Show simple item record

AuthorZeeb, Oliverdc.contributor.author
Date of accession2016-03-15T10:40:23Zdc.date.accessioned
Available in OPARU since2016-03-15T10:40:23Zdc.date.available
Year of creation2015dc.date.created
AbstractThe Reduced Basis Method (RBM) has become a widespread model reduction technique for parametrized partial differential equations in the past few years. Yet, it has not found its way into automated commercial or open-source simulation software so far. One problem that has to be addressed is the Greedy algorithm which classically is based on a parameter grid. The curse of dimensionality let these grids grow exponentially with the number of parameters. For higher dimensions this fact prohibits the usage of sufficiently large training sets in the offine phase, so other techniques have to be used. We investigate an optimization based Greedy algorithm and present different strategies for the choice of the initial values. Further, for the application of the RBM deeper knowledge about the underlying problem, such as its affine decomposition, is usually provided. This is not always the case, especially if commercial software packages are used for the simulation. They are considered as blackboxes where the internal structures are not accessible. With the Operator Extraction Method we present a method that is capable to determine an affine decomposition in this context which in turn can be used for the Reduced Basis Method. It is based on linear independence and interpolation or regression methods. The introduced method is examined with several models to show its applicability. The combination of these two approaches is a step into the direction of automated RBMs which can be included into user friendly software. In the context of this thesis the software package RB-COM was developed and is presented here as well. It is based on RBmatlab and provides a possibility to the automated treatment of linear stationary models which were generated with COMSOL Multiphysics 4.2a with the Reduced Basis Method. No deeper knowledge, neither about COMSOL, nor RBmatlab, nor the underlying model is required.dc.description.abstract
Languageendc.language.iso
PublisherUniversität Ulmdc.publisher
LicenseStandarddc.rights
Link to license texthttps://oparu.uni-ulm.de/xmlui/license_v3dc.rights.uri
KeywordBlackbox solverdc.subject
KeywordGreedy Algorithmdc.subject
KeywordRBmatlabdc.subject
KeywordReduced basis methoddc.subject
Dewey Decimal GroupDDC 510 / Mathematicsdc.subject.ddc
LCSHMaxwell equations; Mathematicsdc.subject.lcsh
LCSHOptimizationdc.subject.lcsh
TitleA numerical framework for semi-automated reduced basis methods with blackbox solversdc.title
Resource typeDissertationdc.type
DOIhttp://dx.doi.org/10.18725/OPARU-3278dc.identifier.doi
PPN830300031dc.identifier.ppn
URNhttp://nbn-resolving.de/urn:nbn:de:bsz:289-vts-95949dc.identifier.urn
GNDGreedy-Algorithmusdc.subject.gnd
GNDOptimierungdc.subject.gnd
GNDReduzierte-Basis-Methodedc.subject.gnd
FacultyFakultät für Mathematik und Wirtschaftswissenschaftenuulm.affiliationGeneral
Date of activation2015-07-03T16:00:46Zuulm.freischaltungVTS
Peer reviewneinuulm.peerReview
Shelfmark print versionW: W-H 14.239uulm.shelfmark
DCMI TypeTextuulm.typeDCMI
VTS ID9594uulm.vtsID
CategoryPublikationenuulm.category
Bibliographyuulmuulm.bibliographie


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record