Multilevel compact radial functions based computational schemes for some elliptic problems

Compactly supported radial basis functions (CS-RBFs) have been recently introduced in the context of the dual reciprocity method as a possible cure of dense matrices and ill-conditioning problems when using the classical radial basis functions. However, the support scaling factor and slow convergence rate of the CS-RBFs have also raised issues on the effectiveness of the CS-RBFs. In this paper, two multilevel schemes have been proposed to alleviate these problems.