Two Algorithms for a Class of Elliptic Problems in Shape Optimization

Two Algorithms for a Class of Elliptic Problems in Shape Optimization

We propose two algorithms for elliptic boundary value problems in shape optimization. With the finite element method, the optimization problem is replaced by a discrete variational problem. We give rules and use them to decide which elements are to be reserved. Those rules are determined by the opt...

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Main Authors: Li Tian, Dai Xiaoxia, Zhang Chengwei
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2015/241837
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spelling doaj-ff5a19a7c6d14877979b1c9e7b234d712020-11-24T22:57:46ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472015-01-01201510.1155/2015/241837241837Two Algorithms for a Class of Elliptic Problems in Shape OptimizationLi Tian0Dai Xiaoxia1Zhang Chengwei2School of Computing Science, Zhejiang University City College, Hangzhou 310015, ChinaSchool of Computing Science, Zhejiang University City College, Hangzhou 310015, ChinaSchool of Computing Science, Zhejiang University City College, Hangzhou 310015, ChinaWe propose two algorithms for elliptic boundary value problems in shape optimization. With the finite element method, the optimization problem is replaced by a discrete variational problem. We give rules and use them to decide which elements are to be reserved. Those rules are determined by the optimization; as a result, we get the optimal design in shape. Numerical examples are provided to show the effectiveness of our algorithms.http://dx.doi.org/10.1155/2015/241837
collection DOAJ
language English
format Article
sources DOAJ
author Li Tian
Dai Xiaoxia
Zhang Chengwei
spellingShingle Li Tian
Dai Xiaoxia
Zhang Chengwei
Two Algorithms for a Class of Elliptic Problems in Shape Optimization
Mathematical Problems in Engineering
author_facet Li Tian
Dai Xiaoxia
Zhang Chengwei
author_sort Li Tian
title Two Algorithms for a Class of Elliptic Problems in Shape Optimization
title_short Two Algorithms for a Class of Elliptic Problems in Shape Optimization
title_full Two Algorithms for a Class of Elliptic Problems in Shape Optimization
title_fullStr Two Algorithms for a Class of Elliptic Problems in Shape Optimization
title_full_unstemmed Two Algorithms for a Class of Elliptic Problems in Shape Optimization
title_sort two algorithms for a class of elliptic problems in shape optimization
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2015-01-01
description We propose two algorithms for elliptic boundary value problems in shape optimization. With the finite element method, the optimization problem is replaced by a discrete variational problem. We give rules and use them to decide which elements are to be reserved. Those rules are determined by the optimization; as a result, we get the optimal design in shape. Numerical examples are provided to show the effectiveness of our algorithms.
url http://dx.doi.org/10.1155/2015/241837
work_keys_str_mv AT litian twoalgorithmsforaclassofellipticproblemsinshapeoptimization
AT daixiaoxia twoalgorithmsforaclassofellipticproblemsinshapeoptimization
AT zhangchengwei twoalgorithmsforaclassofellipticproblemsinshapeoptimization
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