The Overlapping Domain Decomposition Method for Harmonic Equation over Exterior Three-Dimensional Domain

Abstract

In this paper, the overlapping domain decomposition method, which is based on the natural boundary reduction and first suggested in [2], is applied to slove the exterior boundary value problem of harmonic equation over three-dimensional domain. The convergence and error estimates both for the continuous case and the discrete case are given. The contraction factor for the exterior spherical domain is also discussed. Moreover, numerical results are given which show that the accuracy and the convergence are in accord with the theoretical analyses.