A class of RBFs-based DQ methods for the space-fractional diffusion equations on 3D irregular domains

High-dimensional space-fractional PDEs are topics of special focus in applied disciplines, but solving them on irregular domains is challenging and deserves particular attention in scientific computing. In response to this issue, we establish a family of differential quadrature (DQ) methods for the space-fractional diffusion equations on 3D irregular domains. The fractional derivatives in space are represented by weighted linear combinations based on the functional values at scattered nodes with their weights determined by using radial basis functions (RBFs) as trial functions. The resulting system of ordinary differential equations (ODEs) are discretized by the weighted average scheme. The presented DQ methods have the virtues which are shared by the classical DQ methods. Several benchmark problems on typical irregular domains are solved to illustrate their advantages in flexibility and accuracy.