损耗，并准确地模拟宽频率范围内的趋肤效应。通过规范和现实的数值算例验证了所提出的公式的准确性。
英文摘要：
The boundary element method (BEM) enables solving three-dimensional electromagnetic problems using a two-dimensional surface mesh, making it appealing for applications ranging from electrical interconnect analysis to the design of metasurfaces. The BEM typically involves the electric and magnetic fields as unknown quantities. Formulations based on electromagnetic potentials rather than fields have garnered interest recently, for two main reasons: (a) they are inherently stable at low frequencies, unlike many field-based approaches, and (b) potentials provide a more direct interface to quantum physical phenomena. Existing potential-based formulations for electromagnetic scattering have been proposed primarily for perfect conductors. We develop a potential-based BEM formulation which can capture both dielectric and conductive losses, and accurately models the skin effect over broad ranges of frequency. The accuracy of the proposed formulation is validated through canonical and realistic numerical examples.
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