Overlap Splines and Meshless Finite Difference Methods
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908499512918016 |
|---|---|
| author | Davydov, Oleg |
| author_facet | Davydov, Oleg |
| contents | We consider overlap splines that are defined by connecting the patches of piecewise functions via common values at given finite sets of nodes, without using any partitions of the computational domain. It is shown that some classical finite difference methods may be interpreted as collocation with overlap splines. Moreover, several versions of the meshless finite difference methods, such as the RBF-FD method, are equivalent to the collocation or discrete least squares with appropriately chosen spaces of overlap splines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_02391 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Overlap Splines and Meshless Finite Difference Methods Davydov, Oleg Numerical Analysis 41A15, 65N06, 65N35, 65L10 We consider overlap splines that are defined by connecting the patches of piecewise functions via common values at given finite sets of nodes, without using any partitions of the computational domain. It is shown that some classical finite difference methods may be interpreted as collocation with overlap splines. Moreover, several versions of the meshless finite difference methods, such as the RBF-FD method, are equivalent to the collocation or discrete least squares with appropriately chosen spaces of overlap splines. |
| title | Overlap Splines and Meshless Finite Difference Methods |
| topic | Numerical Analysis 41A15, 65N06, 65N35, 65L10 |
| url | https://arxiv.org/abs/2306.02391 |