A D-N Alternating Algorithm for Solving 3D Exterior Helmholtz Problems

Abstract EN

The nonoverlapping domain decomposition method, which is based on the natural boundary reduction, is applied to solve the exterior Helmholtz problem over a three-dimensional domain.

The basic idea is to introduce a spherical artificial boundary; the original unbounded domain is changed into a bounded subdomain and a typical unbounded region; then, a Dirichlet-Nuemann (D-N) alternating method is presented; the finite element method and natural boundary element methods are alternately applied to solve the problems in the bounded subdomain and the typical unbounded subdomain.

The convergence of the D-N alternating algorithm and its discretization are studied.

Some numerical experiments are presented to show the performance of this method.