Smaller stencil preconditioners for polyharmonic spline RBF-FD discretizations
Publication date
2023-05-12
Document type
Preprint
Author
Borne, Sabine Le
Organisational unit
Publisher
Research Square
Part of the university bibliography
✅
Language
English
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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This work is licensed under a CC BY 4.0 License.
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