Analysis of electrostatic and static magnetic field problems by advanced domain decomposition method

Abstract

In this Letter, a finite element-based domain decomposition method (DDM) with a novel transmission condition (TC) for the computation of electromagnetic or other kinds of fields by splitting the original large domain into several small non-overlapping sub-domains is proposed. The TC is derived from the definition of thermal contact resistance and is then imposed through an interior penalty formulation. The advantage of the proposed DDM is that no extra unknowns are introduced and the system matrix arising from the finite element method will be symmetric and positive definite. A Krylov subspace iterative method, preconditioned conjugate gradient, is adopted for the solution of the matrix equation. To verify the reliability and accuracy of the proposed DDM, both three-dimensional electrostatic and static magnetic models are calculated. In some deeper sense, the proposed DDM can be widely used in other fields of computational electromagnetics.