Table Of ContentMS&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
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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
