A method for the forward modelling of 3-D electromagnetic quasi-static problems

We present a solution method for solving electromagnetic problems in three dimensions in parameter regimes where the quasi-static approximation applie s and the permeability is constant. Firstly, by using a potential formulati on with a Coulomb gauge, we circumvent the ill-posed problem in regions of vanishing conductivity, obtaining an elliptic, weakly coupled system of dif ferential equations. The system thus derived is strongly elliptic, which le ads to reliable discretizations. Secondly, we derive a robust finite-volume discretization. Thirdly we solve the resulting large, sparse algebraic sys tems using preconditioned Krylov-space methods. A particularly efficient al gorithm results from the combination of BICGSTAB and a block preconditioner using an incomplete LU-decomposition of the dominant system blocks only. W e demonstrate the efficacy of our method in several numerical experiments.