Mixed Finite-Element Method for 3-D Closed Cavity Problem With Anisotropic and Lossy Media

This paper mainly investigates the 3-D resonant cavity problem with anisotropic and lossy media. When the media are electric lossy and not magnetic lossy, we solve the 3-D cavity model with magnetic field as a working variable by mixed finite-element method (MFEM). A Lagrange multiplier is used to enforce divergence-free condition in a weak sense. In the MFEM, we employ edge basis function of the lowest order to expand the electric field or the magnetic field, and linear element basis function to expand the Lagrange multiplier. Numerical experiments show that the MFEM can eliminate all the spurious modes to solve this type of 3-D closed cavity problem.