Some comments on the use of Radial Basis Functions in the Dual Reciprocity Method

Abstract

We comment on the use of radial basis functions in the dual reciprocity method (DRM), particularly thin plate splines as used in Agnantiaris et al. (1996). We note that the omission of the linear terms could have biased the numerical results as has occurred in several previous studies. Furthermore, we show that a full understanding of the convergence behavior of the DRM requires one to consider both interpolation and BEM errors, since the latter can offset the effect of improved data approximation. For a model Poisson problem this is demonstrated theoretically and the results confirmed by a numerical experiment.