Three-dimensional transient electromagnetic modelling using Rational Krylov methods

Abstract

A computational method is given for solving the forward modelling problem for transient electromagnetic exploration. Its key features are the discretization of the quasi-static Maxwell's equations in space using the first-kind family of curl-conforming Nédélec elements combined with time integration using rational Krylov methods. We show how rational Krylov methods can also be used to solve the same problem in the frequency domain followed by a synthesis of the transient solution using the fast Hankel transform, and we argue that the pure time-domain solution is more efficient. We also propose a new surrogate optimization approach for selecting the pole parameters of the rational Krylov method which leads to convergence within an a priori determined number of iterations independent of mesh size and conductivity structure. These poles are repeated in a cyclic fashion, which, in combination with direct solvers for the discrete problem, results in significantly faster solution times than previously proposed schemes.