Shape and topology optimization for elliptic boundary value problems using a piecewise constant level set method

被引：19
作者：
Zhu, Shengfeng [1 ]
Wu, Qingbiao [1 ]
Liu, Chunxiao [2 ]
机构：
[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China
[2] Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Zhejiang, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2011年 / 61卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Shape optimization; Topology optimization; Piecewise constant level set method; Projection Lagrangian method; INVERSE PROBLEMS; DERIVATIVES; SENSITIVITY; ALGORITHMS; MODEL;
D O I：
10.1016/j.apnum.2011.01.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The aim of this paper is to propose a variational piecewise constant level set method for solving elliptic shape and topology optimization problems. The original model is approximated by a two-phase optimal shape design problem by the ersatz material approach. Under the piecewise constant level set framework, we first reformulate the two-phase design problem to be a new constrained optimization problem with respect to the piecewise constant level set function. Then we solve it by the projection Lagrangian method. A gradient-type iterative algorithm is presented. Comparisons between our numerical results and those obtained by level set approaches show the effectiveness, accuracy and efficiency of our algorithm. (C) 2011 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：752 / 767
页数：16
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