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

Abstract

The boundary node method (BNM) is developed in this paper for solving potential problems in three dimensions. The BNM represents a coupling between boundary integral equations (BIE) and moving least-squares (MLS) interpolants. The main idea here is to retain the dimensionality advantage of the former and the meshless attribute of the later. This results in decoupling of the ‘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 successful implementation of the method. An in-depth and systematic study has been carried out in this paper in order to better understand the effects of various parameters on the performance of the method. Numerical results for spheres and cubes, subjected to different types of boundary conditions, are extremely encouraging. Copyright © 2000 John Wiley & Sons, Ltd.