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.

中文翻译：

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牛顿多网格框架，用于最佳控制流固耦合

在本文中，我们考虑了非线性时变流体结构相互作用的最优控制。为了确定时间相关的控制变量，使用BFGS算法，从而通过对偶问题计算梯度信息。为了解决在状态和对偶方程的每个时间步长中出现的病态线性问题，我们开发了一种高效的整体求解器，该求解器基于近似的牛顿方案（针对原始方程）和预处理的Richardson迭代（针对对偶问题）。数值测试了一个2d和一个3d示例的性能。