Application of the meshless Galerkin boundary node method to potential problems with mixed boundary conditions

In this paper, the meshless Galerkin boundary node method is developed for boundary-only analysis of two- and three-dimensional potential problems with mixed boundary conditions of Dirichlet and Neumann type. This meshless algorithm leads to a symmetric and positive definite system of linear equations. Additionally, boundary conditions can be implemented directly and easily despite the fact that the employed meshless shape functions lack the delta function property. Theoretical error analysis and numerical results indicate that it is an efficient and accurate numerical method.