A Schwarz alternating algorithm for elliptic boundary value problems in an infinite domain with a concave angle

摘要

In this paper, we investigate a Schwarz alternating algorithm for elliptic boundary value problems in an infinite domain with a concave angle, which is an overlapping domain decomposition method based on natural boundary reduction (NBR). The algorithm is constructed, and its convergence is discussed. The finite element and natural boundary element method are alternatively applied to solve a bounded subdomain and a typical unbounded subdomain. It has overcome the difficulty met in standard domain decomposition method for problems with unbounded domains. The convergence rate is analyzed in details for a typical domain. Finally, some numerical examples are presented to show the effectiveness of this method.