Axisymmetric augmented thin plate splines

Abstract

This paper reviews the previous axisymmetric global interpolation functions used in the context of the dual reciprocity boundary element method and the axisymmetric Laplace operator. It upgrades the previous heuristic attempts with the axisymmetric form of the augmented thin plate splines. This new approach, based on the theory of radial basis functions, gives more formal mathematical support to this class of problems. 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 methods like discrete approximative procedures.