A spectral Lanczos decomposition method for solving 3-D low-frequency electromagnetic diffusion by the finite-element method

A very efficient three-dimensional (3-D) solver for the diffusion of the el ectromagnetic fields in an inhomogeneous medium is described, The proposed method employs either the node-based or the edge-based finite-element metho d (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 in frequenc y domain. By analyzing some practical geophysical problems, it is shown tha t the SLDM is extremely fast and, furthermore, the electromagnetic fields a t many frequencies can be evaluated by performing the SLDM iteration only a t the lowest frequency.