Axisymmetric multiquadrics

Abstract

This paper reviews the previous axisymmetric global interpolation functions used in the context of the dual reciprocity boundary element method and dual reciprocity method of fundamental solutions connected to axisymmetric Laplace operator. It complements our axisymmetric thin plate splines [1] with the axisymmetric form of the Hardy's multiquadrics ( r 2 + r 0 2 ) m / 2 ; m=±1. This new functions can be used in the improved Golberg–Chen–Karur [2] type of approximations. The basic equations are accompanied by a set of related expressions that permit straightforward use of the developed global interpolation functions in a broad spectrum of dual reciprocity boundary element method and method of fundamental solutions, and meshless direct collocation like discrete approximate procedures.