Augmented Thin Plate Spline Approximation in DRM

Abstract

The dual reciprocity method (DRM) is a popular mathematical technique to solve non-homogeneous Poisson type equations. The method involves the approximation of the non-homogeneous term by a set of radial basis functions (RBF) and transferring the resultant domain integral to an equivalent boundary integral. In this work, the augmented thin plate spline (ATPS) is shown to be superior to the frequently used linear RBF for DRM approximation in two dimensions. Comparison of the DRM implementation with augmented and unaugmented thin plate spline is also provided. Keywords: Dual reciprocity method, Boundary element method, Radial basis functions, Augmented radial basis functions, Thin plate spline i 1 Introduction The dual reciprocity method (DRM) is a class of boundary element methods (BEM) to solve non-homogeneous partial dioeerential equations (PDE), often referred to as Poisson type equations. In this method, the domain integral resulting from the non-homogeneous term, denoted as b, i..