Title
Kansa–RBF algorithms for elliptic BVPs in annular domains with mixed boundary conditions
Authors
[ 1 ] Instytut Mechaniki Stosowanej, Wydział Inżynierii Mechanicznej, Politechnika Poznańska | [ P ] employee
Scientific discipline (Law 2.0)
Year of publication
2023
Published in
Article type
scientific article
Publication language
english
Keywords
EN
- Radial basis functions
- Kansa method
- Poisson equation
- Biharmonic equation
- Iterative methods
- Circulant matrices
- Matrix decomposition algorithms
Abstract
EN We employ a Kansa–radial basis function (RBF) method for the numerical solution of elliptic boundary value problems in annular domains with mixed Dirichlet/Neumann boundary conditions. By exploiting the circular boundaries and the properties of circulant matrices we employ, in an efficient way, the pre-conditioned Krylov subspace iterative solvers GMRES and BiCGSTAB for the solution of the resulting linear systems. In particular, we employ block circulant pre-conditioners which allow for the efficient solution of the relevant systems in the iterative solution. Moreover, by exploiting the properties of circulant matrices we perform the matrix–vector multiplications involved in the iterative solvers efficiently. The feasibility of the proposed techniques is illustrated by several numerical examples.
Date of online publication
17.11.2022
Pages (from - to)
77 - 104
Ministry points / journal
70.0
Impact Factor
3.601 [List 2021]
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