An approximation for the boundary optimal control problem of a heat equation defined in a variable domain

作     者：于欣 任志刚 许超 

作者机构：Ningbo Institute of Technology Zhejiang University The State Key Laboratory of Industrial Control Technology and Institute of Cyber-Systems & Control Zhejiang University 

出 版 物：《Chinese Physics B》 (中国物理B（英文版）)

年 卷 期：2014年第23卷第4期

页      面：76-82页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 0702[理学-物理学] 

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.61374096 and 61104048) the Natural Science Foundation of Zhejiang Province of China(Grant No.Y6110751) 

主　　题：boundary optimal control heat equation variable domain finite element method control parame-terization method 

摘      要：In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming （SQP） algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.