MULTIDIMENSIONAL INTERPOLATION USING OSCULATORY RADIAL BASIS FUNCTIONS

A procedure has been developed for the interpolation of functions defi ned in two dimensions using the values of the function and its normal derivatives at the boundary. The interpolating functions used are comb inations of two classes of radial basis functions. This permits an int erpolation scheme with osculatory features, i.e., the interpolant has a specified slope at the boundary interpolation points. The improved a ccuracy of the method is demonstrated over interpolation schemes using the traditional radial basis functions (with no osculation), especial ly for the calculation of the derivatives of the function at various i nternal points. A brief discussion on the utility of the new interpola tion technique in solving nonlinear Poisson problems using the dual re ciprocity boundary element method is provided. (C) 1998 Elsevier Scien ce Ltd. All rights reserved.