A variational binary level-set method for elliptic shape optimization problems

被引：5
|
作者：
Zhu, Shengfeng [1 ]
Dai, Xiaoxia [2 ]
Liu, Chunxiao [3 ]
机构：
[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China
[2] Zhejiang Univ City Coll, Hangzhou 310015, Zhejiang, Peoples R China
[3] Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Zhejiang, Peoples R China
来源：
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2011年 / 88卷 / 14期
关键词：
shape optimization; topology optimization; level-set method; binary level-set method; augmented Lagrangian method; INCORPORATING TOPOLOGICAL DERIVATIVES; INVERSE PROBLEMS; DESIGN; MODEL;
D O I：
10.1080/00207160.2011.565873
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a variational binary level-set method to solve a class of elliptic problems in shape optimization. By the 'ersatz material' approach, which amounts to fill the holes by a weak phase, the original shape optimization model is approximated by a two-phase optimization problem. Under the binary level-set framework, we need to optimize a smooth functional under a binary constraint. We propose an augmented Lagrangian method to solve the constrained optimization problem. Numerical results are presented and compared with those obtained by level-set methods, which demonstrate the robustness and efficiency of our method.
引用
收藏
页码：3026 / 3045
页数：20
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