Numerical Eigensolver for Solving Eigenmodes of Cavity Resonators Filled With both Electric and Magnetic Lossy, Anisotropic Media

TL;DR

This paper introduces a novel numerical eigensolver for 3-D cavity resonators with lossy, anisotropic media, effectively eliminating spurious modes and ensuring accurate computation of eigenmodes.

Contribution

It proposes a new method using dummy variables to enforce divergence-free conditions, removing all spurious modes in eigenmode calculations of complex cavity resonators.

Findings

Successfully eliminates all spurious modes in numerical simulations

Proves the theoretical validity of the dummy variable approach

Demonstrates accurate eigenmode computation in lossy, anisotropic media

Abstract

This article presents the numerical eigensolver 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 eigenvalue problem for the electric field, we enforce the divergence-free condition for electric flux density in a weak sense. In addition, by introducing a dummy variable with constant value in the 3-D linear vector Maxwell eigenvalue problem for the magnetic field, we enforce the divergence-free condition for magnetic flux density in a weak sense. Moreover, it is theoretically proved that the novel method of introducing dummy variables can be free of all the spurious modes in solving eigenmodes of the 3-D closed cavity problem. Numerical experiments show that the numerical eigensolver supported by this article can eliminate all the spurious modes, including spurious dc modes.