流固耦合最优控制的牛顿多重网格框架
A Newton multigrid framework for optimal control of fluid-structure interactions
摘要：
本文研究非线性时变流固耦合系统的最优控制。为了确定依赖于时间的控制变量，使用BFGS算法，其中通过对偶问题计算梯度信息。为了解决由此产生的病态线性问题发生在每个时间步的状态和对偶方程，我们开发了一个高效的单片求解器，是基于近似牛顿计划的原始方程和预处理理查森迭代的对偶问题。所提出的算法的性能进行了测试的一个二维和三维的例子数值。
英文摘要：
In this paper we consider optimal control of nonlinear time-dependent fluid structure interactions. To determine a time-dependent control variable a BFGS algorithm is used, whereby gradient information is computed via a dual problem. To solve the resulting ill conditioned linear problems occurring in every time step of state and dual equation, we develop a highly efficient monolithic solver that is based on an approximated Newton scheme for the primal equation and a preconditioned Richardson iteration for the dual problem. The performance of the presented algorithms is tested for one 2d and one 3d example numerically.
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