Neumann problem on a torus
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913534769627136 |
|---|---|
| author | Ashtab, Z. Morais, J. Porter, R. M. |
| author_facet | Ashtab, Z. Morais, J. Porter, R. M. |
| contents | We consider the Dirichlet-to-Neumann mapping and the Neumann problem for the Laplace operator on a torus, given in toroidal coordinates. The Dirichlet-to-Neumann mapping is expressed with respect to series expansions in toroidal harmonics and thereby reduced to algebraic manipulations on the coefficients. A method for computing the numerical solutions of the corresponding Neumann problem is presented, and numerical illustrations are provided. We combine the results for interior and exterior domains to solve the Neumann problem for a toroidal shell. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_00224 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Neumann problem on a torus Ashtab, Z. Morais, J. Porter, R. M. Analysis of PDEs 31B20 (Primary) 35J05 35J25 65N21 (Secondary) We consider the Dirichlet-to-Neumann mapping and the Neumann problem for the Laplace operator on a torus, given in toroidal coordinates. The Dirichlet-to-Neumann mapping is expressed with respect to series expansions in toroidal harmonics and thereby reduced to algebraic manipulations on the coefficients. A method for computing the numerical solutions of the corresponding Neumann problem is presented, and numerical illustrations are provided. We combine the results for interior and exterior domains to solve the Neumann problem for a toroidal shell. |
| title | Neumann problem on a torus |
| topic | Analysis of PDEs 31B20 (Primary) 35J05 35J25 65N21 (Secondary) |
| url | https://arxiv.org/abs/2212.00224 |