One-shot solution of a time-dependent time-periodic PDE-constrained optimization problem / Martin Stoll
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870175017
URN
urn:nbn:de:gbv:3:2-63818
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Beiträger
Erschienen
Magdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, July 19, 2011
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1 Online-Ressource (22 Seiten = 1,01 MB) : Diagramme
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Sprache
eng
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Inhaltliche Zusammenfassung
Abstract: In this paper we describe the efficient solution of a PDE-constrained optimization problem subject to the time-periodic heat equation. We propose a space-time formulation for which we develop a monolithic solver. We present preconditioners well suited to approximate the Schur-complement of the saddle point system associated with the first order conditions. This means that in addition to a Richardson iteration based preconditioner we also introduce a preconditioner based on the tensor product structure of the PDE discretization, which allows the use of a FFT based preconditioner. We also consider additional bound constraints that can be treated using a semi-smooth Newton method. Moreover, we introduce robust preconditioners with respect to the regularization parameter. Numerical results will illustrate the competitiveness and flexibility of our approach.
Schriftenreihe
Max Planck Institute Magdeburg Preprints ; 11-04 ppn:870173030