Greedy Sampling Using Nonlinear Optimization

Type of Publication: Contribution to a collection
Publication status: Published
Author: Urban, Karsten; Volkwein, Stefan; Zeeb, Oliver
Year of publication: 2014
Published in: Reduced order methods for modeling and computational reduction / Quarteroni, Alfio et al. (ed.). - Cham [u.a.] : Springer, 2014. - (Modeling, Simulation & Applications ; 9). - pp. 137-157. - ISBN 978-3-319-02089-1
DOI (citable link): https://dx.doi.org/10.1007/978-3-319-02090-7_5
Summary:
We consider the reduced basis generation in the offline stage. As an alternative for standard Greedy-training methods based upon a-posteriori error estimates on a training subset of the parameter set, we consider a nonlinear optimization combined with a Greedy method. We define an optimization problem for selecting a new parameter value on a given reduced space. This new parameter is then used -in a Greedy fashion- to determine the corresponding snapshot and to update the reduced basis. We show the well-posedness of this nonlinear optimization problem and derive first- and second-order optimality conditions. Numerical comparisons with the standard Greedy-training method are shown.
Subject (DDC): 510 Mathematics
Bibliography of Konstanz: Yes

Cite This

Files in this item

Files Size Format View

There are no files associated with this item.

URBAN, Karsten, Stefan VOLKWEIN, Oliver ZEEB, 2014. Greedy Sampling Using Nonlinear Optimization. In: QUARTERONI, Alfio, ed. and others. Reduced order methods for modeling and computational reduction. Cham [u.a.]:Springer, pp. 137-157. ISBN 978-3-319-02089-1. Available under: doi: 10.1007/978-3-319-02090-7_5

@incollection{Urban2014Greed-32973, title={Greedy Sampling Using Nonlinear Optimization}, year={2014}, doi={10.1007/978-3-319-02090-7_5}, number={9}, isbn={978-3-319-02089-1}, address={Cham [u.a.]}, publisher={Springer}, series={Modeling, Simulation & Applications}, booktitle={Reduced order methods for modeling and computational reduction}, pages={137--157}, editor={Quarteroni, Alfio}, author={Urban, Karsten and Volkwein, Stefan and Zeeb, Oliver} }

<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/32973"> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dc:language>eng</dc:language> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2016-02-15T14:06:11Z</dc:date> <dcterms:issued>2014</dcterms:issued> <dc:contributor>Zeeb, Oliver</dc:contributor> <dcterms:title>Greedy Sampling Using Nonlinear Optimization</dcterms:title> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/32973"/> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:creator>Urban, Karsten</dc:creator> <dc:creator>Zeeb, Oliver</dc:creator> <dc:contributor>Volkwein, Stefan</dc:contributor> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dc:contributor>Urban, Karsten</dc:contributor> <dcterms:abstract xml:lang="eng">We consider the reduced basis generation in the offline stage. As an alternative for standard Greedy-training methods based upon a-posteriori error estimates on a training subset of the parameter set, we consider a nonlinear optimization combined with a Greedy method. We define an optimization problem for selecting a new parameter value on a given reduced space. This new parameter is then used -in a Greedy fashion- to determine the corresponding snapshot and to update the reduced basis. We show the well-posedness of this nonlinear optimization problem and derive first- and second-order optimality conditions. Numerical comparisons with the standard Greedy-training method are shown.</dcterms:abstract> <dc:creator>Volkwein, Stefan</dc:creator> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2016-02-15T14:06:11Z</dcterms:available> </rdf:Description> </rdf:RDF>

This item appears in the following Collection(s)

Search KOPS


Browse

My Account