Mixed Finite Element Simulation for Solving Eigenmodes of Cavity Resonators Filled With Both Electric and Magnetic Lossy, Anisotropic Media

This article presents a mixed finite element method to find the resonant frequencies of 3-D closed cavity resonators filled with both electric and magnetic lossy, anisotropic media. By introducing a dummy variable with zero value in the 3-D linear vector Maxwell's eigenvalue problem for the electric field, the divergence-free condition for electric flux density is enforced in a weak sense. In addition, by introducing a dummy variable with an arbitrary constant in the 3-D linear vector Maxwell's eigenvalue problem for the magnetic field, the divergence-free condition for magnetic flux density is enforced in a weak sense. At the same time, we prove that the eigenmodes of the second-order linear Maxwell's eigenvalue problems with introduced the dummy variables are equivalent to the ones of the original second-order Maxwell's eigenvalue problems. As a consequence, the novel method of introducing dummy variables can be free of all the spurious modes in solving eigenmodes of 3-D closed cavity problems. Finally, two numerical experiments are carried out to show that the numerical eigensolver supported by this article can eliminate all the spurious modes, including spurious zero modes.