Fast simulation of 3D electromagnetic problems using potentials

We consider solving three-dimensional electromagnetic problems in parameter regimes where the quasi-static approximation applies, the permeability is constant, the conductivity may vary significantly, and the range of frequen cies is moderate. The difficulties encountered include handling solution di scontinuities across interfaces and accelerating convergence of traditional iterative methods for the solution of the linear systems of algebraic equa tions that arise when discretizing Maxwell's equations in the frequency dom ain. We use a potential-current formulation (A, phi, (J) over circle) with a Coulomb gauge. The potentials A and phi decompose the electric field E in to components in the active and null spaces of the del x operator. We devel op a finite volume discretization on a staggered grid that naturally employ s harmonic averages for the conductivity at cell faces. After discretizatio n, we eliminate the current and the resulting large, sparse, linear system of equations has a block structure that is diagonally dominant, allowing an efficient solution with preconditioned Krylov space methods. A particularl y efficient algorithm results from the combination of BICGSTAB and an incom plete LU-decomposition. We demonstrate the efficacy of our method in severa l numerical experiments. (C) 2000 Academic Press.