Numerical Methods for Differential Equations, Optimization, and Technological Problems Computational Methods in Applied Sciences Volume27 SeriesEditor E.Oñate InternationalCenterforNumericalMethodsinEngineering(CIMNE) TechnicalUniversityofCatalonia(UPC) EdificioC-1,CampusNorteUPC GranCapitán,s/n 08034Barcelona,Spain [email protected] www.cimne.com Forfurthervolumes: www.springer.com/series/6899 Sergey Repin (cid:2) Timo Tiihonen (cid:2) Tero Tuovinen Editors Numerical Methods for Differential Equations, Optimization, and Technological Problems Dedicated to Professor P. Neittaanmäki on His 60th Birthday Editors SergeyRepin TeroTuovinen MathematicalInformationTechnology MathematicalInformationTechnology UniversityofJyväskylä UniversityofJyväskylä Jyväskylä,Finland Jyväskylä,Finland TimoTiihonen MathematicalInformationTechnology UniversityofJyväskylä Jyväskylä,Finland ISSN1871-3033 ComputationalMethodsinAppliedSciences ISBN978-94-007-5287-0 ISBN978-94-007-5288-7(eBook) DOI10.1007/978-94-007-5288-7 SpringerDordrechtHeidelbergNewYorkLondon LibraryofCongressControlNumber:2012948397 ©SpringerScience+BusinessMediaDordrecht2013 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) Dedicated to Professor Pekka Neittaanmäki on theoccasion ofhis60thbirthday Foreword This book exposes the results in numerical analysis and optimization presented at the ECCOMAS thematic conference “Computational Analysis and Optimization” (CAO2011)inJyväskylä,Finland,onJune9–11,2011,dedicatedtothe60thjubilee ofProfessorPekkaNeittaanmäki.Itconsistsoffiveparts,whicharecloselyrelated tohisscientificactivitiesandinterests. Part I of the book contains new results associated with numerical analysis of nonlinear models in continuum mechanics. It begins with a paper due to R.H.W. HoppeandC.Linsenmann,inwhichtheauthorsstudythemotionofredbloodcells (RBCs) subject to an external incompressible flow in a microchannel and investi- gatetwoversions(semiexplicitandfullyimplicit)oftheFiniteElementImmersed Boundary Method (FE-IB). The paper by E. Laitinen and A. Lapin is focused on iterationmethodsforsaddle-pointproblems.Suchproblemsoftenariseinanalysis ofnonlinearmodelsassociatedwithvariationalinequalities. A survey devoted to analytic-numerical methods for hidden attractors localiza- tionandtheirapplicationtononlineardynamicsystemsispresentedinapaperby G.LeonovandV.Kuznetsov.InapaperbyS.Tureketal.,theauthorsconsidernew numericalschemescreatedtosimulatea3Dmultiphaseflowofimmisciblefluids. ThearticleofH.WangandJ.Periauxisconcernedwithafastmeshlessmethodfor problemsincomputationalfluiddynamics. PartIIcollectspapersassociatedwiththetopic“aposteriorierrorestimatesand reliablecomputersimulationmethods”.ThefirstpaperofR.RannacherandJ.Vi- hharev discusses an important question of balancing discretization and integration errorsinnumericalsolutionscomputedbyfiniteelementmethods.Analysisofthis questionisbasedondual-weightedresidualaposterioriestimates.Inapaperdueto S.RepinandT.Rossi,theauthorsuseanotherclassofaposterioriestimates(esti- mates of the functional type) in order to reformulate the classical inverse problem in the form of an unconstrained minimization problem. A posteriori estimates of thesametypearederivedin thenextpaper,whereO.Maliconsidershigher-order boundaryvalueproblemsinthetheoryofcurvilinearbeams.Onemoremethodof deriving a posteriori estimates is used in the article by S. Matsulevich et al. It is based on the theory of contractive mappings and is applied to the Picard-Lindelöf vii viii Foreword method. Finally, the paper of K. Segeth contains an overview of a posteriori esti- matesforthebiharmonicproblem. Part III contains publications related to optimization methods. It starts with a paper by M.M. Mäkelä et al., where the reader will find a new subgradient-type methodofminimizingnonconvexfunctionals.Inthenextpaper,writtenbyP.Philip andD.Tiba,theauthorsdiscussshapeoptimizationproblemsgovernedbylinearor nonlinearellipticpartialdifferentialequationsviaafixeddomainapproach.Meth- odsofstructuraloptimizationintheapplicationtobiologicalmodelsarediscussed inthepaperofM.Nowak. Part IV is concerned with analysis of “noisy” and uncertain data. The paper of J.-A.Désidérietal.investigatesapproximationpropertiesoftheHermitianinterpo- lationofafunctionwhosenodalvaluesareknownexactlyandthederivativesonly approximately.Theresultscanbeusedinanalysisoftheso-called“meta-models” arising in the theory of design of an experiment. The paper by A. Zerbinati et al. addressesthesametopic.InapaperbyA.Averbuchetal.,theauthorspresentaro- bustalgorithmstartingfrom1Dor2Ddiscretenoiseddatatoapproximatelyinvert theheatequation.ThepaperofG.Wolfetal.isdevotedtoclusteringanddistance analysisofdatasets. PartVisfocusedonproblemsinpapermachineindustryandinformationtech- nology. The paper by N. Banichuk and S. Ivanova studies the effects caused by uncertaintiesincontactmechanicsandshapeoptimizationproblems.Thepaperby J.Jeronenaddresses,inprinciple,thesametopic(analysisofuncertaintiesinareal- life mechanical problem), but from a different point of view. Two other papers of thesameresearchgroup(N.Banichuketal.andT.Saksaetal.)aredevotedtosafety analysisandoptimizationofamovingelasticwebtravellingbetweentworollersata constantaxialvelocity.ThepaperofA.Averbuchetal.isdevotedtonetworkmodels arisingininformationsystems.Finally,thepaperofJ.Hartikainenetal.considers computersimulationmethodsforhighlynonlinearmodelsinsolidmechanics. In alltheparts,wefirst presentpapers ofinvitedspeakers andthencontributed papers joinedbya commontopic.We wouldlike to thankall theauthors for their contributions.Allthepapersincludedinthevolumehavebeenreviewed(normally bytwoindependentreviewers)andmanyofthemhavebeenmodifiedinaccordance withthecommentsreceived.Wewouldliketothankallthereviewersfortheirwork, whichmadeitpossibletoessentiallyimprovesomepublications. TheeditorsaregratefultoalltheauthorsfortheircontributionsandtotheFed- eration of Finnish Learned Societies for financial support. We would like to thank Marja-Leena Rantalainen for her careful work on preparing the electronic version ofthebookandexpresssincerethankstoourcounterpartinSpringer. Jyväskylä,Finland SergeyRepin TimoTiihonen TeroTuovinen Preface Attheoccasionofthe60thbirthdayofProfessorPekkaNeittaanmäkiitistimeto takealookathisversatileactivitiesfromthedecadespassedsofar. YoungAthlete Pekkawasbornin1951inSaarijärvi,CentralFinland—aruralcommunityassoci- atedwithperseveranceandaspiritofhopeevenunderthehardestofconditionsin Finnishpoetry.Saarijärviisalsoknownforitsactivesocietyinathleticswhichmade sportsanaturaltargetforPekka’senergyintheteenyears.Hisongoingrunningand skiingactivitiesstemfromthosetimes.Hismoreextremehobbiesfromthosetimes areperhapslessknown.Polevaultingandskijumpingarecertainlynotthatfrequent inacademicCVs.However,theyaregoodindicatorsofPekka’sdaringattitude. Emergenceof aResearcher In early 70’s Pekka entered the University of Jyväskylä in the early 70’s (with in- tention to graduate fast as math’s teacher). Despite of the desire to graduate fast, Pekka did not ignore the social aspects of life as a student, which in the seventies impliedalsopoliticalactivity,andgatheredastrongpersonalnetworkoffuturede- cision makers that has been an essential asset ever since. Fast graduation caught the attention of Professor I.S. Louhivaara who recruited Pekka for doctoral stud- ies.Louhivaara,whohadbeentrainedastherighthandofRolfNevanlinna,hadan extensiveandactiveinternationalnetworkandabroadunderstandingoftheactive fieldsinmathematics.Thus,inhisthesisworkonboundaryvalueproblemstoplate equation,mentoredbyK.WitschfromBonn,Pekkagotanextensivebackgroundin mathematicalanalysisofPDEs. AfterhisPhDPekkawenttoBonnasapostdocandgotacquaintedwithbotha generationofyoungGermanresearchersand,moreimportantly,thefiniteelement ix x Preface method. When Pekka returned from Bonn, he brought a pile of punch cards con- taining a FEM code and several manuscripts and ideas to be written jointly with R.PicardandJ.SaranenonFEMfordifferentwaveandeigenvalueproblems. BuildingHisOwnGroup Inthebeginningofthe80’sPekkastartedtobeonhisown.TheFEMpapersafter thePhDqualifiedhimtothelevelofadocentanditwastimetostartteachingand recruitingstudents.ThefirstseminararoundFEMwasorganizedinJyväskyläinfall 1982 and it attracted the attention of several promising students. Pekka exploited wellthepositionofFinlandasagatewaybetweenEastandWestandquicklybuilt a collaboration network with Czech and Romanian researchers. This helped him to both deepen and broaden the research activities. By a fortunate mishap Pekka learnedaboutthesuperconvergencephenomenonrelatedtoaveragingandmanaged to analyze it with M. Krizek with whom he continued the FEM track to review articlesandeventuallytomonographs. SimultaneouslyPekkafoundotherlong-lastinginterests:shapeoptimisationwith J.HaslingerandoptimalcontrolwithD.Tiba,bothofthese,inparticular,inthecon- textofvariationalinequalities.Theseopeningslednotonlytonumerouspapersand severalmonographsintheyearstocomebutalsotoafairnumberofPhDstudents and theses, and to the first major industrial collaboration in the field of steel cast- ing. The collaboration with industry was facilitated by Pekka’s short excursion to LappeenrantaUniversityofTechnologyasanassociateprofessorandbyamember- shipintheResearchCouncilofTechnology. TofacilitatehisreturnbacktoJyväskylä,PekkaplayedamajorroleintheUni- versity’sinitiativeof“AppliedScience”andmanagedtoraisesignificantdonations from the region to open new positions in computational and applied sciences, in- cludingtheprofessorshiphehasbeenholdingfrom1988. Shaping theUniversity In thebeginningof the90’stheactivitieswerebooming.Beingestablishedas full professor,knowingtheresearchcouncilsfrominside,havingasuccessfulindustrial case in his portfolio and several young post docs, Pekka could expand the group with new students and attract new industrial partners and international collabora- tors. Simultaneously the situation in Eastern Europe had changed. Pekka was fast to make good contacts in the leading schools in St. Petersburg and Moscow while summarizing the fruits of collaboration with colleagues from Eastern Europe and establishing links to the French school of applied mathematics and the European freeboundarycommunity.ThisallhasmadeJyväskyläacollaborationhubforsci- entistsfrommanycountries.SimultaneouslyPekkawasbusyinternationalizingthe group, by co-initiating the Jyväskylä International Summer Semester, starting the Preface xi organizingofinternationalconferencesandbyrecruitingfirstforeignPhDstudents to the group. This alone would have been more than enough to fill the days of a professor.Butotherthingsemergedinparallel. Pekka was called to serve in a government-level committee of research issues and, after a few months as Dean of the Faculty of Natural Sciences, as the first vice-rector of the University. The period as vice-rector manifested Pekka’s ability torecognizequalitativelynewopportunitiesastheyemerge.Finland,byjoiningthe European Union in the beginning of 1995, became eligible to European regional funding—Jyväskylä region, in particular, because of a major crisis in the regional economy.ThankstoPekka’sinitiatives(andpersonalnetworkofstrategicpeople), JyväskyläwasabletoharnesstheEUfundingtoarealstructuralchangeinthelocal economy,largelythroughexpansionandmodernizationofuniversityeducationby targetedmasterprograms. ThemasterprogramsandotheractionsexpandedtheIT-relatedactivitiessothat theyfittedneitherinthefacilitiesnortheorganizationoftheUniversity.Thisleadto thecreationoftheFacultyofInformationTechnology,splittinguptheDepartment of Mathematics, and forming the Department of Mathematical Information Tech- nology.SimultaneouslyanewbuildingwasneededandPekkawasakeypersonin the conceptualizationof a site that linked several academicdisciplines and related enterprisesunderacommonroof.Toimplementtheideatimely,newtypesoffinan- cialinstrumentshadtobepilotedatthesametime.AllthishelpedtheUniversityto movequalitativelyforwardtothenewmillennium. CollaborationAcrosstheDisciplines In 2000 Pekka turned towards new challenges. Giving up the vice-rector duties, hestartedtopromotecollaborationbetweencomputationalsciencesandhumanori- entedsciencesactively.Hesawtheneedofaplatformformultidisciplinaryresearch andcollaborationandhelpedtoestablishAgoraCenterassuchaunit.Servingsev- eralyearsastheheadofAgoraCenter,Pekkahashelpedseveralmultidisciplinary groupstofindcollaboratorsandnewfundingopportunities.OnceagainPekkahas beenalertandabletoreacttothechangesinthesocietyandourregionbylaunching animpressiveseriesofactionstocounterbalancetheeffectsoftheglobalfinancial crisisof2008bytargetededucationalandresearchprograms. To parallel his activities in multidisciplinary research, Pekka has expanded his personal research interests to game theory, data mining, and the like. When doing thishehasnotforgottenhisroots.Hisfirstlove,plateequationandwavephenom- ena,hasledhimtoactivecollaborationandcontributionsinthefieldofnanotechnol- ogy.Errorestimatesforfiniteelementsarestillarelevanttopic,nowinthecontext ofreliableaposterioriestimates. PekkahascontinuedtobeactiveinfatherlysupervisionofhisPhDstudents,now passingover60incumulativecount.