Finite Element Method for Resonant Cavity Problem with Complex Geometrical Structure and Anisotropic Fully Conducting Media

In this paper, the resonant cavity problem with anisotropic fully conducting media, complex geometrical structure and perfect electric conductor walls is investigated. We solve this problem based on the finite element method (FEM) with tangential and linear normal (CT/LN) element and standard linear element. An effective numerical method is proposed by us such that it is free of nonphysical modes. After the FEM discretization, we need to solve a quadratic algebraic eigenvalue problem with a linear constraint condition. In order to overcome this difficulty in the field of numerical algebra, we change this algebraic eigenvalue problem into a generalized eigenvalue problem by introducing an auxiliary zero eigenvector. Moreover, when the permittivity and conductivity are two constants, both the eigenmodes of infinite algebraic multiplicity and all the nonphysical modes are also removed by linearization method. Several numerical experiments show that computational method in this paper can suppress all the spurious modes.