Paper Info
Title
A Kansa-Radial Basis Function Method for Elliptic Boundary Value Problems in Annular Domains
Abstract
We employ a Kansa-radial basis function (RBF) method for the numerical solution of elliptic boundary value problems in annular domains. This discretization leads, with an appropriate selection of collocation points and for any choice of RBF, to linear systems in which the matrices possess block circulant structures. These linear systems can be solved efficiently using matrix decomposition algorithms and fast Fourier transforms. A suitable value for the shape parameter in the various RBFs used is found using the leave-one-out cross validation algorithm. In particular, we consider problems governed by the Poisson equation, the inhomogeneous biharmonic equation and the inhomogeneous Cauchy---Navier equations of elasticity. In addition to its simplicity, the proposed method can both achieve high accuracy and solve large-scale problems. The feasibility of the proposed techniques is illustrated by several numerical examples.
Year
DOI
Venue
2015
10.1007/s10915-015-0009-4
Journal of Scientific Computing
Keywords
Field
DocType
Radial basis functions, Poisson equation, Biharmonic equation, Cauchy–Navier equations of elasticity, Fast Fourier transforms, Kansa method, Primary 65N35, Secondary 65N21, 65N38
Discretization,Boundary value problem,Mathematical optimization,Mathematical analysis,Matrix (mathematics),Matrix decomposition,Basis function,Spectral method,Biharmonic equation,Kansa method,Mathematics
Journal
Volume
Issue
ISSN
65
3
1573-7691
Citations 
PageRank 
References 
6
0.52
12
Authors
3
Name
Order
Citations
PageRank
Xiaoyan Liu110919.35
Andreas Karageorghis220447.54
C. S. Chen3508.45