Table Of ContentInternational 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
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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
