Galerkin Boundary Node Method for Exterior Neumann Problems

Abstract

In this paper, we present a meshless Galerkin scheme of boundary integral equations (BIEs), known as the Galerkin boundary node method (GBNM), for two-dimensional exterior Neumann problems that combines the moving least-squares (MLS) approximations and a variational formulation of BIEs. In this approach, boundary conditions can be implemented directly despite the MLS approximations lack the delta function property. Besides, the GBNM keeps the symmetry and positive definiteness of the variational problems. A rigorous error analysis and convergence study of the method is presented in Sobolev spaces. Numerical examples are also given to illustrate the capability of the method.