Spectral Lanczos decomposition method for efficient time-domain and frequency-domain finite-element solution of Maxwell's equations

Abstract

An efficient three-dimensional solver that combines the spectral Lanczos decomposition method (SLDM) and the finite-element method (FEM) is described for the solution of Maxwell's equations in both time and frequency domains. The FEM based on Whitney forms is used to discretize Maxwell's equations and the resultant matrix equation is solved using the SLDM. Our technique is an implicit, unconditionally stable finite-element time- and frequency-domain scheme that requires the implementation of the Lanczos process only at the largest frequency or time of interest. Therefore, a multiple time- and frequency-domain analysis of the electromagnetic fields is performed with minimal amount of extra computing time. We illustrate the efficiency, validity, and accuracy of this new method by considering numerical examples of an air-filled and a partially-loaded lossy dielectric cavity.