Simultaneous single-step one-shot optimization with unsteady PDEs

• Stefanie Günther ^[2] ; Nicolas R. Gauger ^[2] ; Qiqi Wang ^[1]
  1. [1] Massachusetts Institute of Technology

     Massachusetts Institute of Technology

     City of Cambridge, Estados Unidos

     
  2. [2] Technischen Universität Kaiserslautern, Germany
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 294, Nº 1 (1 March 2016), 2016, págs. 12-22
• Idioma: inglés
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• Resumen

  • 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.