Page 2 Editors Hans-Georg Bock Frank de Hoog Avner Friedman Arvind Gupta Helmut Neunzert ...

463 Pages·2008·4.12 MB·English

MATHEMATICS IN INDUSTRY 13
Editors
Hans-Georg Bock
Frank de Hoog
Avner Friedman
Arvind Gupta
Helmut Neunzert
William R. Pulleyblank
Torgeir Rusten
Fadil Santosa
Anna-Karin Tornberg
THE EUROPEAN CONSORTIUM
FOR MATHEMATICS IN INDUSTRY
SUBSERIES
Managing Editor
Vincenzo Capasso
Editors
Luis L. Bonilla
RRoobbeerrtt MMaatttthheeiijj
HHeellmmuutt NNeeuunnzzeerrtt
OOttmmaarr SScchheerrzzeerr
Wilhelmus H.A. Schilders
Henk A. van der Vorst
Joost Rommes
Editors
Model Order Reduction:
Theory, Research Aspects
and Applications
With 133 Figures , 53 in color and 9 Tables
123
AuthorsandEditors
WilhelmusH.A.Schilders JoostRommes
NXPSemiconductors NXPSemiconductors
CorporateI&T/DTF/Design Methods CorporateI&T/DTF/Design Methods
PhysicalDesignMethods−Mathematics PhysicalDesignMothods
HighTechCampus37 HighTechCampus37
5656AEEindhoven 5656AEEindhoven
TheNetherlands TheNetherlands
[email protected] [email protected]
HenkA.vanderVorst
MathematicalInstitute
UtrechtUniversity
Budapestlaan 6
3508TAUtrecht^
The Netherlands
[email protected]
ISBN:978-3-540-78840-9 e-ISBN:978-3-540-78841-6
DOI:10.1007/978-3-540-78841-6
LibraryofCongressControlNumber:2008929907
MathematicsSubjectClassification(2000):65,93
(cid:1)c 2008Springer-VerlagBerlinHeidelberg
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Printedonacid-freepaper
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springer.com
Preface
The idea for this book originated during the workshop “Model order reduction,
coupledproblemsandoptimization”heldattheLorentzCenterinLeidenfromSep-
tember 19–23, 2005. During one of the discussion sessions, it became clear that a
bookdescribingthestateoftheartinmodelorderreduction,startingfromthevery
basicsandcontaininganoverviewofallrelevanttechniques,wouldbeofgreatuse
forstudents,youngresearchersstartinginthefield,andexperiencedresearchers.The
observationthatmostofthetheoryonmodelorderreductionisscatteredovermany
goodpapers,makingitdifficulttofindagoodstartingpoint,wassupportedbymost
oftheparticipants.Moreover,mostofthespeakersattheworkshopwerewillingto
contributetothebookthatisnowinfrontofyou.
Thegoalofthisbook,asdefinedduringthediscussionsessionsattheworkshop,
is three-fold: first, it should describe the basics of model order reduction. Second,
both general and more specialized model order reduction techniques for linear and
nonlinearsystemsshouldbecovered,includingtheuseofseveralrelatednumerical
techniques.Third,theuseofmodelorderreductiontechniquesinpracticalapplica-
tionsandcurrentresearchaspectsshouldbediscussed.
We have organized the book according to these goals. In Part I, the rationale
behind model order reduction is explained, and an overview of the most common
methods is described. Furthermore, in the second chapter, an introduction is given
to background material from numerical linear algebra needed to assess the theory
andmethodspresentedlaterinthebook.Thisisveryimportantandusefulinforma-
tion,asadvancesinnumericallinearalgebraoftenleadtonewresultsintheareaof
modelorderreduction.Thus,thefirsttwochaptersserveasanintroductiontoreaders
who are not familiar with the subject. In Part II, model order reduction techniques
and related numerical problems are described from different points of view: both
frameworksforstructure-preservingtechniquesandmorespecializedtechniquesare
presented, while numerical methods for (closely) related problems and approaches
fornonlinearsystemsareconsideredaswell.Thispartservesasthetheoreticalback-
boneofthebook,containinganoverviewoftechniquesusedandareascovered.In
PartIIIthefocusisonresearchaspectsandapplicationsofmodelorderreduction.A
varietyofexperimentswithreal-lifeexamplesshowsthatdifferentproblemsrequire
VI Preface
differenttechniques,whileapplicationofthetechniquesleadstonewresearchtopics
thataredescribedaswell.
Despitethefactthattheworkshopwasorganizedalreadyin2005,thisbookcon-
tainsmanyrecentadvancesinmodelorderreduction.Moreover,itpresentsseveral
open problems for which techniques arestillindevelopment, related tobothlinear
systems, which become larger and more complex mainly due to industrial require-
ments, and nonlinear systems, which demand a completely new theory. The latter
illustratesthefinalandmostimportantgoalofthisbook,namelytoserveasasource
ofinspirationforitsreaders,whowilldiscoverthatmodelorderreductionisavery
excitingandlivelyfield.
At this point we would like to thank all authors of the chapters in this book.
Withoutthecontributionsoftheseexperts,itwouldnotbepossibletocoverthewide
andrapidlydevelopingfieldofmodelorderreductioninonebook.
Leiden,Utrecht,Eindhoven WilSchilders
September2005–May2008 HenkvanderVorst
JoostRommes
Contents
PartI BasicConcepts
IntroductiontoModelOrderReduction
WilSchilders ..................................................... 3
LinearSystems,Eigenvalues,andProjection
HenkvanderVorst ................................................ 33
PartII Theory
Structure-PreservingModelOrderReductionofRCLCircuitEquations
RolandW.Freund ................................................. 49
A Unified Krylov Projection Framework for Structure-Preserving
ModelReduction
ZhaojunBai,Ren-cangLi,andYangfengSu ............................ 75
ModelReductionviaProperOrthogonalDecomposition
Rene´ Pinnau ..................................................... 95
PMTBR: A Family of Approximate Principal-components-like
ReductionAlgorithms
JoelR.Phillips,ZhenhaiZhu,andL.MiguelSilveira .....................111
ASurveyonModelReductionofCoupledSystems
TimoReisandTatjanaStykel ........................................133
SpaceMappingandDefectCorrection
DavidEcheverr´ıa,DomenicoLahaye,andPietW.Hemker.................157
ModalApproximationandComputationofDominantPoles
JoostRommes ....................................................177
VIII Contents
SomePreconditioningTechniquesforSaddlePointProblems
MicheleBenziandAndrewJ.Wathen..................................195
TimeVariantBalancingandNonlinearBalancedRealizations
E.I.Verriest ......................................................213
Singular Value Analysis and Balanced Realizations for Nonlinear
Systems
KenjiFujimotoandJacquelienM.A.Scherpen...........................251
PartIII ResearchAspectsandApplications
MatrixFunctions
AndreasFrommerandValeriaSimoncini...............................275
ModelReductionofInterconnectedSystems
AntoineVandendorpeandPaulVanDooren.............................305
QuadraticInverseEigenvalueProblemandItsApplications
toModelUpdating—AnOverview
MoodyT.Chu∗∗ ..................................................323
Data-DrivenModelOrderReductionUsingOrthonormalVectorFitting
DirkDeschrijverandTomDhaene....................................341
Model-OrderReductionofHigh-SpeedInterconnectsUsingIntegrated
CongruenceTransform
EmadGad,MichelNakhla,andRamAchar.............................361
ModelOrderReductionforMEMS:MethodologyandComputational
EnvironmentforElectro-ThermalModels
TamaraBechtold,EvgeniiB.Rudnyi,andJanG.Korvink..................403
ModelOrderReductionofLargeRCCircuits
NickP.vanderMeijs ..............................................421
Reduced Order Models of On-Chip Passive Components
andInterconnects,WorkbenchandTestStructures
DanielIoanandGabrielaCiuprina ...................................447
Index ............................................................. 469
List of Contributors
RamAchar GabrielaCiuprina
DeptartmentofElectronics PolitehnicaUniversityofBucharest
CarletonUniversity Romania
Ottawa,ON,Canada,K1S5B6 [email protected]
[email protected]
DirkDeschrijver
ZhaojunBai GhentUniversity
DepartmentofComputerScience SintPietersnieuwstraat41
UniversityofCalifornia
9000Gent,Belgium
OneShieldsAvenue dirk.deschrijver@intec.
Davis,CA95616
ugent.be
[email protected]
TomDhaene
TamaraBechtold
GhentUniversity
NXPSemiconductors
SintPietersnieuwstraat41
HighTechCampus37,WY4.042
9000Gent,Belgium
5656AEEindhoven,TheNetherlands
[email protected]
[email protected]
David Echeverr´ıa
MicheleBenzi
CWI
DepartmentofMathematics
Kruislaan413
andComputerScience
1054ALAmsterdam,TheNetherlands
EmoryUniversity
[email protected]
Atlanta,Georgia30322,USA
[email protected]
RolandW.Freund
MoodyT.Chu DepartmentofMathematics
DepartmentofMathematics UniversityofCaliforniaatDavis
NorthCarolinaStateUniversity OneShieldsAvenue
Raleigh,NC27695-8205,USA Davis,CA95616,U.S.A
[email protected] [email protected]
X ListofContributors
AndreasFrommer NickP.vanderMeijs
Department of Mathematics and FacultyofEEMCS
Science DelftUniversityofTechnology
UniversityofWuppertal Delft,TheNetherlands
D-42097Wuppertal,Germany [email protected]
[email protected]
KenjiFujimoto MichelNakhla
DepartmentofMechanicalScienceand DeptartmentofElectronics,
Engineering CarletonUniversity
NagoyaUniversity Ottawa,ON,Canada,K1S5B6
[email protected] [email protected]
EmadGad
SchoolofInformationTechnologyand JoelR.Phillips
Engineering(SITE) CadenceBerkeleyLaboratories
UniversityofOttawa Berkeley,CA94704,U.S.A
Ottawa,ON,Canada,K1N6N5 [email protected]
[email protected]
PietW.Hemker Rene´ Pinnau
CWI FachbereichMathematik
Kruislaan413
TechnischeUniversita¨tKaiserslautern
1054ALAmsterdam,TheNetherlands
D-67663Kaiserslautern,Germany
[email protected]
[email protected]
DanielIoan
PolitehnicaUniversityofBucharest
TimoReis
Romania
Institutfu¨rMathematik,MA4-5
[email protected]
TechnischeUniversita¨tBerlin
JanG.Korvink Straßedes17.Juni136
IMTEK,UniversityofFreiburg 10623BerlinGermany
Georges-Koehler-Allee102 [email protected]
D-79110,Germany
[email protected]
JoostRommes
DomenicoLahaye NXPSemiconductors
CWI HighTechCampus37,WY4.042
Kruislaan413 5656AEEindhoven,TheNetherlands
1054ALAmsterdam,TheNetherlands [email protected]
[email protected]
Ren-cangLi EvgeniiB.Rudnyi
DepartmentofMathematics CAD-FEMGmbH
UniversityofTexas Marktplatz2
Arlington,TX76019 85567Grafing,Germany
[email protected] [email protected]