Open this publication in new window or tab >>2022 (English)In: Dolomites Research Notes on Approximation, ISSN 2035-6803, Vol. 15, no 5, p. 78-95Article in journal (Refereed) Published
Abstract [en]
In a recent paper by Tominec, Larsson and Heryudono a convergence proof for an oversampled version of the RBF-FD method, using polyharmonic spline basis functions augmented with polynomials, was derived. In this paper, we take a closer look at the individual estimates involved in this proof. We investigate how large the bounds are and how they depend on the node layout, the stencil size, and the polynomial degree. We find that a moderate amount of oversampling is sufficient for the method to be stable when Halton nodes are used for the stencil approximations, while a random node layout may require a very high oversampling factor. From a practical perspective, this indicates the importance of having a locally quasi uniform node layout for the method to be stable and give reliable results. We see an overall growth of the error constant with the polynomial degree and with the stencil size.
Place, publisher, year, edition, pages
Padova University Press, 2022
Keywords
Radial Basis Functions, RBF-FD, error estimates, numerical analysis, least squares, oversampling
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-492668 (URN)10.14658/pupj-drna-2022-5-8 (DOI)000979620400009 ()
Projects
eSSENCE - An eScience Collaboration
Funder
Swedish Research Council, 2020-03488eSSENCE - An eScience CollaborationSwedish National Infrastructure for Computing (SNIC), 2021/22-457Swedish Research Council, 2018-05973
2023-01-092023-01-092023-10-31Bibliographically approved