Sparse grids and applications PDF
Preview Sparse grids and applications
Lecture Notes in Computational Science 88 and Engineering Editors: TimothyJ. Barth MichaelGriebel DavidE. Keyes RistoM. Nieminen DirkRoose TamarSchlick Forfurthervolumes: http://www.springer.com/series/3527 (cid:127) Jochen Garcke Michael Griebel (cid:2) Editors Sparse Grids and Applications 123 Editors JochenGarcke MichaelGriebel Institutfu¨rNumerischeSimulation Universita¨tBonn Bonn Germany ISSN1439-7358 ISBN978-3-642-31702-6 ISBN978-3-642-31703-3(eBook) DOI10.1007/978-3-642-31703-3 SpringerHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2012950005 MathematicsSubjectClassification(2010):65D99,65M12,65N99,65Y20,65N12,62H99 (cid:2)c Springer-VerlagBerlinHeidelberg2013 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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Coverillustration:BycourtesyofDirkPflu¨ger Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface Intherecentdecade,therehasbeengrowinginterestinthenumericaltreatmentof high-dimensionalproblems.Itiswellknownthatclassicalnumericaldiscretization schemesfailinmorethanthreeorfourdimensionsduetothecurseofdimension- ality.Thetechniqueofsparsegridsallowstoovercomethisproblemtosomeextent undersuitableregularityassumptions.Thisdiscretizationapproachisobtainedfrom amulti-scalebasisbyatensorproductconstructionandsubsequenttruncationofthe resultingmultiresolutionseriesexpansion. Hans-JoachimBungartz,JochenGarcke,MichaelGriebel,andMarkusHegland organizeda workshop specifically to strengthen the research on the mathematical understandingandanalysisofsparsegriddiscretization.Particularfocuswasgiven to aspectsarising fromapplications.More than 40 researchersfromfour different continentsattendedtheworkshopinBonn,Germany,fromMay16–20,2011. ThisvolumeofLNCSEnowcomprisesselectedcontributionsfromattendeesof the workshop. The contents range from numerical analysis and stochastic partial differentialequationstoapplicationsindataanalysis,finance,andphysics. The workshop was hosted by the Institut fu¨r Numerische Simulation and the HausdorffResearch Institute for Mathematics(HIM) of the Rheinische Friedrich- Wilhelms-Universita¨tBonnaspartoftheTrimesterProgramAnalysisandNumerics forHighDimensionalProblems.Financialsupportof theHIM iskindlyacknowl- edged. We especially thank Christian Rieger for his efforts and enthusiasm in the localorganizationoftheworkshopandthestaffoftheHIMfortheirassistance. Bonn,Germany JochenGarcke MichaelGriebel v (cid:127) Contents AnAdaptiveSparseGridApproachforTimeSeriesPrediction ........... 1 BastianBohnandMichaelGriebel EfficientAnalysisofHighDimensionalDatainTensorFormats........... 31 Mike Espig, Wolfgang Hackbusch, Alexander Litvinenko, HermannG.Matthies,andElmarZander SparseGridsinaNutshell ...................................................... 57 JochenGarcke IntradayForeignExchangeRateForecastingUsingSparseGrids......... 81 JochenGarcke,ThomasGerstner,andMichaelGriebel Dimension-andTime-AdaptiveMultilevelMonteCarloMethods......... 107 ThomasGerstnerandStefanHeinz AnEfficientSparseGridGalerkinApproachfortheNumerical ValuationofBasketOptionsUnderKou’sJump-DiffusionModel......... 121 MichaelGriebelandAlexanderHullmann TheUseofSparseGridApproximationforther-TermTensor Representation.................................................................... 151 WolfgangHackbusch On Multilevel Quadraturefor Elliptic Stochastic Partial DifferentialEquations........................................................... 161 HelmutHarbrecht,MichaelPeters,andMarkusSiebenmorgen LocalandDimension AdaptiveStochasticCollocationfor UncertaintyQuantification...................................................... 181 JohnD.JakemanandStephenG.Roberts TheCombinationTechniquefortheInitialValueProblemin LinearGyrokinetics.............................................................. 205 ChristophKowitz,DirkPflu¨ger,FrankJenko,andMarkusHegland vii viii Contents ModelReductionwiththeReducedBasisMethodandSparseGrids...... 223 Benjamin Peherstorfer,Stefan Zimmer, and Hans-Joachim Bungartz SpatiallyAdaptiveRefinement ................................................. 243 DirkPflu¨ger AsymptoticExpansionAroundPrincipalComponentsandthe ComplexityofDimensionAdaptiveAlgorithms.............................. 263 ChristophReisinger Contributors Bastian Bohn Institute for Numerical Simulation, University of Bonn, Bonn, Germany Hans-JoachimBungartz TechnischeUniversita¨tMu¨nchen,Garching,Germany Mike Espig Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany Jochen Garcke Institut fu¨r Numerische Simulation, Universita¨t Bonn, Bonn, Germany FraunhoferSCAI,SchlossBirlinghoven,SanktAugustin,Germany ThomasGerstner Institutfu¨rMathematik,JohannWolfgangGoethe-Universita¨t, FrankfurtamMain,Germany Michael Griebel Institute for Numerical Simulation, University of Bonn, Bonn, Germany Wolfgang Hackbusch Max Planck Institute for Mathematics in the Sciences, Leipzig,Germany HelmutHarbrecht MathematischesInstitut,Basel,Switzerland MarkusHegland AustralianNationalUniversity,Canberra,Australia Stefan Heinz Institut fu¨r Mathematik, Johann Wolfgang Goethe-Universita¨t, FrankfurtamMain,Germany Alexander Hullmann Institute for Numerical Simulation, University of Bonn, Bonn,Germany JohnD.Jakeman DepartmentofMathematics,PurdueUniversity,WestLafayette, IN,USA FrankJenko Max-Planck-Institutfu¨rPlasmaphysik,Garching,Germany ix
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