TY - JOUR
T1 - A variational binary level-set method for elliptic shape optimization problems
AU - Zhu, Shengfeng
AU - Dai, Xiaoxia
AU - Liu, Chunxiao
PY - 2011/9
Y1 - 2011/9
N2 - 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.
AB - 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.
KW - augmented Lagrangian method
KW - binary level-set method
KW - level-set method
KW - shape optimization
KW - topology optimization
UR - https://www.scopus.com/pages/publications/80052176385
U2 - 10.1080/00207160.2011.565873
DO - 10.1080/00207160.2011.565873
M3 - 文章
AN - SCOPUS:80052176385
SN - 0020-7160
VL - 88
SP - 3026
EP - 3045
JO - International Journal of Computer Mathematics
JF - International Journal of Computer Mathematics
IS - 14
ER -