Simultaneous single-step one-shot optimization with unsteady PDEs
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Stefanie Günther [2] ; Nicolas R. Gauger [2] ; Qiqi Wang [1]
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[1] Massachusetts Institute of Technology
Massachusetts Institute of Technology
City of Cambridge, Estados Unidos
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[2] Technischen Universität Kaiserslautern, Germany
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- Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 294, Nº 1 (1 March 2016), 2016, págs. 12-22
- Idioma: inglés
- DOI: 10.1016/j.cam.2015.07.033
- Enlaces
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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.
