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POD‐Galerkin approximations in PDE‐constrained optimization
Author(s) -
Sachs Ekkehard W.,
Volkwein Stefan
Publication year - 2010
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201010015
Subject(s) - point of delivery , galerkin method , snapshot (computer storage) , nonlinear system , mathematics , proper orthogonal decomposition , partial differential equation , approximations of π , mathematical optimization , computer science , mathematical analysis , physics , quantum mechanics , agronomy , biology , operating system
Proper orthogonal decomposition (POD) is one of the most popular model reduction techniques for nonlinear partial differential equations. It is based on a Galerkin‐type approximation, where the POD basis functions contain information from a solution of the dynamical system at pre‐specified time instances, so‐called snapshots. POD models have been applied very successfully in the area of optimization with PDEs or feedback control laws. Nevertheless, various issues are still unclear and are currently under research, e.g. timely updates of the snapshot information and error analyses for the POD approximations (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)