A METHOD FOR THE FORWARD MODELLING OF 3-D ELECTROMAGNETIC QUASI-STATIC PROBLEMS

Abstract

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