Rapid evaluation of Newtonian potentials on planar domains
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916184440438784 |
|---|---|
| author | Shen, Zewen Serkh, Kirill |
| author_facet | Shen, Zewen Serkh, Kirill |
| contents | The accurate and efficient evaluation of Newtonian potentials over general 2-D domains is important for the numerical solution of Poisson's equation and volume integral equations. In this paper, we present a simple and efficient high-order algorithm for computing the Newtonian potential over a planar domain discretized by an unstructured mesh. The algorithm is based on the use of Green's third identity for transforming the Newtonian potential into a collection of layer potentials over the boundaries of the mesh elements, which can be easily evaluated by the Helsing-Ojala method. One important component of our algorithm is the use of high-order (up to order 20) bivariate polynomial interpolation in the monomial basis, for which we provide extensive justification. The performance of our algorithm is illustrated through several numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_10443 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rapid evaluation of Newtonian potentials on planar domains Shen, Zewen Serkh, Kirill Numerical Analysis The accurate and efficient evaluation of Newtonian potentials over general 2-D domains is important for the numerical solution of Poisson's equation and volume integral equations. In this paper, we present a simple and efficient high-order algorithm for computing the Newtonian potential over a planar domain discretized by an unstructured mesh. The algorithm is based on the use of Green's third identity for transforming the Newtonian potential into a collection of layer potentials over the boundaries of the mesh elements, which can be easily evaluated by the Helsing-Ojala method. One important component of our algorithm is the use of high-order (up to order 20) bivariate polynomial interpolation in the monomial basis, for which we provide extensive justification. The performance of our algorithm is illustrated through several numerical experiments. |
| title | Rapid evaluation of Newtonian potentials on planar domains |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2208.10443 |