Kansa-RBF algorithms for elliptic problems in regular polygonal domains
Date
2018ISSN
1572-9265Source
Numerical AlgorithmsVolume
79Issue
2Pages
399-421Google Scholar check
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We propose matrix decomposition algorithms for the efficient solution of the linear systems arising from Kansa radial basis function discretizations of elliptic boundary value problems in regular polygonal domains. These algorithms exploit the symmetry of the domains of the problems under consideration which lead to coefficient matrices possessing block circulant structures. In particular, we consider the Poisson equation, the inhomogeneous biharmonic equation, and the inhomogeneous Cauchy-Navier equations of elasticity. Numerical examples demonstrating the applicability of the proposed algorithms are presented.