Multidimensional interpolation and numerical integration by boundary element method

This paper presents a multidimensional interpolation method and a numerical integration for a bounded region using boundary integral equations and a polyharmonic function. In the method using B-spline, points must be assigned in a gridiron layout for two-dimensional cases. In the method presented in this paper, using the polyharmonic function, arbitrary points can be assigned instead of using a gridiron layout, making interpolation an easy process. This method requires the use of boundary geometry of the region and arbitrary internal points. Values at an arbitrary point and the integral value are calculated after solving the discretized boundary integral equations. Numerical integration is performed using this interpolation. In order to investigate the efficiency of this method, several examples are given. (C) 2001 Elsevier Science Ltd. All rights reserved.