Simultaneous single-step one-shot optimization with unsteady PDEs
Author(s)
Günther, Stefanie; Gauger, Nicolas R.; Wang, Qiqi
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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
Date issued
2015-08Department
Massachusetts Institute of Technology. Department of Aeronautics and AstronauticsJournal
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
ISSN
0377-0427