Type of Publication:  Diploma thesis 
URI (citable link):  http://nbnresolving.de/urn:nbn:de:bsz:3520283508 
Author:  Beermann, Dennis 
Year of publication:  2015 
Summary: 
The thesis investigates a onedimensional, hyperbolic evolution equation containing one structural variable, with a particular focus on a model of erythropoiesis developed by Fürtinger et al. in 2012. Three di erent discretization techniques which all result in socalled highfidility or detailed solutions are introduced and discussed. The methods used include Finite Differences and a polynomial representation of the structural variable. Viewed from the perspective of Optimal control, the model takes the form of a Parametrized Partial Di erential Equation (P2DE) where both the control and other data values are treated as parameters of the equation. This places the problem into a multiquery context, making model order reduction (MOR) techniques conceivable. Reduced basis (RB) strategies are employed to reduce the dimension of the utilized discretization spaces with a Galerkin projection. The reduced space is generated by applying a Greedy algorithm with methods including both the addition of single snapshots as well as Proper Orthogonal Decomposition (POD). In order to assess the error between the detailed and the reduced solution, two aposteriori estimators are introduced and analyzed. Algorithmically, an offine/online decomposition scheme is used to enable e cient computations of both the reduced solutions and the estimators. Lastly, numerical experiments are presented to evaluate the feasibility of model order reduction techniques for the problem at hand.

Dissertation note:  Master thesis, Univ. 
Subject (DDC):  510 Mathematics 
Keywords:  model order reduction, reduced basis, aposteriori error estimates, proper orthogonal decomposition, greedy algorithm, erythropoiesis 
Comment on publication:  Diplomarbeit 
Link to License:  In Copyright 
Bibliography of Konstanz:  Yes 
BEERMANN, Dennis, 2015. Reducedorder methods for a parametrized model for erythropoiesis involving structured population equations with one structural variable [Master thesis]. Konstanz: Univ.
@mastersthesis{Beermann2015Reduc30201, title={Reducedorder methods for a parametrized model for erythropoiesis involving structured population equations with one structural variable}, year={2015}, address={Konstanz}, school={Univ.}, author={Beermann, Dennis}, note={Diplomarbeit} }
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22rdfsyntaxns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digitalrepositories.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.unikonstanz.de/rdf/resource/123456789/30201"> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <bibo:uri rdf:resource="http://kops.unikonstanz.de/handle/123456789/30201"/> <dcterms:issued>2015</dcterms:issued> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">20150311T13:10:38Z</dcterms:available> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:abstract xml:lang="eng">The thesis investigates a onedimensional, hyperbolic evolution equation containing one structural variable, with a particular focus on a model of erythropoiesis developed by Fürtinger et al. in 2012. Three di erent discretization techniques which all result in socalled highfidility or detailed solutions are introduced and discussed. The methods used include Finite Differences and a polynomial representation of the structural variable. Viewed from the perspective of Optimal control, the model takes the form of a Parametrized Partial Di erential Equation (P2DE) where both the control and other data values are treated as parameters of the equation. This places the problem into a multiquery context, making model order reduction (MOR) techniques conceivable. Reduced basis (RB) strategies are employed to reduce the dimension of the utilized discretization spaces with a Galerkin projection. The reduced space is generated by applying a Greedy algorithm with methods including both the addition of single snapshots as well as Proper Orthogonal Decomposition (POD). In order to assess the error between the detailed and the reduced solution, two aposteriori estimators are introduced and analyzed. Algorithmically, an offine/online decomposition scheme is used to enable e cient computations of both the reduced solutions and the estimators. Lastly, numerical experiments are presented to evaluate the feasibility of model order reduction techniques for the problem at hand.</dcterms:abstract> <dc:contributor>Beermann, Dennis</dc:contributor> <dspace:hasBitstream rdf:resource="https://kops.unikonstanz.de/bitstream/123456789/30201/3/Beermann_0283508.pdf"/> <dc:language>eng</dc:language> <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/> <dcterms:isPartOf rdf:resource="https://kops.unikonstanz.de/rdf/resource/123456789/39"/> <dc:rights>termsofuse</dc:rights> <dcterms:hasPart rdf:resource="https://kops.unikonstanz.de/bitstream/123456789/30201/3/Beermann_0283508.pdf"/> <dc:creator>Beermann, Dennis</dc:creator> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">20150311T13:10:38Z</dc:date> <dcterms:title>Reducedorder methods for a parametrized model for erythropoiesis involving structured population equations with one structural variable</dcterms:title> <dspace:isPartOfCollection rdf:resource="https://kops.unikonstanz.de/rdf/resource/123456789/39"/> </rdf:Description> </rdf:RDF>
Beermann_0283508.pdf  529 