Tests of radial basis functions in the 3D DRM-MD

摘要

Several global as well as compactly supported radial basis functions were tested in the boundary element dual reciprocity method-multi domain approach (DRM-MD) applied to 3D potential problems. Compactly supported radial basis functions (CS-RBFs) showed the highest accuracy, while the augmented thin plate splines (ATPS) showed the highest consistency in terms of accuracy and convergence for the two examples considered, the Poisson and the advection-diffusion equations. A problem for implementation of the CS-RBFs is the lack of guidelines in choosing the size of the support, which showed to have large influence on the accuracy and convergence when these types of RBFs are used. The ATPS showed satisfactory accuracy and since its use does not involve any extra parameters, at the moment it is this function that is the choice of the authors for use in the DRM-MD.