Frequency-domain and time-domain finite-element solution of Maxwell's equations using spectral Lanczos decomposition method

Abstract

An efficient solver is described for the solution of the electromagnetic fields in both time and frequency domains. The proposed method employs the node-based and the edge-based finite-element method (FEM) to discretize Maxwell's equations. The resultant matrix equation is solved by the spectral Lanczos decomposition method (SLDM), which is based on the Krylov subspace (Lanczos) approximation of the solution. First, a new explicit axisymmetric solver for the diffusion of electromagnetic fields in an inhomogeneous medium is introduced. The procedure is then extended to treat the three-dimensional problems in the low frequency regime. Finally, Maxwell's equations, in their general form, are solved in frequency and time domains. Depending on the application, our method requires the implementation of the Lanczos process only at the largest or smallest time or frequency of interest. Consequently, a multiple time and frequency domain analysis of the electromagnetic fields is achieved in a negligible amount of extra computing time. The efficiency and effectiveness of this new technique are illustrated by using various practical numerical examples.