Node subsampling for multilevel meshfree elliptic PDE solvers

Andrew P. Lawrence, Morten Eggert Nielsen, Bengt Fornberg

Publikation: Working paper/PreprintPreprint

Abstract

Subsampling of node sets is useful in contexts such as multilevel methods,
polynomial approximation, and numerical integration. On uniform grid-based node
sets, the process of subsampling is simple. However, on non-uniform node sets,
the process of coarsening a node set through node elimination is nontrivial. A
novel method for such subsampling is presented here. Additionally, boundary
preservation techniques and two novel node set quality measures are presented.
The new subsampling method is demonstrated on the test problems of solving the
Poisson and Laplace equations by multilevel radial basis function-generated
finite differences (RBF-FD) iterations.
OriginalsprogEngelsk
UdgiverarXiv
DOI
StatusUdgivet - 2023

Emneord

  • Node set
  • Point cloud
  • Subsampling
  • Elimination
  • Thinning
  • Agglomeration
  • Coarsening
  • Multilevel
  • Multicloud
  • Multiresolution
  • Meshfree
  • RBF
  • RBF-FD
  • Laplace equation
  • Poisson equation

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