Radial basis function selection in 3D DRM-MD for potential problems

The DRM based procedures are sensitive to the selection of the function used in the DRM approximation, and hence the Dual Reciprocity Method - Multi Domain approach (DRM-MD) encounters the same drawback. For 3D problems, there is no information available on the performance of DRM-MD using different approximation functions. Here, the accuracy of two DRM-MD codes that solve the Poisson and the advection-diffusion equations in 3 3D domains have been tested using nine different approximation functions. The most accurate results were obtained using Compactly Supported Radial Basis Functions (CS-RBF), however accurate results with these functions can be obtained only if the suitable size of the support is known a priori. As a general procedure to determine the optimum value of the size of the support is not available, the Augmented Thin Plate Splines are recommended as they produced accurate and stable results and their implementation is straightforward.