Recent Advances in Radial Basis Function Collocation Methods

✍ Scribed by Wen Chen, Zhuo-Jia Fu, C.S. Chen (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2014
• Tongue: English
• Leaves: 98
• Series: SpringerBriefs in Applied Sciences and Technology
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-x
Introduction....Pages 1-4
Radial Basis Functions....Pages 5-28
Different Formulations of the Kansa Method: Domain Discretization....Pages 29-50
Boundary-Type RBF Collocation Methods....Pages 51-87
Open Issues and Perspectives....Pages 89-90

✦ Subjects

Theoretical and Applied Mechanics;Computational Science and Engineering;Numerical and Computational Physics