A Parallel Schwarz Algorithm For Two-dimesional Helmholtz Equation On Irregular Unbounded Domain

For some PDE on unbounded domain, many methods have been discussed. Usuallywe solve the exterior boundary value problem in regular domain by naturalboundary reduction. As for the exterior boundary value problem in irregular domain,the finite elment method and natual boundary elment are applied to solve a boundedsubdomain and a typical unbounded subdomain. We need to proof the problem iswell-posed and the coupling method is reasonable. Much has been done in thisrespect, In this paper, we consider the parallel schwarz algorithm through naturalboundary reduction theorem for neumann problems of helmholtz equation. Theconvergence of this algorithm is given. It is explained that the algorithm iseffective.