IMPROVED DISCRETE BOUNDARY TYPE SHAPE GRADIENTS FOR PDE-CONSTRAINED SHAPE OPTIMIZATION
文献类型：期刊论文
| 作者 | Gong, Wei1,2; Li, Jiajie3; Zhu, Shengfeng4,5 |
| 刊名 | SIAM JOURNAL ON SCIENTIFIC COMPUTING
 |
| 出版日期 | 2022 |
| 卷号 | 44期号:4页码:A2464-A2505 |
| 关键词 | shape optimization shape gradient boundary formulation boundary correction gradient recovery finite element method |
| ISSN号 | 1064-8275 |
| DOI | 10.1137/21M1457400 |
| 英文摘要 | We propose in this paper two kinds of continuity preserving discrete shape gradients of boundary type for PDE-constrained shape optimizations. First, a modified boundary shape gradient formula for shape optimization problems governed by elliptic Dirichlet problems was proposed recently based on the discrete variational outward normal derivatives. The advantages of this new formula over the previous one lie in the improved numerical accuracy and the continuity along the boundary. In the current paper we generalize this new formula to other shape optimization problems including the Laplace and Stokes eigenvalue optimization problems, the shape optimization of Stokes or Navier-Stokes flows, and the interface identification problems. We verify this new formula's numerical accuracy in different shape optimization problems and investigate its performance in several popular shape optimization algorithms. The second contribution of this paper is to propose a continuous discrete shape gradients of boundary type for Neumann problems, by using the ideas of gradient recovery techniques. The continuity property of the discrete boundary shape gradient is helpful in certain shape optimization algorithms and provides certain flexibility compared to the previous discontinuous ones, which are extensively discussed in the current paper. |
| 资助项目 | Strategic Priority Research Program of the Chinese Academy of Sciences[XDB 41000000] ; National Key Basic Research Program[2018YFB0704304] ; NSFC[12071149] ; Science and Technology Commission of Shanghai Municipality[18dz2271000] ; Science and Technology Commission of Shanghai Municipality[21JC1402500] ; Science and Technology Commission of Shanghai Municipality[19ZR1414100] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000881310800018 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60431]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Gong, Wei |
| 作者单位 | 1.Chinese Acad Sci, NCMIS, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China 3.East China Normal Univ, Dept Math, Shanghai 200241, Peoples R China 4.East China Normal Univ, Shanghai Key Lab Pure Math & Math Practice, Shanghai 200241, Peoples R China 5.East China Normal Univ, Dept Math, Shanghai 200241, Peoples R China |
| 推荐引用方式 GB/T 7714 | Gong, Wei,Li, Jiajie,Zhu, Shengfeng. IMPROVED DISCRETE BOUNDARY TYPE SHAPE GRADIENTS FOR PDE-CONSTRAINED SHAPE OPTIMIZATION[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2022,44(4):A2464-A2505. |
| APA | Gong, Wei,Li, Jiajie,&Zhu, Shengfeng.(2022).IMPROVED DISCRETE BOUNDARY TYPE SHAPE GRADIENTS FOR PDE-CONSTRAINED SHAPE OPTIMIZATION.SIAM JOURNAL ON SCIENTIFIC COMPUTING,44(4),A2464-A2505. |
| MLA | Gong, Wei,et al."IMPROVED DISCRETE BOUNDARY TYPE SHAPE GRADIENTS FOR PDE-CONSTRAINED SHAPE OPTIMIZATION".SIAM JOURNAL ON SCIENTIFIC COMPUTING 44.4(2022):A2464-A2505. |
入库方式： OAI收割
来源：数学与系统科学研究院
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