FreeFEM++ code for reaction-diffusion equation–based topology optimization: for high-resolution boundary representation using adaptive mesh refinement
In this article, we present a simple FreeFEM++ code to represent high-resolution boundaries of the optimal shape using reaction-diffusion equation–based topology optimization and adaptive mesh refinement. The design algorithm is divided into two parts to achieve a high quality of the boundary. In th...
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| Veröffentlicht in: | Structural and multidisciplinary optimization 2020-07, Vol.62 (1), p.439-455 |
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| creator | Kim, Cheolwoong Jung, Mingook Yamada, Takayuki Nishiwaki, Shinji Yoo, Jeonghoon |
| description | In this article, we present a simple FreeFEM++ code to represent high-resolution boundaries of the optimal shape using reaction-diffusion equation–based topology optimization and adaptive mesh refinement. The design algorithm is divided into two parts to achieve a high quality of the boundary. In the first part, loop 1, the ordinary method for a reaction-diffusion equation–based topology optimization, is applied to obtain the optimal shape. In the second part, loop 2, a modified reaction-diffusion equation combined with a double well potential, is employed as an optimizer and the adaptive mesh refinement is used with a gradual decrease of the diffusion coefficient. Because the code is intended for educational purposes, this paper provides background knowledge for understanding of the finite element method and topology optimization. Various numerical examples are discussed to confirm the robustness of the proposed design algorithm. The corresponding code may be downloaded from the website
http://ssd.yonsei.ac.kr
. |
| doi_str_mv | 10.1007/s00158-020-02498-3 |
| format | Article |
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http://ssd.yonsei.ac.kr
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http://ssd.yonsei.ac.kr
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Jung, Mingook ; Yamada, Takayuki ; Nishiwaki, Shinji ; Yoo, Jeonghoon</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3003-87ef147f7f1e42bb031264849f1d85908a5087ced8f448c151f75a256917481c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Adaptive algorithms</topic><topic>Boundary representation</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Diffusion</topic><topic>Diffusion coefficient</topic><topic>Educational Paper</topic><topic>Engineering</topic><topic>Engineering Design</topic><topic>Finite element method</topic><topic>Grid refinement (mathematics)</topic><topic>High resolution</topic><topic>Mathematical analysis</topic><topic>Nonlinear programming</topic><topic>Optimization</topic><topic>Reaction-diffusion equations</topic><topic>Robustness (mathematics)</topic><topic>Theoretical and Applied Mechanics</topic><topic>Topology optimization</topic><topic>Websites</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kim, Cheolwoong</creatorcontrib><creatorcontrib>Jung, Mingook</creatorcontrib><creatorcontrib>Yamada, Takayuki</creatorcontrib><creatorcontrib>Nishiwaki, Shinji</creatorcontrib><creatorcontrib>Yoo, Jeonghoon</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>Structural and multidisciplinary optimization</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kim, Cheolwoong</au><au>Jung, Mingook</au><au>Yamada, Takayuki</au><au>Nishiwaki, Shinji</au><au>Yoo, Jeonghoon</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>FreeFEM++ code for reaction-diffusion equation–based topology optimization: for high-resolution boundary representation using adaptive mesh refinement</atitle><jtitle>Structural and multidisciplinary optimization</jtitle><stitle>Struct Multidisc Optim</stitle><date>2020-07-01</date><risdate>2020</risdate><volume>62</volume><issue>1</issue><spage>439</spage><epage>455</epage><pages>439-455</pages><issn>1615-147X</issn><eissn>1615-1488</eissn><abstract>In this article, we present a simple FreeFEM++ code to represent high-resolution boundaries of the optimal shape using reaction-diffusion equation–based topology optimization and adaptive mesh refinement. 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http://ssd.yonsei.ac.kr
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| subjects | Adaptive algorithms Boundary representation Computational Mathematics and Numerical Analysis Diffusion Diffusion coefficient Educational Paper Engineering Engineering Design Finite element method Grid refinement (mathematics) High resolution Mathematical analysis Nonlinear programming Optimization Reaction-diffusion equations Robustness (mathematics) Theoretical and Applied Mechanics Topology optimization Websites |
| title | FreeFEM++ code for reaction-diffusion equation–based topology optimization: for high-resolution boundary representation using adaptive mesh refinement |
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