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Article


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)

[2.8] Mechanical engineering

Year of publication

2023

Published in

Mathematics and Computers in Simulation

Journal year: 2023 | Journal volume: vol. 206

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

DOI

10.1016/j.matcom.2022.11.006

URL

https://www.sciencedirect.com/science/article/pii/S0378475422004554

Ministry points / journal

70.0

Impact Factor

3.601 [List 2021]

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