Solving singularity problems in unbounded domains by coupling of natural BEM and composite grid FEM Original Research Article

In this paper, based on the natural boundary reduction method advanced by Feng and Yu, we discuss a coupled FEM–BEM for Dirichlet exterior problems. In this method, the finite element grids consist of fine and coarse grids (i.e., composite grids), so that the singularity at the corner points can be handled conveniently by the fast adaptive composite grid method (FAC). We prove that the corresponding approximation has optimal error estimates. To solve the coupled system efficiently, we propose an iteration that combines FAC with classical steepest descent. We show that this method converges with a rate that is bounded independent of the mesh sizes.