Trends in PDE constrained optimization PDF
Preview Trends in PDE constrained optimization
International Series of Numerical Mathematics Günter Leugering 165 Peter Benner Sebastian Engell Andreas Griewank Helmut Harbrecht Michael Hinze Rolf Rannacher Stefan Ulbrich Editors Trends in PDE Constrained Optimization ISNM InternationalSeries ofNumerical Mathematics Volume165 ManagingEditors: K.-H.Hoffmann,München,Germany G.Leugering,Erlangen-Nürnberg,Germany AssociateEditors: Z.Chen,Beijing,China R.H.W.Hoppe,Augsburg,Germany/Houston,USA N.Kenmochi,Chiba,Japan V.Starovoitov,Novosibirsk,Russia HonoraryEditor: J.Todd,Pasadena,USA(cid:2) Moreinformationaboutthisseriesat http://www.springer.com/series/4819 GuRnter Leugering (cid:129) Peter Benner (cid:129) Sebastian Engell (cid:129) Andreas Griewank (cid:129) Helmut Harbrecht (cid:129) Michael Hinze (cid:129) Rolf Rannacher (cid:129) Stefan Ulbrich Editors Trends in PDE Constrained Optimization Editors GuRnterLeugering PeterBenner DepartmentMathematik InstitutfuRrDynamikkomplexer UniversitaRtErlangen-NuRrnberg technischerSysteme Erlangen Max-Planck-Institut Germany Magdeburg Germany SebastianEngell AndreasGriewank DepartmentofBiochemicalandChemical DepartmentofMathematics Engineering Humboldt-UniversitaRtzuBerlin TechnischeUniversitaRtDortmund Berlin Dortmund Germany Germany HelmutHarbrecht MichaelHinze MathematischesInstitut FachbereichMathematikOptimierung UniversitaRtBasel undApproximation Basel UniversitaRtHamburg Switzerland Hamburg Germany RolfRannacher StefanUlbrich InstitutfuRrAngewandteMathematik FachbereichMathematik Ruprecht-Karls-UniversitaRtHeidelberg TechnischeUniversitaRtDarmstadt Heidelberg Darmstadt Germany Germany ISSN0373-3149 ISSN2296-6072(electronic) ISBN978-3-319-05082-9 ISBN978-3-319-05083-6(eBook) DOI10.1007/978-3-319-05083-6 SpringerChamHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2014958298 MathematicsSubjectClassification(2010):35K55,35Q93,49J20,49K20,49M25,65K10,65M60, 65N15,65N30,76D55,90C30 ©SpringerInternationalPublishingSwitzerland2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Contents Introduction ...................................................................... 1 Günter Leugering, Andreas Griewank, Stefan Ulbrich, HelmutHarbrecht,PeterBenner,RolfRannacher,MichaelHinze, andSebastianEngell PartI ConstrainedOptimization,IdentificationandControl IntroductiontoPartIConstrainedOptimization,Identification andControl....................................................................... 7 StefanUlbrichandAndreasGriewank OptimalControlofAllen-CahnSystems ...................................... 11 Luise Blank, M. Hassan Farshbaf-Shaker,Claudia Hecht, JosefMichl,andChristophRupprecht Optimal Control of Elastoplastic Processes: Analysis, Algorithms,NumericalAnalysisandApplications........................... 27 RolandHerzog,ChristianMeyer,andGerdWachsmuth One-ShotApproachestoDesignOptimzation ................................ 43 Torsten Bosse, Nicolas R. Gauger, Andreas Griewank, StefanieGünther,andVolkerSchulz OptimalDesignwith Bounded Retardationfor Problems withNon-separableAdjoints ................................................... 67 Torsten Bosse, Nicolas R. Gauger, Andreas Griewank, Stefanie Günther, Lena Kaland, Claudia Kratzenstein, LutzLehmann,AnilNemili,EmreÖzkaya,andThomasSlawig Ona FullyAdaptiveSQP MethodforPDAE-Constrained OptimalControlProblemswithControlandStateConstraints............ 85 Stefanie Bott, Debora Clever, Jens Lang, Stefan Ulbrich, JanCarstenZiems,andDirkSchröder v vi Contents OptimalControlofNonlinearHyperbolicConservationLaws withSwitching.................................................................... 109 SebastianPfaff,StefanUlbrich,andGünterLeugering EllipticMathematicalProgramswithEquilibriumConstraints inFunctionSpace:OptimalityConditionsandNumericalRealization.... 133 Michael Hintermüller,Antoine Laurain, Caroline Löbhard, CarlosN.Rautenberg,andThomasM.Surowiec Models and Optimal Controlin Freezing and Thawing ofLivingCellsandTissues...................................................... 155 Karl-HeinzHoffmann,NikolaiD.Botkin,andVarvaraL.Turova OptimalControl-BasedFeedbackStabilizationofMulti-field FlowProblems.................................................................... 173 EberhardBänsch,PeterBenner,JensSaak,andHeikoK.Weichelt PartII ShapeandTopologyOptimization IntroductiontoPartII ShapeandTopologyOptimization............................................. 191 HelmutHarbrecht Two-StageStochasticOptimizationMeetsTwo-ScaleSimulation.......... 193 SergioConti,BenedictGeihe,MartinRumpf,andRüdigerSchultz OnShapeOptimizationwithParabolicStateEquation ..................... 213 HelmutHarbrechtandJohannesTausch Multi-materialPhaseFieldApproachtoStructuralTopology Optimization...................................................................... 231 Luise Blank, M. Hassan Farshbaf-Shaker,Harald Garcke, ChristophRupprecht,andVanessaStyles PartIII AdaptivityandModelReduction IntroductiontoPartIII AdaptivityandModelReduction............................................... 249 PeterBennerandRolfRannacher ModelReductionbyAdaptiveDiscretizationinOptimalControl.......... 251 RolfRannacher Graded Meshes in Optimal Control for Elliptic Partial DifferentialEquations:AnOverview.......................................... 285 ThomasApel,JohannesPfefferer,andArndRösch ModelOrderReductionforPDEConstrainedOptimization............... 303 PeterBenner,EkkehardSachs,andStefanVolkwein Contents vii AdaptiveTrust-RegionPODMethodsinPIDE-Constrained Optimization...................................................................... 327 EkkehardW.Sachs,MarinaSchneider,andMatthiasSchu PartIV Discretization:ConceptsandAnalysis IntroductiontoPartIVDiscretization:ConceptsandAnalysis ............ 345 MichaelHinze OptimalControlforTwo-PhaseFlows ........................................ 347 MalteBraack,MarkusKlein,AndreasProhl,andBenjaminTews A-PrioriErrorBoundsforFiniteElement Approximation ofEllipticOptimalControlProblemswithGradientConstraints.......... 365 KlausDeckelnickandMichaelHinze Space-TimeNewton-MultigridStrategiesforNonstationary DistributedandBoundaryFlowControlProblems.......................... 383 MichaelHinze,MichaelKöster,andStefanTurek ConvergenceofAdaptiveFiniteElementsforOptimalControl ProblemswithControlConstraints............................................ 403 KristinaKohls,ArndRösch,andKunibertG.Siebert Petrov-GalerkinCrank-Nicolson Scheme for Parabolic OptimalControlProblemsonNonsmoothDomains......................... 421 ThomasG.Flaig,DominikMeidner,andBorisVexler PartV Applications IntroductiontoPartV:Applications........................................... 439 Optimal Treatment Planning in Radiotherapy Based onBoltzmannTransportEquations............................................ 441 RichardC.Barnard,MartinFrank,andMichaelHerty OptimalControlofSelf-ConsistentClassicalandQuantum ParticleSystems.................................................................. 455 MartinBurger,RenéPinnau,MarcisseFouego,andSebastianRau Modeling,Analysis andOptimizationofParticleGrowth, NucleationandRipeningbytheWayofNonlinearHyperbolic Integro-PartialDifferentialEquations......................................... 471 MichaelGröschel,WolfgangPeukert,andGünterLeugering StabilizationofNetworkedHyperbolicSystemswithBoundary Feedback.......................................................................... 487 MarkusDick,MartinGugat,MichaelHerty,GünterLeugering, SonjaSteffensen,andKeWang viii Contents OptimalControlofSurfaceAcousticWaveActuatedSorting ofBiologicalCells ................................................................ 505 ThomasFranke,RonaldH.W.Hoppe,ChristopherLinsenmann, LotharSchmid,andAchimWixforth Real-TimePDEConstrainedOptimalControlofaPeriodic MulticomponentSeparationProcess........................................... 521 Malte Behrens, Hans Georg Bock, Sebastian Engell, PhawitphornKhobkhun,andAndreasPotschka OPTPDE:ACollectionofProblemsinPDE-Constrained Optimization...................................................................... 539 Roland Herzog, Arnd Rösch, Stefan Ulbrich, andWinnifriedWollner Contributors Thomas Apel Institute for Mathematics and Civil Engineering Informatics, UniversitätderBundeswehrMünchen,Germany EberhardBänsch LehrstuhlfürAngewandteMathematik3,Friedrich-Alexander- UniversitätErlangen-Nürnberg,Erlangen,Germany Richard C. Barnard Institute for Mathematics and Scientific Computing, UniversityofGraz,Graz,Austria MalteBehrens DepartmentofBiochemicalandChemicalEngineering,TUDort- mund,Dortmund,Germany Peter Benner Research Group Computational Methods in Systems and Control Theory(CSC),MaxPlanckInstituteforDynamicsofComplexTechnicalSystems Magdeburg,Magdeburg,Germany Luise Blank Fakultät für Mathematik, Universität Regensburg, Regensburg, Germany Hans Georg Bock InterdisciplinaryCenter for Scientific Computing,Heidelberg University,Heidelberg,Germany Torsten Bosse Department of Mathematics, Humboldt-Universität zu Berlin, Berlin,Germany Nikolai D. Botkin Zentrum Mathematik, Technische Universität München, München,Germany StefanieBott DepartmentofMathematicsandGraduateSchoolofComputational Engineering,TechnischeUniversitätDarmstadt,Darmstadt,Germany Malte Braack Mathematical Seminar, Christian-Albrechts-University of Kiel, Kiel,Germany ix
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