High-order numerical method for solving elliptic partial differential equations on unfitted node sets
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913440459653120 |
|---|---|
| author | Nielsen, Morten E. Fornberg, Bengt |
| author_facet | Nielsen, Morten E. Fornberg, Bengt |
| contents | In this paper, we present how high-order accurate solutions to elliptic partial differential equations can be achieved in arbitrary spatial domains using radial basis function-generated finite differences (RBF-FD) on unfitted node sets (i.e., not adjusted to the domain boundary). In this novel method, we only collocate on nodes interior to the domain boundary and enforce boundary conditions as constraints by means of Lagrange multipliers. This combination enables full geometric flexibility near boundaries without compromising the high-order accuracy of the RBF-FD method. The high-order accuracy and robustness of two formulations of this approach are illustrated by numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15825 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-order numerical method for solving elliptic partial differential equations on unfitted node sets Nielsen, Morten E. Fornberg, Bengt Numerical Analysis 65N22, 35J05 In this paper, we present how high-order accurate solutions to elliptic partial differential equations can be achieved in arbitrary spatial domains using radial basis function-generated finite differences (RBF-FD) on unfitted node sets (i.e., not adjusted to the domain boundary). In this novel method, we only collocate on nodes interior to the domain boundary and enforce boundary conditions as constraints by means of Lagrange multipliers. This combination enables full geometric flexibility near boundaries without compromising the high-order accuracy of the RBF-FD method. The high-order accuracy and robustness of two formulations of this approach are illustrated by numerical experiments. |
| title | High-order numerical method for solving elliptic partial differential equations on unfitted node sets |
| topic | Numerical Analysis 65N22, 35J05 |
| url | https://arxiv.org/abs/2407.15825 |