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

The boundary node method (BNM) is developed in this paper for solving potential problems in three dimen- sions. 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 `meshʹ and the interpolation procedure for the eld 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 e ects of various parameters on the performance of the method. Numerical results for spheres and cubes, subjected to di erent types of boundary conditions, are extremely encouraging. C