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 electromagnetic fields in an inhomogeneous medium is described. The proposed method employs either the node-based or 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 in the frequency domain. By analyzing some practical geophysical problems, it is shown that the SLDM is extremely fast and, furthermore, the electromagnetic fields at many frequencies can be evaluated by performing the SLDM iteration only at the lowest frequency.