周期热传导方程优化控制问题的一种迭代解法  

An iterative solver for time-periodic heat optimal control problems

作　　者：李科 郭大立[1] 赵云祥 LI Ke;GUODa-Li;ZHAO Yun-Xiang(School of Science,Southwest Petroleum University,Chengdu 610500,China;School of Mathematics and Statistics,Sichuan University of Science and Engineering,Zigong 643000,China;School of Science,Civil Aviation Flight University o£China,Deyang 618300,China)

机构地区：[1]西南石油大学理学院,成都610500 [2]四川轻化工大学数学与统计学院,自贡643000 [3]中国民航飞行学院理学院,德阳618300

出　　处：《四川大学学报（自然科学版）》2022年第4期10-16,共7页Journal of Sichuan University(Natural Science Edition)

基　　金：国家重大专项基金(2016ZX05065,2016ZX05042-003)

摘　　要：本文研究了一类以时间周期热传导方程为约束条件的优化控制问题,该优化问题旨在寻求使得目标泛函达到最小的源项.本文提出了一种迭代求解算法.该算法应用最优性条件将问题转化为两个耦合的时间周期热传导方程,然后将这两个方程迭代解耦,再以Gauss-Seidel模式交替求解.数值算例显示,算法的收敛速度对离散参数是稳健的.In this paper,an iterative algorithm is introduced for solving a class of optimal control problems constrained by time-periodic heat equation,where the optimization is concerned by searching a best source term of the heat equation to minimize the objective function.By applying the optimality condition,the problem is firstly transformed into two coupled time-periodic heat equations.Then the iterative algorithm is applied to decouple the coupled PDE system.Finally,the equations are separately solved in the Gauss-Seidel pattern.Numerical examples are presented to illustrate the robustness of the convergence rate of algorithm with respect to the discretization parameters.

关 键 词：周期热传导方程 优化控制 迭代 

分 类 号：O242.1[理学—计算数学]