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...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
The Japan Society of Mechanical Engineers
2014-08-01
|
| Series: | Mechanical Engineering Journal |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/mej/1/4/1_2014cm0039/_pdf/-char/en |
| _version_ | 1831771213315178496 |
|---|---|
| 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 |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-22T07:55:19Z |
| format | Article |
| id | doaj.art-20d4254b076a447a9b6c6c2d3f5926b0 |
| institution | Directory Open Access Journal |
| issn | 2187-9745 |
| language | English |
| last_indexed | 2024-12-22T07:55:19Z |
| publishDate | 2014-08-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Mechanical Engineering Journal |
| spelling | doaj.art-20d4254b076a447a9b6c6c2d3f5926b02022-12-21T18:33:22ZengThe Japan Society of Mechanical EngineersMechanical Engineering Journal2187-97452014-08-0114CM0039CM003910.1299/mej.2014cm0039mejA topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element methodHiroshi ISAKARI0Kohei KURIYAMA1Shinya HARADA2Takayuki YAMADA3Toru TAKAHASHI4Toshiro MATSUMOTO5Department of Mechanical Science and Engineering, Nagoya UniversityDepartment of Mechanical Science and Engineering, Nagoya UniversityDepartment of Mechanical Science and Engineering, Nagoya UniversityDepartment of Mechanical Engineering and Science, Kyoto UniversityDepartment of Mechanical Science and Engineering, Nagoya UniversityDepartment of Mechanical Science and Engineering, Nagoya UniversityWe 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.https://www.jstage.jst.go.jp/article/mej/1/4/1_2014cm0039/_pdf/-char/enfast multipole methodboundary element methodacousticslevel set methodtopology optimisationwave scatteringtopological derivative |
| spellingShingle | 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 Mechanical Engineering Journal fast multipole method boundary element method acoustics level set method topology optimisation wave scattering topological derivative |
| title | 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_short | 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 |
| topic | fast multipole method boundary element method acoustics level set method topology optimisation wave scattering topological derivative |
| url | https://www.jstage.jst.go.jp/article/mej/1/4/1_2014cm0039/_pdf/-char/en |
| work_keys_str_mv | AT hiroshiisakari atopologyoptimisationforthreedimensionalacousticswiththelevelsetmethodandthefastmultipoleboundaryelementmethod AT koheikuriyama atopologyoptimisationforthreedimensionalacousticswiththelevelsetmethodandthefastmultipoleboundaryelementmethod AT shinyaharada atopologyoptimisationforthreedimensionalacousticswiththelevelsetmethodandthefastmultipoleboundaryelementmethod AT takayukiyamada atopologyoptimisationforthreedimensionalacousticswiththelevelsetmethodandthefastmultipoleboundaryelementmethod AT torutakahashi atopologyoptimisationforthreedimensionalacousticswiththelevelsetmethodandthefastmultipoleboundaryelementmethod AT toshiromatsumoto atopologyoptimisationforthreedimensionalacousticswiththelevelsetmethodandthefastmultipoleboundaryelementmethod AT hiroshiisakari topologyoptimisationforthreedimensionalacousticswiththelevelsetmethodandthefastmultipoleboundaryelementmethod AT koheikuriyama topologyoptimisationforthreedimensionalacousticswiththelevelsetmethodandthefastmultipoleboundaryelementmethod AT shinyaharada topologyoptimisationforthreedimensionalacousticswiththelevelsetmethodandthefastmultipoleboundaryelementmethod AT takayukiyamada topologyoptimisationforthreedimensionalacousticswiththelevelsetmethodandthefastmultipoleboundaryelementmethod AT torutakahashi topologyoptimisationforthreedimensionalacousticswiththelevelsetmethodandthefastmultipoleboundaryelementmethod AT toshiromatsumoto topologyoptimisationforthreedimensionalacousticswiththelevelsetmethodandthefastmultipoleboundaryelementmethod |