A domain decomposition method for the exterior Helmholtz problem

A new domain decomposition method is presented for the exterior Helmholtz p roblem. The nonlocal Dirichlet-to-Neumann (DW) map is used as a nonreflecti ng condition on the outer computational boundary. The computational domain is divided into nonoverlapping subdomains with Sommerfeld-type conditions o n the adjacent subdomain boundaries to ensure uniqueness. An iterative sche me is developed, where independent subdomain boundary-value problems are ob tained by applying the DtN operator to values from the previous iteration. The independent problems are then discretized with finite elements and can be solved concurrently. Numerical results are presented for a two-dimension al model problem, and both the solution accuracy and convergence rate are i nvestigated. (C) 1998 Academic Press.