Boundary-Type RBF Collocation Methods

Authors

Wen Chen, Hohai UniversityFollow
Zhuo Jia Fu, Hohai UniversityFollow
C. S. Chen, University of Southern MississippiFollow

Document Type

Book Chapter

Publication Date

11-9-2013

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

The mesh generation in the standard BEM is still not trivial as one may imagine, especially for high-dimensional moving boundary problems. To overcome this difficulty, the boundary-type RBF collocation methods have been proposed and endured a fast development in the recent decade thanks to being integration-free, spectral convergence, easy-to-use, and inherently truly meshless. First, this chapter introduces the basic concepts of the method of fundamental solutions (MFS). Then a few recent boundary-type RBF collocation schemes are presented to tackle the issue of the fictitious boundary in the MFS, such as boundary knot method (BKM), regularized meshless method, and singular boundary method. Following this, an improved multiple reciprocity method (MRM), the recursive composite MRM (RC-MRM), is introduced to establish a boundary-only discretization of nonhomogeneous problems. Finally, numerical demonstrations show the convergence rate and stability of these boundary-type RBF collocation methods for several benchmark examples.

Publication Title

Recent Advances In Radial Basis Function Collocation Methods

First Page

51

Last Page

87

Recommended Citation

Chen, W., Fu, Z., Chen, C. (2013). Boundary-Type RBF Collocation Methods. Recent Advances In Radial Basis Function Collocation Methods, 51-87.
Available at: https://aquila.usm.edu/fac_pubs/19979