Adaptive POD basis computation for parametrized nonlinear systems using optimal snapshot location

Oliver Lass () and Stefan Volkwein ()

Computational Optimization and Applications, 2014, vol. 58, issue 3, 645-677

Abstract: The construction of reduced-order models for parametrized partial differential systems using proper orthogonal decomposition (POD) is based on the information of the so-called snapshots. These provide the spatial distribution of the nonlinear system at discrete parameter and/or time instances. In this work a strategy is used, where the POD reduced-order model is improved by choosing additional snapshot locations in an optimal way; see Kunisch and Volkwein (ESAIM: M2AN, 44:509–529, 2010 ). These optimal snapshot locations influences the POD basis functions and therefore the POD reduced-order model. This strategy is used to build up a POD basis on a parameter set in an adaptive way. The approach is illustrated by the construction of the POD reduced-order model for the complex-valued Helmholtz equation. Copyright Springer Science+Business Media New York 2014

Keywords: Proper orthogonal decomposition; Optimal control; Optimality conditions; Reduced-order modeling (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10589-014-9646-z

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