Mixed Finite-Element Method for Resonant Cavity Problem With Complex Geometric Topology and Anisotropic Lossless Media

摘要

Electromagnetic eigenvalue problems are contaminated by nonphysical zero modes in the conventional finite-element method (FEM) with edge elements. Here, we investigate the cavities with anisotropic lossless media, complex geometry structure, and perfect electric conductor (PEC) walls and eliminate all nonphysical zero and nonzero modes successfully. We introduce a Lagrangian multiplier to deal with the constraint of divergence-free condition. Our method is based on the mixed FEM employing the first-order edge basis functions to expand electric field and linear element basis functions to expand Lagrangian multiplier. The validity of our method is confirmed by several numerical experiments. Meanwhile, the numerical experiments show that when the cavity has a connected boundary, there is no physical zero mode; when the cavity has several disconnected boundaries, then the number of physical zero modes is equal to one less than the number of disconnected PEC boundaries.