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

An efficient solver is described for the solution of the electromagnetic fi elds in both time and frequency domains. The proposed method employs the no de-based and the edge-based finite-element method (FEM) to discretize Maxwe ll's equations. The resultant matrix equation is solved by the spectral Lan czos decomposition method (SLDM), which is based on the Krylov subspace (La nczos) approximation of the solution. First, a new explicit axisymmetric so lver for the diffusion of electromagnetic fields in an inhomogeneous medium is introduced. The procedure is then extended to treat the three-dimension al problems in the low frequency regime. Finally, Maxwell's equations, in t heir general form, are solved in frequency and time domains. Depending on t he application, our method requires the implementation of the Lanczos proce ss only at the largest or smallest time or frequency of interest. Consequen tly, a multiple time and frequency domain analysis of the electromagnetic f ields is achieved in a negligible amount of extra computing time. The effic iency and effectiveness of this new technique are illustrated by using vari ous practical numerical examples. (C) 1999 Elsevier Science S.A. All rights reserved.