具有非定常偏微分方程的同时单步单触发Optimization
Simultaneous Single-Step One-Shot Optimization with Unsteady PDEs
摘要：
单步一次法已被证明是非常有效的偏微分方程（PDE）的约束优化求解的迭代不动点求解器。在这种方法中，仿真和优化任务在一次迭代中同时执行。如果偏微分方程是不稳定的，找到一个适当的不动点迭代是不平凡的。在本文中，我们提供了一个框架，使单步一杆法适用于非定常偏微分方程，解决了经典的时间推进计划。将单次法应用于非定常不可压Navier-斯托克斯方程的最优控制问题，并通过工业标准模拟代码求解。将范德波尔振荡器作为一般模型问题，利用自适应时间尺度进一步改进了改进的仿真方案。最后给出了对流-扩散方程的数值结果。
英文摘要：
The single-step one-shot method has proven to be very efficient for PDE-constrained optimization where the partial differential equation (PDE) is solved by an iterative fixed point solver. In this approach, the simulation and optimization tasks are performed simultaneously in a single iteration. If the PDE is unsteady, finding an appropriate fixed point iteration is non-trivial. In this paper, we provide a framework that makes the single-step one-shot method applicable for unsteady PDEs that are solved by classical time-marching schemes. The One-shot method is applied to an optimal control problem with unsteady incompressible Navier-Stokes equations that are solved by an industry standard simulation code. With the Van-der-Pol oscillator as a generic model problem, the modified simulation scheme is further improved using adaptive time scales. Finally, numerical results for the advection-diffusion equation are presented.
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