Fast Simulation of 3D Electromagnetic Problems Using Potentials

doi:10.1006/jcph.2000.6545

Journal of Computational Physics

Volume 163, Issue 1, 1 September 2000, Pages 150-171

https://doi.org/10.1006/jcph.2000.6545 Get rights and content

Abstract

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 frequencies is moderate. The difficulties encountered include handling solution discontinuities across interfaces and accelerating convergence of traditional iterative methods for the solution of the linear systems of algebraic equations that arise when discretizing Maxwell's equations in the frequency domain. We use a potential-current formulation (A, φ ,Ĵ) with a Coulomb gauge. The potentials A and φ decompose the electric field E into components in the active and null spaces of the ∇×operator. We develop a finite volume discretization on a staggered grid that naturally employs harmonic averages for the conductivity at cell faces. After discretization, 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 particularly efficient algorithm results from the combination of BICGSTAB and an incomplete LU-decomposition. We demonstrate the efficacy of our method in several numerical experiments.

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Regular ArticleFast Simulation of 3D Electromagnetic Problems Using Potentials

Abstract

Numerical Methods for PDE's

J. Comput. Phys.

Journal of Computational Physics

Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods

On the use of the magnetic vector potential in the finite element analysis of three-dimensional eddy currents

IEEE Trans. Magnet.

Computational Electromagnetism. Variational Formulation, Complementarity, Edge Elements

Yee-like schemes on staggered cellular grids: A synthesis between fit and fem approaches

COMPUMAG

Mixed and Hybrid Finite Element Methods