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Kansa-RBF algorithms for elliptic problems in regular polygonal domains

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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… Click to show full abstract

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.

Keywords: kansa rbf; polygonal domains; algorithms elliptic; problems regular; regular polygonal; rbf algorithms

Journal Title: Numerical Algorithms
Year Published: 2017

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