Worst-case shape optimization for the Dirichlet energy

被引:7
|
作者
Bellido, Jose Carlos [1 ]
Buttazzo, Giuseppe [2 ]
Velichkov, Bozhidar [3 ]
机构
[1] Univ Castilla La Mancha, Dept Matemat, ETSII, E-13071 Ciudad Real, Spain
[2] Univ Pisa, Dipartimento Matemat, Largo B Pontecorvo 5, I-56127 Pisa, Italy
[3] Univ Grenoble, Lab Jean Kuntzmann, F-88041 Grenoble 09, France
关键词
Shape optimization; Dirichlet energy; Worst-case optimization;
D O I
10.1016/j.na.2016.05.014
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider the optimization problem for a shape cost functional F(Omega, f) which depends on a domain Omega varying in a suitable admissible class and on a "right-hand side" f. More precisely, the cost functional F is given by an integral which involves the solution u of an elliptic PDE in Omega with right-hand side f; the boundary conditions considered are of the Dirichlet type. When the function f is only known up to some degree of uncertainty, our goal is to obtain the existence of an optimal shape in the worst possible situation. Some numerical simulations are provided, showing the difference in the optimal shape between the case when f is perfectly known and the case when only the worst situation is optimized. (C) 2016 Elsevier Ltd. All rights reserved.
引用
收藏
页码:117 / 129
页数:13
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