Simultaneous single-step one-shot optimization with unsteady PDEs
Name
Wang_Simultaneous single-step.pdf
Size
1.38 MB
Format
Adobe PDF
Checksum (MD5)
3771398c2a1ebc8494691a3f02ecb6a1
Author(s)
Günther, Stefanie
Gauger, Nicolas R.
Wang, Qiqi
Date Issued
August 2015
Journal
Journal of Computational and Applied Mathematics
Publisher
Elsevier
Citation
Günther, Stefanie et al. “Simultaneous Single-Step One-Shot Optimization with Unsteady PDEs.” Journal of Computational and Applied Mathematics 294 (March 2016): 12–22 © 2015 Elsevier B.V.
Version
Author's final manuscript
Abstract
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. Keywords: Simultaneous optimization; One-shot method; PDE-constrained optimization; Unsteady PDE; Adaptive time scale
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.cam.2015.07.033
