A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method

We have been investigating applications of a topology optimisation method with the level set method. In this study, to further enhance the applicability of the method, we investigate a topology optimisation method for three-dimensional scalar wave scattering problems which can be defined in an unbou...

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Autores principales:	Hiroshi ISAKARI, Kohei KURIYAMA, Shinya HARADA, Takayuki YAMADA, Toru TAKAHASHI, Toshiro MATSUMOTO
Formato:	article
Lenguaje:	EN
Publicado:	The Japan Society of Mechanical Engineers 2014
Materias:	fast multipole method boundary element method acoustics level set method topology optimisation wave scattering topological derivative Mechanical engineering and machinery TJ1-1570
Acceso en línea:	https://doaj.org/article/20d4254b076a447a9b6c6c2d3f5926b0
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spelling	oai:doaj.org-article:20d4254b076a447a9b6c6c2d3f5926b02021-11-26T06:09:52ZA topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method2187-974510.1299/mej.2014cm0039https://doaj.org/article/20d4254b076a447a9b6c6c2d3f5926b02014-08-01T00:00:00Zhttps://www.jstage.jst.go.jp/article/mej/1/4/1_2014cm0039/_pdf/-char/enhttps://doaj.org/toc/2187-9745We have been investigating applications of a topology optimisation method with the level set method. In this study, to further enhance the applicability of the method, we investigate a topology optimisation method for three-dimensional scalar wave scattering problems which can be defined in an unbounded domain. To this end, the fast multipole boundary element method (FMBEM), which can deal with the unbounded domain accurately and efficiently, is implemented in the proposed optimisation method. A detail of the algorithm of the topology optimisation with the level set method and the FMBEM is presented. Also, a rigorous derivation of the topological derivative, which characterises the sensitivity of the objective function when an infinitely small spherical object appears, using spherical functions is presented. After validating the topological derivatives with approximated ones, we show the efficiency of the proposed optimisation method with a numerical benchmark. Through these numerical experiments, we conclude that the proposed topological optimisation with the level set method and the FMBEM can be applied to scattering problems in acoustics.Hiroshi ISAKARIKohei KURIYAMAShinya HARADATakayuki YAMADAToru TAKAHASHIToshiro MATSUMOTOThe Japan Society of Mechanical Engineersarticlefast multipole methodboundary element methodacousticslevel set methodtopology optimisationwave scatteringtopological derivativeMechanical engineering and machineryTJ1-1570ENMechanical Engineering Journal, Vol 1, Iss 4, Pp CM0039-CM0039 (2014)
institution	DOAJ
collection	DOAJ
language	EN
topic	fast multipole method boundary element method acoustics level set method topology optimisation wave scattering topological derivative Mechanical engineering and machinery TJ1-1570
spellingShingle	fast multipole method boundary element method acoustics level set method topology optimisation wave scattering topological derivative Mechanical engineering and machinery TJ1-1570 Hiroshi ISAKARI Kohei KURIYAMA Shinya HARADA Takayuki YAMADA Toru TAKAHASHI Toshiro MATSUMOTO A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method
description	We have been investigating applications of a topology optimisation method with the level set method. In this study, to further enhance the applicability of the method, we investigate a topology optimisation method for three-dimensional scalar wave scattering problems which can be defined in an unbounded domain. To this end, the fast multipole boundary element method (FMBEM), which can deal with the unbounded domain accurately and efficiently, is implemented in the proposed optimisation method. A detail of the algorithm of the topology optimisation with the level set method and the FMBEM is presented. Also, a rigorous derivation of the topological derivative, which characterises the sensitivity of the objective function when an infinitely small spherical object appears, using spherical functions is presented. After validating the topological derivatives with approximated ones, we show the efficiency of the proposed optimisation method with a numerical benchmark. Through these numerical experiments, we conclude that the proposed topological optimisation with the level set method and the FMBEM can be applied to scattering problems in acoustics.
format	article
author	Hiroshi ISAKARI Kohei KURIYAMA Shinya HARADA Takayuki YAMADA Toru TAKAHASHI Toshiro MATSUMOTO
author_facet	Hiroshi ISAKARI Kohei KURIYAMA Shinya HARADA Takayuki YAMADA Toru TAKAHASHI Toshiro MATSUMOTO
author_sort	Hiroshi ISAKARI
title	A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method
title_short	A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method
title_full	A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method
title_fullStr	A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method
title_full_unstemmed	A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method
title_sort	topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method
publisher	The Japan Society of Mechanical Engineers
publishDate	2014
url	https://doaj.org/article/20d4254b076a447a9b6c6c2d3f5926b0
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A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method

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