Smaller stencil preconditioners for linear systems in RBF-FD discretizations

Publication date
2024-04-20
Document type
Forschungsartikel
Author
Koch, Michael
Le Borne, Sabine
Organisational unit
DOI
URI
ISSN
Series or journal
Numerical Algorithms
Peer-reviewed
✅
Part of the university bibliography
✅
DDC Class
000 Informatik, Wissen & Systeme
500 Naturwissenschaften
Keyword
Preconditioner
Radial basis function finite difference (RBF-FD)
Meshfree method
Polyharmonic spline
Polynomial augmentation
Iterative solver
Abstract
Radial basis function finite difference (RBF-FD) discretization has recently emerged as an alternative to classical finite difference or finite element discretization of (systems) of partial differential equations. In this paper, we focus on the construction of preconditioners for the iterative solution of the resulting linear systems of equations. In RBF-FD, a higher discretization accuracy may be obtained by increasing the stencil size. This, however, leads to a less sparse and often also worse conditioned stiffness matrix which are both challenges for subsequent iterative solvers. We propose to construct preconditioners based on stiffness matrices resulting from RBF-FD discretization with smaller stencil sizes compared to the one for the actual system to be solved. In our numerical results, we focus on RBF-FD discretizations based on polyharmonic splines (PHS) with polynomial augmentation. We illustrate the performance of smaller stencil preconditioners in the solution of the three-dimensional convection-diffusion equation.
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Der Originalartikel steht unter der Lizenz CC-BY-4.0

Erscheint auch in Print: ISSN 1017-1398
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