Some observations regarding the RBF-FD approximation accuracy dependence on stencil size

Kolar-Požun, Andrej (author), Jančič, Mitja (author), Rot, Miha (author), Kosec, Gregor (author)

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).

• Language: English
• Keywords: meshless methods, stencil, RBF-FD, PHS
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 12 str.
• Numbering: Vol. 79, art. 102284
• PID: 20.500.12556/RUL-156334
• UDC: 51-7
• ISSN on article: 1877-7503
• DOI: 10.1016/j.jocs.2024.102284
• COBISS.SI-ID: 194478851
• Publication date in RUL: 20.05.2024

Record is a part of a journal

• Title: Journal of computational science
• Publisher: Elsevier
• ISSN: 1877-7503
• COBISS.SI-ID: 519422233

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: komunikacije, brezmrežne metode, numerične metode