20.500.12556/RUL-156334 Some observations regarding the RBF-FD approximation accuracy dependence on stencil size When solving partial differential equations on scattered nodes using the Radial Basis Function-generated Finite Difference (RBF-FD) method, one of the parameters that must be chosen is the stencil size. Focusing on Polyharmonic Spline RBFs with monomial augmentation, we observe that it affects the approximation accuracy in a particularly interesting way — the solution error oscillates under increasing stencil size. We find that we can connect this behaviour with the spatial dependence of the signed approximation error. Based on this observation we are able to introduce a numerical quantity that could indicate whether a given stencil size is locally optimal. This work is an extension of our ICCS 2023 conference paper (Kolar-Požun et al., 2023). meshless methods stencil RBF-FD PHS komunikacije brezmrežne metode numerične metode true false true Angleški jezik Slovenski jezik Članek v reviji 2024-05-20 15:13:09 2024-05-20 15:13:12 2024-05-21 03:46:45 0000-00-00 00:00:00 2024 0 0 12 str. art. 102284 Vol. 79 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51-7 1877-7503 10.1016/j.jocs.2024.102284 194478851 1-s2.0-S1877750324000772-main.pdf 1-s2.0-S1877750324000772-main.pdf 1 9F34E97BC2F9C1BAA55EF6A498AFF191 61c0bd26a1b4edfd5c444caab80f9741e099553219214ab9befceacce3680793 e447081e-16aa-11ef-b600-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=183741 https://www.sciencedirect.com/science/article/pii/S1877750324000772 0 df4d555c-16aa-11ef-b600-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=183740 Fakulteta za matematiko in fiziko 0 0 0