Kansa-RBF algorithms for elliptic problems in axisymmetric domains
Date
2016ISSN
1064-8275Source
SIAM Journal on Scientific ComputingVolume
38Issue
1Pages
A435-A470Google Scholar check
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We employ a Kansa-radial basis function method for the numerical solution of elliptic boundary value problems in three-dimensional axisymmetric domains. We consider problems governed by the Poisson equation, the inhomogeneous biharmonic equation, and the inhomogeneous Cauchy-Navier equations. Appropriate discretizations lead to linear systems, the coefficient matrices of which possess block circulant structures. These systems are then solved efficiently by means of matrix decomposition algorithms and fast Fourier transforms. Methods for choosing appropriate values of the shape parameter are also proposed. The effectiveness of the proposed algorithms is demonstrated by considering several numerical examples. © 2016 Society for Industrial and Applied Mathematics.
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