Optimal actuator design based on shape calculus

被引：15

作者：

Kalise, Dante ^{[1
]}

Kunisch, Karl ^{[2
,3
]}

Sturm, Kevin ^{[4
]}

机构：

[1] Imperial Coll London, Dept Math, South Kensington Campus, London SW7 2AZ, England

[2] Johann Radon Inst Computat & Appl Math, Altenbergerstr 69, Linz, Austria

[3] Karl Franzens Univ Graz, Inst Anal & Sci Comp, Heinrichstr, A-368010 Graz, Austria

[4] Vienna Univ Technol, Inst Anal & Sci Comp, Hauptstr 8-10, A-1040 Vienna, Austria

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2018年 / 28卷 / 13期

基金：

欧盟地平线“2020”;

关键词：

Shape optimization; optimal feedback control; topological derivative; shape derivative; level-set method; OPTIMAL LOCATION; OPTIMIZATION; DIFFERENTIABILITY; CONTROLLERS; EQUATION; SYSTEMS;

D O I：

10.1142/S0218202518500586

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An approach to optimal actuator design based on shape and topology optimization techniques is presented. For linear diffusion equations, two scenarios are considered. For the first one, best actuators are determined depending on a given initial condition. In the second scenario, optimal actuators are determined based on all initial conditions not exceeding a chosen norm. Shape and topological sensitivities of these cost functionals are determined. A numerical algorithm for optimal actuator design based on the sensitivities and a level-set method is presented. Numerical results support the proposed methodology.

引用

页码：2667 / 2717

页数：51

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