Kansa-RBF Algorithms for Elliptic Problems In Regular Polygonal Domains
Document Type
Article
Publication Date
12-6-2017
Department
Mathematics
School
Mathematics and Natural Sciences
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.
Publication Title
Numerical Algorithms
Volume
79
First Page
399
Last Page
421
Recommended Citation
Karageorghis, A.,
Jankowska, M. A.,
Chen, C.
(2017). Kansa-RBF Algorithms for Elliptic Problems In Regular Polygonal Domains. Numerical Algorithms, 79, 399-421.
Available at: https://aquila.usm.edu/fac_pubs/16963