Node subsampling for multilevel meshfree elliptic PDE solvers
| Autor: | Lawrence, Andrew P., Nielsen, Morten Eggert, Fornberg, Bengt |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
Elimination
Agglomeration Meshfree Node set RBF Numerical Analysis (math.NA) Laplace equation Poisson equation Multilevel Point cloud Coarsening 65N50 65N22 (Primary) 65F10 65N06 65N55 (Secondary) FOS: Mathematics Multicloud RBF-FD Mathematics - Numerical Analysis Thinning Multiresolution Subsampling |
| Zdroj: | Lawrence, A P, Nielsen, M E & Fornberg, B 2023, ' Node subsampling for multilevel meshfree elliptic PDE solvers ', ArXiv . < http://arxiv.org/abs/2303.09080 > |
| Popis: | Subsampling of node sets is useful in contexts such as multilevel methods, computer graphics, and machine learning. On uniform grid-based node sets, the process of subsampling is simple. However, on node sets with high density variation, the process of coarsening a node set through node elimination is more interesting. A novel method for the subsampling of variable density node sets is presented here. Additionally, two novel node set quality measures are presented to determine the ability of a subsampling method to preserve the quality of an initial node set. 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. High-order solutions with robust convergence are achieved in linear time with respect to node set size. Comment: 21 pages, 12 figures |
| Databáze: | OpenAIRE |
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