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.
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Acknowledgments
This research was supported in part by the PLGrid Infrastructure. The computations were performed on the cluster BEM in the Wroclaw Centre for Networking and Supercomputing (Wroclaw, Poland).
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Karageorghis, A., Jankowska, M.A. & Chen, C.S. Kansa-RBF algorithms for elliptic problems in regular polygonal domains. Numer Algor 79, 399–421 (2018). https://doi.org/10.1007/s11075-017-0443-5
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DOI: https://doi.org/10.1007/s11075-017-0443-5
Keywords
- Kansa method
- Radial basis functions
- Poisson equation
- Biharmonic equation
- Cauchy-Navier equations
- Matrix decomposition algorithms