The Method of Fundamental Solution for the Dirichlet Problem in with the Boundary of the two Spheres
In this paper we deal with the method of fundamental solution for the three-dimensional Dirichlet problem, where the fundamental solution of Laplace operator is used. First we construct the arrangement of the collocation points on the spherical surface. We deal with the three problems: the problem o...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SAGE Publishing
2012-06-01
|
| Series: | Journal of Algorithms & Computational Technology |
| Online Access: | https://doi.org/10.1260/1748-3018.6.2.281 |
| _version_ | 1818210498328395776 |
|---|---|
| author | Ryu Kinugawa Hiromichi Yamamoto Heihachiro Hara |
| author_facet | Ryu Kinugawa Hiromichi Yamamoto Heihachiro Hara |
| author_sort | Ryu Kinugawa |
| collection | DOAJ |
| description | In this paper we deal with the method of fundamental solution for the three-dimensional Dirichlet problem, where the fundamental solution of Laplace operator is used. First we construct the arrangement of the collocation points on the spherical surface. We deal with the three problems: the problem of the concentric ring domain, the problem of the non-concentric ring domain, and the problem of the unbounded domain with the boundary of the two spheres. For these problems, we have developed some algorithms by rearranging the singular points. By our algorithms we can obtain the accurate approximation even if the distance of the two spheres is small. |
| first_indexed | 2024-12-12T05:17:34Z |
| format | Article |
| id | doaj.art-c233a9f5eeef4d26a3517592273bc715 |
| institution | Directory Open Access Journal |
| issn | 1748-3018 1748-3026 |
| language | English |
| last_indexed | 2024-12-12T05:17:34Z |
| publishDate | 2012-06-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Algorithms & Computational Technology |
| spelling | doaj.art-c233a9f5eeef4d26a3517592273bc7152022-12-22T00:36:44ZengSAGE PublishingJournal of Algorithms & Computational Technology1748-30181748-30262012-06-01610.1260/1748-3018.6.2.281The Method of Fundamental Solution for the Dirichlet Problem in with the Boundary of the two SpheresRyu KinugawaHiromichi YamamotoHeihachiro HaraIn this paper we deal with the method of fundamental solution for the three-dimensional Dirichlet problem, where the fundamental solution of Laplace operator is used. First we construct the arrangement of the collocation points on the spherical surface. We deal with the three problems: the problem of the concentric ring domain, the problem of the non-concentric ring domain, and the problem of the unbounded domain with the boundary of the two spheres. For these problems, we have developed some algorithms by rearranging the singular points. By our algorithms we can obtain the accurate approximation even if the distance of the two spheres is small.https://doi.org/10.1260/1748-3018.6.2.281 |
| spellingShingle | Ryu Kinugawa Hiromichi Yamamoto Heihachiro Hara The Method of Fundamental Solution for the Dirichlet Problem in with the Boundary of the two Spheres Journal of Algorithms & Computational Technology |
| title | The Method of Fundamental Solution for the Dirichlet Problem in with the Boundary of the two Spheres |
| title_full | The Method of Fundamental Solution for the Dirichlet Problem in with the Boundary of the two Spheres |
| title_fullStr | The Method of Fundamental Solution for the Dirichlet Problem in with the Boundary of the two Spheres |
| title_full_unstemmed | The Method of Fundamental Solution for the Dirichlet Problem in with the Boundary of the two Spheres |
| title_short | The Method of Fundamental Solution for the Dirichlet Problem in with the Boundary of the two Spheres |
| title_sort | method of fundamental solution for the dirichlet problem in with the boundary of the two spheres |
| url | https://doi.org/10.1260/1748-3018.6.2.281 |
| work_keys_str_mv | AT ryukinugawa themethodoffundamentalsolutionforthedirichletprobleminwiththeboundaryofthetwospheres AT hiromichiyamamoto themethodoffundamentalsolutionforthedirichletprobleminwiththeboundaryofthetwospheres AT heihachirohara themethodoffundamentalsolutionforthedirichletprobleminwiththeboundaryofthetwospheres AT ryukinugawa methodoffundamentalsolutionforthedirichletprobleminwiththeboundaryofthetwospheres AT hiromichiyamamoto methodoffundamentalsolutionforthedirichletprobleminwiththeboundaryofthetwospheres AT heihachirohara methodoffundamentalsolutionforthedirichletprobleminwiththeboundaryofthetwospheres |