Koch, MichaelMichaelKochLe Borne, SabineSabineLe BorneLeinen, WilliWilliLeinen2024-10-042024-10-042024-04-20Numerical Algorithms (in Press): (2024)https://hdl.handle.net/11420/49351Radial 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.en1017-13982024Springerhttps://creativecommons.org/licenses/by/4.0/65D1265D2565F0865F1065F5565M1265N22Iterative solverMeshfree methodPolyharmonic splinePolynomial augmentationPreconditionerRadial basis function finite difference (RBF-FD)Natural Sciences and Mathematics::519: Applied Mathematics, ProbabilitiesJournal Article10.15480/882.1335710.1007/s11075-024-01835-710.15480/882.13357Journal Article