Recent Advances in Radial Basis Function Collocation Methods

This book surveys the latest advances in radial basis function (RBF) meshless collocation methods which emphasis on recent novel kernel RBFs and new numerical schemes for solving partial differential equations. The RBF collocation methods are inherently free of integration and mesh, and avoid tedious mesh generation involved in standard finite element and boundary element methods. This book focuses primarily on the numerical algorithms, engineering applications, and highlights a large class of novel boundary-type RBF meshless collocation methods. These methods have shown a clear edge over the traditional numerical techniques especially for problems involving infinite domain, moving boundary, thin-walled structures, and inverse problems.

Due to the rapid development in RBF meshless collocation methods, there is a need to summarize all these new materials so that they are available to scientists, engineers, and graduate students who are interest to apply these newly developed methods for solving real world's problems. This book is intended to meet this need.

Prof. Wen Chen and Dr. Zhuo-Jia Fu work at Hohai University. Prof. C.S. Chen works at the University of Southern Mississippi.

Systematically introduces various RBF collocation methods for domain and boundary-only discretization, including some very recent techniques not covered elsewhere Introduces new approaches to constructing characteristic kernel RBFs Provides illustrative benchmark examples Includes open-source codes

Inhalt

Introduction.- Radial basis functions.- Different formulations of the Kansa method domain discretization.- Boundary-type RBF collocation methods.- Open issues and Perspectives.