Modified Binary Tree in the Fast PIES for 2D Problems with Complex Shapes

The paper presents a modified binary tree in the fast multipole method (FMM) included into the modified parametric integral equations system (PIES), called the fast PIES, in solving potential 2D boundary value problems with complex shapes. The modified binary tree proposed in this paper is built bas...

Descripción completa

Detalles Bibliográficos
Autores principales: Kużelewski, Andrzej, Zieniuk, Eugeniusz, Bołtuć, Agnieszka, Szerszeń, Krzystof
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7302565/
http://dx.doi.org/10.1007/978-3-030-50417-5_1
_version_ 1783547872771309568
author Kużelewski, Andrzej
Zieniuk, Eugeniusz
Bołtuć, Agnieszka
Szerszeń, Krzystof
author_facet Kużelewski, Andrzej
Zieniuk, Eugeniusz
Bołtuć, Agnieszka
Szerszeń, Krzystof
author_sort Kużelewski, Andrzej
collection PubMed
description The paper presents a modified binary tree in the fast multipole method (FMM) included into the modified parametric integral equations system (PIES), called the fast PIES, in solving potential 2D boundary value problems with complex shapes. The modified binary tree proposed in this paper is built based on a one-dimensional reference system contrary to a quad-tree (based on a two-dimensional reference system) which is applied in the fast multipole boundary element method (FM-BEM). Application of the proposed tree allows reducing the number of numerical computations performed during its construction and fast multipole calculations in the fast PIES. The proposed modification of the tree in the fast PIES allows obtaining accurate solutions in engineering problems with complex shapes on a standard personal computer in a short time.
format Online
Article
Text
id pubmed-7302565
institution National Center for Biotechnology Information
language English
publishDate 2020
record_format MEDLINE/PubMed
spelling pubmed-73025652020-06-19 Modified Binary Tree in the Fast PIES for 2D Problems with Complex Shapes Kużelewski, Andrzej Zieniuk, Eugeniusz Bołtuć, Agnieszka Szerszeń, Krzystof Computational Science – ICCS 2020 Article The paper presents a modified binary tree in the fast multipole method (FMM) included into the modified parametric integral equations system (PIES), called the fast PIES, in solving potential 2D boundary value problems with complex shapes. The modified binary tree proposed in this paper is built based on a one-dimensional reference system contrary to a quad-tree (based on a two-dimensional reference system) which is applied in the fast multipole boundary element method (FM-BEM). Application of the proposed tree allows reducing the number of numerical computations performed during its construction and fast multipole calculations in the fast PIES. The proposed modification of the tree in the fast PIES allows obtaining accurate solutions in engineering problems with complex shapes on a standard personal computer in a short time. 2020-06-15 /pmc/articles/PMC7302565/ http://dx.doi.org/10.1007/978-3-030-50417-5_1 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Kużelewski, Andrzej
Zieniuk, Eugeniusz
Bołtuć, Agnieszka
Szerszeń, Krzystof
Modified Binary Tree in the Fast PIES for 2D Problems with Complex Shapes
title Modified Binary Tree in the Fast PIES for 2D Problems with Complex Shapes
title_full Modified Binary Tree in the Fast PIES for 2D Problems with Complex Shapes
title_fullStr Modified Binary Tree in the Fast PIES for 2D Problems with Complex Shapes
title_full_unstemmed Modified Binary Tree in the Fast PIES for 2D Problems with Complex Shapes
title_short Modified Binary Tree in the Fast PIES for 2D Problems with Complex Shapes
title_sort modified binary tree in the fast pies for 2d problems with complex shapes
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7302565/
http://dx.doi.org/10.1007/978-3-030-50417-5_1
work_keys_str_mv AT kuzelewskiandrzej modifiedbinarytreeinthefastpiesfor2dproblemswithcomplexshapes
AT zieniukeugeniusz modifiedbinarytreeinthefastpiesfor2dproblemswithcomplexshapes
AT bołtucagnieszka modifiedbinarytreeinthefastpiesfor2dproblemswithcomplexshapes
AT szerszenkrzystof modifiedbinarytreeinthefastpiesfor2dproblemswithcomplexshapes

Ejemplares similares