The Method of Fundamental Solution for the Dirichlet Problem in with the Boundary of the two Spheres

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...

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Main Authors: Ryu Kinugawa, Hiromichi Yamamoto, Heihachiro Hara
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
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spelling doaj-c233a9f5eeef4d26a3517592273bc7152020-11-25T03:45:05ZengSAGE 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
collection DOAJ
language English
format Article
sources DOAJ
author Ryu Kinugawa
Hiromichi Yamamoto
Heihachiro Hara
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
author_facet Ryu Kinugawa
Hiromichi Yamamoto
Heihachiro Hara
author_sort Ryu Kinugawa
title 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_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_sort method of fundamental solution for the dirichlet problem in with the boundary of the two spheres
publisher SAGE Publishing
series Journal of Algorithms & Computational Technology
issn 1748-3018
1748-3026
publishDate 2012-06-01
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.
url https://doi.org/10.1260/1748-3018.6.2.281
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AT hiromichiyamamoto themethodoffundamentalsolutionforthedirichletprobleminwiththeboundaryofthetwospheres
AT heihachirohara themethodoffundamentalsolutionforthedirichletprobleminwiththeboundaryofthetwospheres
AT ryukinugawa methodoffundamentalsolutionforthedirichletprobleminwiththeboundaryofthetwospheres
AT hiromichiyamamoto methodoffundamentalsolutionforthedirichletprobleminwiththeboundaryofthetwospheres
AT heihachirohara methodoffundamentalsolutionforthedirichletprobleminwiththeboundaryofthetwospheres
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