Currents in Industrial Mathematics: From Concepts to Research to Education

440 Pages·2015·15.546 MB·English

by  Helmut Neunzert, Dieter Prätzel-Wolters (eds.)

Helmut Neunzert
Dieter Prätzel-Wolters Eds.
Currents
in Industrial
Mathematics
From Concepts
to Research to Education
Currents in Industrial Mathematics
Helmut Neunzert (cid:2) Dieter Prätzel-Wolters
Editors
Currents in Industrial
Mathematics
From Concepts to Research to Education
Translated from German by William Uber
Editors
HelmutNeunzert DieterPrätzel-Wolters
FraunhoferInstituteforIndustrial FraunhoferInstituteforIndustrial
MathematicsITWM MathematicsITWM
Kaiserslautern,Germany Kaiserslautern,Germany
TranslationoftheGermanEdition:MathematikimFraunhofer-Institut.Problemgetrieben–Modell-
bezogen–Lösungsorientiert,publishedbySpringer-VerlagGmbH2014,©2015.Allrightsreserved.
ISBN978-3-662-48257-5 ISBN978-3-662-48258-2(eBook)
DOI10.1007/978-3-662-48258-2
LibraryofCongressControlNumber:2015953325
Mathematics Subject Classification (2010): 00-02, 00A07, 00A35, 00A69, 01A74, 00A71, 34-XX, 35-XX,
60Gxx,62-07,93-XX,76-XX,91Gxx,97-XX
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Foreword
The employees of a mathematical Fraunhofer Institute spend a great deal of their time
discussingproblemswithindustrialclientsandthensolvingtheseproblemswiththehelp
of mathematics and computers. The periods of reflection occasionally made possible by
publicprojectsandself-financedpreliminaryresearcharenormallyusedtobuildthemath-
ematical foundation necessary for finding our clients’ solutions. Taking a step back to
critically examine one’s own activities and then to precisely and understandably articu-
late them requires great inspiration and an enormous commitment of time. Nonetheless,
18employeesand5othermathematicianscloselyconnectedtotheInstitutehaveventured
toreportontheirthoughtsandactionsinthisbook.
Our point of entry is represented by the four basic concepts that determine our work:
modeling, computing, optimizing and analyzing data. What these terms mean to us is
describedinfourrelativelyshortconceptchapters.
Next,fiveprojects—perhapsbetterreferredtoasprojectgroups—arepresentedasex-
amples;andhere,wetakethisbusinessofpresentingveryseriously.First,wedescribethe
non-mathematicalproblemandexplainthedeficienciesinthestandardapproachesforits
solution.Wealsoexplainwhytheexistingmathematicsisofteninadequateanddescribe
how many preliminary works surrounding question clarification have already emerged
from the Institute for Industrial Mathematics ITWM, in the form of doctoral theses, for
example. The core of these five research chapters, however, is solid mathematics—the
models and their numerical evaluation. Finally, we describe the “solution,” that is, what
thecustomergetsfromus,whichoftenincludessoftware.
In a closing chapter, we describe in detail how this problem-driven, model-based,
solution-oriented mathematics can be integrated into mathematics instruction in our
schools, in order to emphasize its significance and to promote students’ joy in learning
mathematics.
Inwritingthisbook,wehavekeptquitediversegroupsofreadersinmind:First,there
arethepeopleinindustryandbusiness,towhomwewishtomakeclearthatmathemati-
ciansdon’tjustdiscussor analyzeproblems,theyalsosolvethem.Second,therearethe
universitymathematicians,whomwewanttoconvincethatthisapproachcanalsoprovide
v
vi Foreword
newimpulsestomathematics.Third,thereareuniversitystudents,whowanttoknow,and
withgoodreason,whattheywillreallybedoinglaterintheirprofessionallives—foronly
asmallnumberofthemwilllectureatuniversities.Andfinally,therearethosewhowant
tobecometeachersorwhoalreadyare;thisgroupcanreadhowmathematicsinstruction
intheclassroomcanberevitalized.
IsamathematicalFraunhoferInstitutereallyentitledtoclaimthatitcanfulfillallthese
promises? There are more than65 institutes in theFraunhofer-Gesellschaft,and three of
themarebasedonmathematicalmethods:TheITWMinKaiserslautern,theSCAI(Insti-
tute for Algorithms and Scientific Computing) in Sankt Augustin, and MEVIS (Institute
for Medical Image Computing) in Bremen. Among these, the ITWM today enjoys the
highest industrial revenues and the most rapid growth. The Institute’s fantastic growth
over the nearly 20 years of its existence is shining evidence that mathematics really has
become a key technology. For this reason, we believe that we can indeed turn all of our
readersintofansofourkindofmathematics!
Kaiserslautern,Germany
June2015
DieterPrätzel-Wolters
HelmutNeunzert
Contents
PartI Introduction
Problems Trump Methods: A Somewhat Different Mathematics
fromaSomewhatDifferentInstitute . . . . . . . . . . . . . . . . . . . . 3
DieterPrätzel-WoltersandHelmutNeunzert
PartII Concepts
Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
HelmutNeunzert
Numerics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
OlegIliev,KonradSteiner,andOliverWirjadi
DataAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
PatrickLangandJürgenFranke
OptimizationProcessesinPractice . . . . . . . . . . . . . . . . . . . . . . . . 83
Karl-HeinzKüfer
PartIII Research
VirtualProductionofFilamentsandFleeces . . . . . . . . . . . . . . . . . . 103
RaimundWegener,NicoleMarheineke,andDietmarHietel
ModelingandSimulationofFiltrationProcesses . . . . . . . . . . . . . . . . 163
OlegIliev,RalfKirsch,ZahraLakdawala,StefanRief,andKonradSteiner
MaximalMaterialYieldinGemstoneCutting . . . . . . . . . . . . . . . . . . 229
Karl-HeinzKüfer,VolkerMaag,andJanSchwientek
RobustStateEstimationofComplexSystems . . . . . . . . . . . . . . . . . . 291
JanHauth,PatrickLang,andAndreasWirsen
vii
viii Contents
OptionPricinginPractice—Heston’sStochasticVolatilityModel . . . . . . . 351
SaschaDesmettre,RalfKorn,andTilmanSayer
PartIV Education
AppliedSchoolMathematics—MadeinKaiserslautern . . . . . . . . . . . . 403
WolfgangBockandMartinBracke
Part I
Introduction
Problems Trump Methods: A Somewhat Different
Mathematics from a Somewhat Different Institute
DieterPrätzel-WoltersandHelmutNeunzert
Thisbookisdedicatedtomathematics-basedtopicsthataredrivenbypracticalproblems
whose solutions generate innovation. The formulations of these problems have arisen in
the context of projects carried out at the Fraunhofer Institute for Industrial Mathematics
(ITWM), and the majority of the authors of this book are either employed at the Fraun-
hofer ITWM or are closely affiliated with it. Fraunhofer Institutes dedicate their work
to problemsin industry; a mathematicalFraunhoferInstitute therefore makes “Industrial
Mathematics”.
Thebook’seditorsoriginallysuggested“FraunhoferMathematics”asatitle.Thissug-
gestionwasdiscarded,however,sinceitfoundnoconsensusamongtheauthors.Abook
about“FraunhoferMathematics”mighthavealsohadapolarizingeffect.Formanymath-
ematicians,itwouldhavealsobeenaprovocativetitle,onethatgeneratesconfusionabout
whatexactly“FraunhoferMathematics”refersto.
Mathematics is the science with the highest degree of abstraction; there is virtually
one hundred percent agreement about what is recognized as mathematics; and mathe-
matical results are highly objective, intrinsically verifiable, and formulated in a largely
standardized language. Mathematics is divided into the categories of pure and applied,
although making even this basic distinction is somewhat difficult. It also happens occa-
sionally that the works of important mathematicians become identified with their origi-
nators, so that one then speaks, for example, of Hilbertian or Riemannian mathematics.
There are also schools that have developed particular structural edifices of mathematical
thoughtandwhoseworksarethencited,forexample,asBourbakiorconstructivistmath-
ematics.
D.Prätzel-Wolters·H.Neunzert(B)
FraunhoferInstitutfürTechno-undWirtschaftsmathematikITWM,Kaiserslautern,Germany
e-mail:[email protected]
©Springer-VerlagBerlinHeidelberg2015 3
H.Neunzert,D.Prätzel-Wolters(eds.),CurrentsinIndustrialMathematics,
DOI10.1007/978-3-662-48258-2_1