Model reduction of parametrized systems PDF
Preview Model reduction of parametrized systems
MS&A – Modeling, Simulation and Applications 17 Peter Benner · Mario Ohlberger Anthony Patera · Gianluigi Rozza Karsten Urban Editors Model Reduction of Parametrized Systems MS&A Volume 17 Editor-in-Chief A.Quarteroni SeriesEditors T.Hou C.LeBris A.T.Patera E.Zuazua Moreinformationaboutthisseriesathttp://www.springer.com/series/8377 Peter Benner • Mario Ohlberger (cid:129) Anthony Patera (cid:129) Gianluigi Rozza (cid:129) Karsten Urban Editors Model Reduction of Parametrized Systems 123 Editors PeterBenner MarioOhlberger ComputationalMethodsinSystems InstituteforComputationalandApplied andControlTheory Mathematics MaxPlanckInstituteforDynamics UniversityofMuRnster ofComplexTechnicalSystems MuRnster,Germany Magdeburg,Germany AnthonyPatera GianluigiRozza MassachusettsInstituteofTechnology SISSAmathLab MIT InternationalSchoolforAdv.Studies Cambridge Trieste Massachusetts,USA Italy KarstenUrban InstituteofNumericalMathematics UlmUniversity Ulm Germany ISSN2037-5255 ISSN2037-5263 (electronic) MS&A–Modeling,Simulation&Applications ISBN978-3-319-58785-1 ISBN978-3-319-58786-8 (eBook) DOI10.1007/978-3-319-58786-8 LibraryofCongressControlNumber:2017947450 ©SpringerInternationalPublishingAG2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. Coverillustration:velocitymagnitudefieldaroundacylinderimmersedinanunsteadyviscousflowat ReD4000. CourtesyofS.Hijazi,G.Stabile,A.Mola,G.Rozza,SISSAmathLab,2017 Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface This volume contains selected peer-reviewed contributions from the MoRePaS conference, Model Reduction of Parametrized Systems, third edition, held at SISSA,InternationalSchoolforAdvancedStudies,Trieste,ItalyonOctober13–16, 2015:http://www.sissa.it/morepas2015,followingits2009,firstedition,inMünster (hosted by the Westfälische Wilhelms-Universität Münster, Germany) and 2012, second edition, Schloss Reisensburg (hosted by Ulm University, Germany). The nextMoRePaS2018willbeinNantes,France. TheMoRePaSworkshopseriesaimstofosterinternationalexchangeofnewcon- ceptsandideasin numericalanalysis,appliedmathematics,engineering,scientific computing,andprogrammingwithrespecttothefollowingtopics: – Reducedbasismethods – Properorthogonaldecomposition – Propergeneralizeddecomposition – Approximationtheoryrelatedtomodelreduction – Learningtheoryandcompressedsensing – Stochasticandhigh-dimensionalproblems – System-theoreticmethods – Nonlinearmodelreduction – Reductionofcoupledproblems/multiphysics – Optimizationandoptimalcontrol – Stateestimationandcontrol – Reducedordermodelsanddomaindecompositionmethods – Krylovsubspaceandinterpolatorymethods – Applicationtoreal,industrialandcomplexproblems The model reduction community is growing rapidly and during the past decade has achieved a high level of visibility in the computational science and engineering (CSE) global community, as is evident from the 30 contributions selected to appear in this special volume, which cover a broad range of modern topics as well as applications. A further collection of open access posters related to MoRePaS 2015 is available at www.scienceopen.com, doi:10.14293/S2199-1006.1.SOR-MATH.CLI8YJR.v1. v vi Preface The MoRePaS organization also supports a website (www.morepas.org) col- lecting research software, preprints, organization of annual PhD student summer schools,openpositionsandseveralotheractivities. This book represents the current state of the art in developments in applied mathematics,computationalmathematicsandengineeringtodealwiththeincrease in the complexityof modelled systems, to improveparametric computing,to deal with uncertainty quantification and to develop real-time computing. The need for acomputationalcollaborationbetweenfullorderclassicaldiscretizationtechniques andreducedordermethodsishighlighted. We would like to thank the MoRePaS 2015 scientific committee for the editorial revision of this volume, as well as the COST EU-MORNET network (www.eu-mor.net)—European Union Cooperation in Science and Technology Model Reduction Network (TD1307)—for the support. We would like to say a big “thank you” to all the contributors, especially the invited speakers at the conference.SpecialthanksarealsoduetoAngelaVanegasandFrancescaBonadei fromSpringerItaliafortheireditorialassistance. Trieste,Italy GianluigiRozza Magdeburg,Germany PeterBenner Münster,Germany MarioOhlberger Cambridge,MA,USA AnthonyT.Patera Ulm,Germany KarstenUrban June2017 MoRePaS2015GroupPictureatSISSA,Trieste,Italy Contents 1 TwoWaystoTreatTimeinReducedBasisMethods................... 1 SilkeGlas,AntoniaMayerhofer,andKarstenUrban 2 SimultaneousEmpiricalInterpolationandReduced Basis Method:ApplicationtoNon-linearMulti-PhysicsProblem........... 17 CécileDaversinandChristophePrud’homme 3 A Certified Reduced Basis Approach for Parametrized OptimalControlProblemswithTwo-SidedControlConstraints..... 37 EduardBader,MartinA.Grepl,andKarenVeroy 4 AReducedBasisMethodwithanExactSolutionCertificate and Spatio-ParameterAdaptivity:Applicationto Linear Elasticity..................................................................... 55 MasayukiYano 5 A Reduced Basis MethodforParameterFunctionsUsing WaveletApproximations................................................... 77 AntoniaMayerhoferandKarstenUrban 6 Reduced Basis Isogeometric Mortar Approximations forEigenvalueProblemsinVibroacoustics.............................. 91 ThomasHorger,BarbaraWohlmuth,andLinusWunderlich 7 Reduced Basis Approximationsfor Maxwell’s Equations inDispersiveMedia ........................................................ 107 PeterBennerandMartinHess 8 OfflineErrorBoundsfortheReducedBasisMethod .................. 121 RobertO’ConnorandMartinGrepl 9 ArbiLoMod: LocalSolutionSpaces by RandomTraining inElectrodynamics......................................................... 137 Andreas Buhr, Christian Engwer, Mario Ohlberger, andStephanRave vii viii Contents 10 Reduced-OrderSemi-ImplicitSchemesforFluid-Structure InteractionProblems....................................................... 149 FrancescoBallarin,GianluigiRozza,andYvonMaday 11 TrueErrorControlfortheLocalizedReducedBasisMethod forParabolicProblems..................................................... 169 MarioOhlberger,StephanRave,andFelixSchindler 12 EfficientReductionofPDEsDefinedonDomainswithVariable Shape......................................................................... 183 AndreaManzoniandFedericoNegri 13 LocalizedReducedBasisApproximationofaNonlinearFinite VolumeBatteryModelwithResolvedElectrodeGeometry ........... 201 MarioOhlbergerandStephanRave 14 A-PosterioriError Estimation of Discrete POD Models forPDE-ConstrainedOptimalControl .................................. 213 MartinGubisch,IraNeitzel,andStefanVolkwein 15 Hi-PODSolutionofParametrizedFluidDynamicsProblems: PreliminaryResults ........................................................ 235 Davide Baroli, Cristina Maria Cova, Simona Perotto, LorenzoSala,andAlessandroVeneziani 16 AdaptiveSamplingforNonlinearDimensionalityReduction BasedonManifoldLearning.............................................. 255 ThomasFranz,RalfZimmermann,andStefanGörtz 17 Cross-Gramian-BasedModelReduction:AComparison.............. 271 ChristianHimpeandMarioOhlberger 18 Truncated Gramians for Bilinear Systems andTheirAdvantagesinModelOrderReduction...................... 285 PeterBenner,PawanGoyal,andMartinRedmann 19 LeveragingSparsityandCompressiveSensingforReduced OrderModeling............................................................. 301 J.NathanKutz,SyuzannaSargsyan,andStevenL.Brunton 20 AHJB-PODApproachtotheControloftheLevelSetEquation..... 317 AlessandroAlla,GiuliaFabrini,andMaurizioFalcone 21 ModelOrder ReductionApproachesfor Infinite Horizon OptimalControlProblemsviatheHJBEquation...................... 333 AlessandroAlla,AndreasSchmidt,andBernardHaasdonk 22 Interpolatory Methods for H Model Reduction 1 ofMulti-Input/Multi-OutputSystems.................................... 349 AlessandroCastagnotto,ChristopherBeattie,andSerkanGugercin Contents ix 23 Model Reduction of Linear Time-Varying Systems withApplicationsforMovingLoads ..................................... 367 M.CruzVaronaandB.Lohmann 24 InterpolationStrategyforBT-BasedParametricMORofGas Pipeline-Networks.......................................................... 387 Y.Lu,N.Marheineke,andJ.Mohring 25 EnergyStableModelOrderReductionfortheAllen-Cahn Equation..................................................................... 403 MuratUzuncaandBülentKarasözen 26 MOR-Based Uncertainty Quantificationin Transcranial MagneticStimulation ...................................................... 421 Lorenzo Codecasa, Konstantin Weise, Luca Di Rienzo, andJensHaueisen 27 Model Order Reduction of Nonlinear Eddy Current ProblemsUsingMissingPointEstimation............................... 439 Y.Paquay,O.Brüls,andC.Geuzaine 28 OnEfficientApproachesforSolvingaCakeFiltrationModel UnderParameterVariation ............................................... 455 S.Osterroth,O.Iliev,andR.Pinnau 29 ModelReductionforCoupledNear-WellandReservoirModels UsingMultipleSpace-TimeDiscretizations.............................. 471 Walid Kheriji, Yalchin Efendiev, Victor Manuel Calo, andEduardoGildin 30 Time-Dependent Parametric Model Order Reduction forMaterialRemovalSimulations........................................ 491 MichaelBaumann,DominikHamann,andPeterEberhard
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