The boundary node method for three-dimensional problems in potential theory

The boundary node method (BNM) is developed in this paper for solving poten tial problems in three dimensions. The BNM represents a coupling between bo undary integral equations (BIE) and moving least-squares (MLS) interpolants . The main idea here is to retain the dimensionality advantage of the forme r and the meshless attribute of the later. This results in decoupling of th e 'mesh' and the interpolation procedure for the field variables. A general BNM computer code for 3-D potential problems has been developed. Several parameters involved in the BNM need to be chosen carefully for a su ccessful implementation of the method. An in-depth and systematic study has been carried out in this paper in order to better understand the effects o f various parameters on the performance of the method Numerical results for spheres and cubes, subjected to different types of boundary conditions, ar e extremely encouraging. Copyright (C) 2000 John Wiley & Sons, Ltd.