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

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.