Simultaneous single-step one-shot optimization with unsteady PDEs

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• 作者：Stefanie Gü ; nther^a ; ^{stefanie.guenther@scicomp.uni-kl.de" class="auth_mail" title="E-mail the corresponding author} ; Nicolas R. Gauger^a ; Qiqi Wang^b
• 关键词：Simultaneous optimization ; One-shot method ; PDE-constrained optimization ; Unsteady PDE ; Adaptive time scale
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：1 March 2016
• 年：2016
• 卷：294
• 期：Complete
• 页码：12-22
• 全文大小：1471 K

文摘

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.