ABSTRACT
Since Kansa [31] introduced the radial basis functions (RBFs) to solve PDEs in 1990, there has been a growing interest in this subject. In this chapter, we will introduce this fascinating area to the reader. In Sec. 10.1, we provide a brief overview of the meshless methods related to RBFs. Then in Sec. 10.2, we introduce some widely used RBFs and their mathematical properties. In Sec. 10.3, we present the method of fundamental solutions (MFS) and several techniques by coupling MFS with RBFs. After that, we discuss Kansa’s method and its variants in Sec. 10.4. In order to help readers understand the algorithm better, we present some MATLAB codes in Sec. 10.5 to solve both elliptic and biharmonic problems in 2-D. Finally, in Sec. 10.6, we extend the discussion to domain decomposition methods coupled with Kansa’s method. One numerical example is also presented.
