Document Type

Article

Publication Date

3-21-2015

School

Computing Sciences and Computer Engineering

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.

Comments

This is a post-peer-review, pre-copyedit version of an article published in Journal of Scientific Computing. The final authenticated version is available online at: https://doi.org/10.1007/s10915-015-0009-4.

Publication Title

Journal of Scientific Computing

Volume

65

Issue

3

First Page

1240

Last Page

1269

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