Numerical Methods for Differential Equations, Optimization, and Technological Problems: Dedicated to Professor P. Neittaanmäki on His 60th Birthday

445 Pages·2013·11.178 MB·English

by  Ronald H. W. Hoppe, Christopher Linsenmann (auth.), Sergey Repin, Timo Tiihonen, Tero Tuovinen (eds.)

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
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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.