کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4638103 | 1631997 | 2016 | 11 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Simultaneous single-step one-shot optimization with unsteady PDEs Simultaneous single-step one-shot optimization with unsteady PDEs](/preview/png/4638103.png)
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.
Journal: Journal of Computational and Applied Mathematics - Volume 294, 1 March 2016, Pages 12–22