## 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.

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.

Originalsprog | Engelsk |
---|---|

Udgiver | arXiv |

DOI | |

Status | Udgivet - 2023 |

## Emneord

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