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Adaptive reduced basis methods for PDE-constrained optimization and optimal input design

Adaptive reduced basis methods for PDE-constrained optimization and optimal input design

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PETROCCHI, Andrea, Matthias K. SCHARRER, Stefan VOLKWEIN, 2022. Adaptive reduced basis methods for PDE-constrained optimization and optimal input design

@techreport{Petrocchi2022Adapt-56711.3, title={Adaptive reduced basis methods for PDE-constrained optimization and optimal input design}, year={2022}, author={Petrocchi, Andrea and Scharrer, Matthias K. and Volkwein, Stefan}, note={Corrected and updated version of:
http://nbn-resolving.de/urn:nbn:de:bsz:352-2-1l9b7uuht7b1s0} }

<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/123456789/56711.3"> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dc:rights>terms-of-use</dc:rights> <dc:creator>Volkwein, Stefan</dc:creator> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2022-08-02T11:18:55Z</dc:date> <dcterms:title>Adaptive reduced basis methods for PDE-constrained optimization and optimal input design</dcterms:title> <dc:contributor>Petrocchi, Andrea</dc:contributor> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/56711.3"/> <dc:creator>Scharrer, Matthias K.</dc:creator> <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/56711.3/3/Petrocchi_2-1t8ot6e09vv2e9.pdf"/> <dc:contributor>Volkwein, Stefan</dc:contributor> <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/> <dcterms:issued>2022</dcterms:issued> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:contributor>Scharrer, Matthias K.</dc:contributor> <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/56711.3/3/Petrocchi_2-1t8ot6e09vv2e9.pdf"/> <dc:creator>Petrocchi, Andrea</dc:creator> <dc:language>eng</dc:language> <dcterms:abstract xml:lang="eng">In this paper we propose an algorithm for the bi-level optimal input design involving a parameter-dependent evolution problem. In the inner cycle a control is fixed and the parameter is optimized in order to minimize a cost function that measure the discrepancy from some data. In the outer cycle the found parameter is fixed and the control is now optimized in order to minimize a suitable measure of uncertainty of the parameters. The inner cycle uses a trust-region reduced basis approximation of the model with creation and enrichment of the reduced basis on-the-fly. Numerical examples illustrate the efficiency of the proposed approach.In the inner cycle a control is fixed and the parameter is optimized in order to minimize a cost function that measure the discrepancy from some data. In the outer cycle the found parameter is fixed and the control is now optimized in order to minimize a suitable measure of uncertainty of the parameters. The inner cycle uses a trust-region reduced basis approximation of the model with creation and enrichment of the reduced basis on-the-fly. Numerical examples illustrate the efficiency of the proposed approach.</dcterms:abstract> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2022-08-02T11:18:55Z</dcterms:available> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> </rdf:Description> </rdf:RDF>

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