A Preconditioner for Coupling System of Natural Boundary Element and Composite Grid Finite Element

Abstract

In this paper, based on the natural boundary reduction advanced by Feng and Yu, we discuss a coupling BEM with FEM for the Dirichlet exterior problems. In this method the finite element grids consist of fine grid and coarse grid so that the singularity at the corner points can be handled conveniently. In order to solve the coupling system by the preconditioning conjugate gradient method, we construct a simple preconditioner for the "stiffness" matrix. Some error estimates of the corresponding approximate solution and condition number estimate of the preconditioned matrix are also obtained.