Simultaneous Single-Step One-Shot Optimization with Unsteady PDEs
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.
Cite
@article{arxiv.1503.00884,
title = {Simultaneous Single-Step One-Shot Optimization with Unsteady PDEs},
author = {Stefanie Günther and Nicolas R. Gauger and Qiqi Wang},
journal= {arXiv preprint arXiv:1503.00884},
year = {2015}
}