HYBRID APPROXIMATION FUNCTIONS IN THE DUAL RECIPROCITY BOUNDARY ELEMENT METHOD

Abstract

The dual reciprocity boundary element method traditionally uses the linear radial basis function r for interpolation. Recently, however, the use of the r function has been questioned both in relation to accuracy and in relation to the number and position of internal nodes required to obtain satisfactory solutions. Much research has been done in an attempt to fix criteria for choosing which approximation function should be used. One of the alternatives recently suggested is the augmented thin plate spline function, which consists of a thin plate spline function, r2 log(r), augmented with the first three terms of a Pascal triangle expansion. In this paper families of similar functions are obtained by augmenting radial basis functions with appropriate global expansions: these functions will be called hybrid approximate functions. It will be shown that using an appropriate hybrid function accurate results can be obtained for many body forces or pseudo body forces in elasticity without the need for internal nodes.© 1997 John Wiley & Sons, Ltd.