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Kansa–RBF algorithms for elliptic BVPs in annular domains with mixed boundary conditions

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  • Jankowska, Malgorzata A.
  • Karageorghis, Andreas
  • Chen, C.S.

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.

Suggested Citation

  • Jankowska, Malgorzata A. & Karageorghis, Andreas & Chen, C.S., 2023. "Kansa–RBF algorithms for elliptic BVPs in annular domains with mixed boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 77-104.
    • Handle: RePEc:eee:matcom:v:206:y:2023:i:c:p:77-104
    DOI: 10.1016/j.matcom.2022.11.006
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    References listed on IDEAS

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    1. Suranon Yensiri & Ruth J. Skulkhu, 2017. "An Investigation of Radial Basis Function-Finite Difference (RBF-FD) Method for Numerical Solution of Elliptic Partial Differential Equations," Mathematics, MDPI, vol. 5(4), pages 1-14, October.
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