Spectral approach to solving three‐dimensional Maxwell's diffusion equations in the time and frequency domains

Abstract

We describe a new explicit three‐dimensional solver for the diffusion of electromagnetic fields in arbitrarily heterogeneous conductive media. The proposed method is based on a global Krylov subspace (Lanczos) approximation of the solution in the time and frequency domains. We derive solutions stable to spurious curl‐free modes and provide estimates of the computer complexity involved in the calculations. Such estimates together with numerical experiments attest to a computationally efficient method suitable for large‐scale problems. Also included are modeling examples drawn from practical geophysical applications.