Implementation of boundary conditions in BIEs-based meshless methods: A dual boundary node method

A new implementation of the boundary node method (BNM) is developed in this paper for two- and three-dimensional potential problems. In our implementation, here called the dual boundary node method (DBNM), the conventional BIE is applied on the Dirichlet boundary and the hypersingular BIE is applied on the Neumann boundary. The DBNM can apply the boundary conditions directly and easily. And the number of both unknowns and system equations in the DBNM is only half of that in the BNM, thus the computing speed and efficiency are higher. The present method is applicable to other BIEs-based meshless methods, such as the boundary cloud method, the boundary element-free method and the boundary face method, in which the used shape functions lack the delta function property. Some numerical examples are given to demonstrate the method.