Meshfree Extrapolation with Application to Enhanced Near-Boundary Approximation with Local Lagrange Kernels

Anat Amir, David Levin, Francis J. Narcowich*, Joseph D. Ward

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The paper deals with the problem of extrapolating data derived from sampling a Cm function at scattered sites on a Lipschitz region Ω in Rd to points outside of Ω in a computationally efficient way. While extrapolation problems go back to Whitney and many such problems have had successful theoretical resolutions, practical, computationally efficient implementations seem to be lacking. The goal here is to provide one way of obtaining such a method in a solid mathematical framework. The method utilized is a novel two-step moving least squares procedure (MLS) where the second step incorporates an error term obtained from the first MLS step. While the utility of the extrapolation degrades as a function of the distance to the boundary of Ω, the method gives rise to improved meshfree approximation error estimates when using the local Lagrange kernels related to certain radial basis functions.

Original languageEnglish
JournalFoundations of Computational Mathematics
Volume22
Issue number1
DOIs
StatePublished - Feb 2022

Funding

FundersFunder number
National Science Foundation

    Keywords

    • Extrapolation
    • Local Lagrangian kernels
    • Meshfree approximation
    • Moving least squares

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