 Kansa–RBF algorithms for elliptic BVPs in annular domains with mixed boundary conditionsMalgorzata A. Jankowska, Andreas Karageorghis and C.S. Chen Mathematics and Computers in Simulation (MATCOM), 2023, vol. 206, issue C, 77-104 Abstract: 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. Keywords: Radial basis functions; Kansa method; Poisson equation; Biharmonic equation; Iterative methods; Circulant matrices; Matrix decomposition algorithms (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:206:y:2023:i:c:p:77-104 DOI: 10.1016/j.matcom.2022.11.006 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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