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DFG Research Center MATHEONMathematics for key technologies
DFG Research Center MATHEON
Mathematics for key technologies:Modelling, simulation, and optimization
of real-world processes
CO@W Berlin
Martin GrötschelOctober 7, 2009
DFG Research Center Matheon 2
Outline
MATHEON Introduction
A: Life Sciences
B: Logistics, Traffic, Telecommunication Networks
C: Production
D: Circuit Simulation and Opto-Electronic Devices
E: Finance
F: Visualization
Z: Education, Outreach, Administration
DFG Research Center Matheon 3
German Research Foundation (DFG)
DFG Research Center Matheon 4
DFG Coordinated Programs
Ordered by amount of funding:
Research units (Forschergruppen)
Priority programs (Schwerpunktsprogramme)
Research training groups (Graduiertenkollegs)
Collaborative research centers (Sonderforschungsbereiche)
Research Centers (Forschungszentren)
Excellence Initiative:
Graduate schools (Graduiertenschulen)
Excellence clusters (Exzellenzcluster) (excellence cluster ≈ research center + graduate school)
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DFG Research Centers
Flexibility indistributing fundschoosing research focuses
Internal and external evaluation for high research standards
Structural impact bycreating new branches of researchenhancing technology transfer into applications, namely key technologiesbuilding and extending networks
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Overview DFG Research Centers
rcomOcean margins, Bremen (2001)
CFNFunctional nanostructures, Karlsruhe (2001)
Rudolf-Virchow-CenterExperimental biomedicine, Würzburg (2001)
MATHEONMathematics for key technologies, Berlin (2002)
CMPBMolecular physiology of the brain, Göttingen (2002)
CRTDRegenerative therapies, Dresden (2006)
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History of the DFG Research Center MATHEON
2000 first call, open topics 89 proposalsBerlin proposal I
early 2001 second call, special topic 14 proposals“Modelling and simulation in science,engineering, and social sciences”Berlin proposal II
July 2001 detailed proposal (approx. 400 pages) 3 finalists
January 2002 final international peer review
May 2002 “the winner takes it all ... Berlin” 1 winner
November 2005 submission new proposal (540+1000 pages)
January 2006 peer review by the DFG
May 2006 MATHEON prolongation until May 2010
2006—2011 Berlin Mathematical School (BMS)
October 2009 submission of next (and last) proposal
May 2010 MATHEON prolongation until May 2014
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MATHEON Application and Reapplication
November 2001400 pages
November 2005540 pages + 1000 pages on CD
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Opening Ceremony 2002
Audimax, TU Berlin: more than 1000 guests at the opening ceremony on November 20, 2002
DFG Research Center Matheon 10
Festival of Mathematics 2006
Approximately 1000 participants, Audimax, TU Berlin, on November 16, 2006
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Supporting Institutions (Trägerinstitute)
Freie Universität BerlinInstitute of Mathematics and Computer Science
Humboldt-Universität zu BerlinInstitute of Mathematics and Institute of Computer Science
Technische Universität Berlin (Host university, Sprecheruniversität)Institute of Mathematics
Weierstraß Institute for Applied Analysis and Stochastics (WIAS)
Zuse Institute Berlin (ZIB)
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Funding 2007 (Million Euros per Year)
DFG 5.6TU, HU, FU, ZIB, WIAS 3.0State of Berlin 0.1Technology Foundation Berlin 0.05Total budget: 8.75plus significant industry fundingGrant period: 4+4+4* years* subject to successful peer review
6 full professors (2+2+2)7 junior research groups (3+2+2)
65 researchers21 research students
Total: about 200 members, including ~40 professors
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Central Location of MATHEON
3rd floor of math building at TU Berlin
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MATHEON Executive Board
Alexander MielkeWIAS/HU
Volker MehrmannTU, Chair
Peter DeuflhardZIB/FU
Jürg KramerHU
Konrad PolthierFU
Andreas BleyTU
Christoph SchütteFU, Deputy Chair
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Mathematical Fields
I Optimization and discrete mathematicsWerner Römisch, Martin Skutella, Günter M. Ziegler
II Numerical analysis and scientific computingRalf Kornhuber, Reinhold Schneider, Harry Yserentant
III Applied and stochastic analysisPeter Imkeller, Caroline Lasser, Alexander Mielke
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Application Areas
A Life sciencesAlexander Bockmayr, Peter Deuflhard, Christof Schütte
B Logistics, traffic, and telecommunication networksMartin Grötschel, Rolf Möhring, Martin Skutella
C ProductionCarsten Carstensen, Dietmar Hömberg, Fredi
D Circuit simulation and opto-electronic devicesVolker Mehrmann, Alexander Mielke, Frank Schmidt
E FinanceDirk Becherer, Peter Imkeller
F VisualizationKonrad Polthier, John M. Sullivan, Günter M.
Z Education, Outreach, AdministrationJürg Kramer
from 6/2010
DFG Research Center Matheon 17
Spin-Off Companies
Indeed Visual Concepts (www.amiravis.com):3D data visualization (Amira), today: Mercury
JCMwave (www.jcmwave.com):Simulation software for nano-optical components
atesio (www.atesio.de):Plan, configure, and optimize telecommunication networks
Löbel, Borndörfer & Weider GbR (www.lbw-berlin.de)Optimization and consulting for public transport
Synoptio (www.synoptio.net)Mathematical consulting and software
Lenné 3D (www.lenne3d.de)Digital botany and real-time landscapes
inbion GmbH (inbion.math.fu-berlin.de)Bioinformatics solutions for life sciences
and more
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Selection of Industry Cooperations
BASF, Bayer, Schering, ...
Siemens, IBM, Infineon, Microsoft, NEC, Philips, ...
Deutsche Telekom (T-Systems), E-Plus, ...
DaimlerChrysler, BMW, Volkswagen, Tebis, Bosch, ...
Deutsche Bahn, BVG, IVU, Lufthansa, ABB, ADAC, Herlitz, ...
EdF, Vattenfall, E.ON Gastransport, DREWAG, BHP Billiton, ...
AMRO Bank, Bankgesellschaft Berlin, Commerzbank, Deutsche Bank, IKB, Reuters Financial Software, ...
Numerous small and medium enterprises (SME)
DFG Research Center Matheon 19
Outline
MATHEON Introduction
A: Life Sciences
B: Logistics, Traffic, Telecommunication Networks
C: Production
D: Circuit Simulation and Opto-Electronic Devices
E: Finance
F: Visualization
Z: Education, Outreach, Administration
DFG Research Center Matheon 20
A: Life Sciences
Topics:
computer-assisted surgery
patient-specific therapy planning
protein data base analysis
protein conformation dynamics
systems biology
pharmacokinetics
Domains of Expertise
Mathematical modelling of molecular processes
Computational surgery and therapy planning
Mathematical systems biology
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A1: Hyperthermia Treatment Planning
Regional Hyperthermia: local tumor heating by radiowave radiation
Aim: optimal control of antennas
Problems: handling of state constraintsperfusion modelling
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A1: Interior Point Methods in Function Space
Idea: model state constraints by barrier functionals
homotopy in function space
inexact Newton path-following
adaptive multilevel method
Homotopy Path:
existence and convergence
Lipschitz continuity
Lavrentiev Regularization:
regular Lagrange multipliers
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A2: Osteotomic Surgery Planning
Towards forward dynamics for a human knee joint
Patient-specific geometry
Finite element discretization
Time integration with inequality constraints
Unconditionally stableFew spurious oscillations
Static two-body contact problemsMortar discretizationParametrized boundariesMultigrid convergence
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A2: Two-Body Contact Problems
Fast solvers for multi-body contact problems
Monotone multigrid: asymptotic multigrid convergence rate
Nonsmooth Newton multigrid: faster than equivalent linear problem!
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A2: Real-World Data
Example using real-world data
Distal femur and proximal tibia from the Visible Human data set
Contact between the bones; foundation as rigid obstacle
Three grid levels, ≈220,000 degrees of freedom
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A3: Noise Reduction in fMRI
fMRI — functional Magnetic Resonance Imaging
Aim: Noise reduction while preserving shapes of activation areas.Method:Structural adaptive denoising (lower right)
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A4: Towards a Mathematics of Biomolecular Flexibility
Conformation Dynamics
1.3 µs simulation of 12-Alanine with implicit solvent
Three conformations visible: conformation switches on nanosecond timescale
Aims: Efficient sampling of state space, identification of conformations, intra-conformation flexibility, accurate transition rates, transition pathways
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target
activesite
amira@ZIB
ligand
target structure
diffe
rent
con
form
atio
nsConformation Dynamics & Ligand Design
A4: Towards a Mathematics of Biomolecular Flexibility
DFG Research Center Matheon 29
A6: Stochastic Modelling in Pharmacokinetics
Pharmacokinetics:
Absorption
Distribution
Metabolism
Excretion
of drugs in the body
Aim: Mathematical modelling and theoretical analysis of pharmacokinetics processes, including variability & uncertainty
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?
DFG Research Center Matheon 30
A6: Stochastic Modelling in Pharmacokinetics
Model design: development of consistent and modular pharmacokinetic models
Hybrid stochastic-deterministic models: coupling pharmacokinetic models to cellular processes
Non-linear sensitivity analysis: analyzing the effects of parameter variability
))(div()( tuFtut ⋅−=∂
Software: Virtual Lab for Modelling and Simulation in Pharmacokinetics (coop CiT)
DFG Research Center Matheon 31
A8: Systems Biology
Molecular biology:study components of a biological system in isolation
Systems biology:understand how the components interact to perform biological function
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A8: Gene Regulatory Networks
Discrete modeling approach: discrete variables and parameters
Logical analysis of the network dynamics model checking
Incorporating time constraints hybrid discrete/continuous modeling
Relating topology and dynamics of the network
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Outline
MATHEON Introduction
A: Life Sciences
B: Logistics, Traffic, Telecommunication Networks
C: Production
D: Circuit Simulation and Opto-Electronic Devices
E: Finance
F: Visualization
Z: Education, Outreach, Administration
DFG Research Center Matheon 34
B: Logistics, Traffic, Telecommunication Networks
Topics:planning of optical, multilayer, and UMTS telecommunication networksline planning, periodic timetabling, and revenue management in public transport networksoptimization in logistics, scheduling and material flowsoptimization under uncertaintysymmetries in integer programminggame theoretic methods in network design
Domains of ExpertiseTelecommunication Logistics Traffic and transport Energy and utilities
DFG Research Center Matheon 35
B3: Integrated Planning of Multi-layer Networks
Telecom network planning:
Discrete link capacities
Node hardware
Survivable routing
Multi-layer networks:
Several technological layers (IP, SDH, WDM) with strong interdependencies
Upper layer links are lower layer paths
Goal: integrated planning of all layers
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B4: UMTS Radio Network Design
Antenna
Cell
Find antenna locations and configuration for optimal network
Capacity
Coverage
Cost
Task
Network adjusts transmit powers continuously to traffic and radio conditions
Coverage depends on interference
Strong coupling between cells
Soft capacity
Evaluation of expected performance costly
Challenges with UMTS
DFG Research Center Matheon 37
B7: Focus 2: Wireless Networks
Motivation: provide location-based services (emergency, commercial) to mobile network users.
Aim: localize a mobile device using available information (without e.g. additional GPS).
One basic mathematical question: What is the information gain when superposing the geometric knowledge from two different cellular networks?
DFG Research Center Matheon 38
B8: Flows over Time
Applications
Control of traffic lights
Flow of materials in storage areasShunting of trains
Routing in a container terminal
DFG Research Center Matheon 39
B8: Flows over Time
Static network flows + time dimensions = flows over time
Task:
maximize throughput within a given time or
minimize time for a given throughput
Challenge:
develop theory and methods for efficient handling of real-world problems
exploit underlying network structureexplore complexity and develop algorithmshandle large networks
DFG Research Center Matheon 40
B13: Applications & Industrial Cooperations
flexible resource assignment impact on duration and cost
The goal is to find anoptimal project duration(cost for resource assignment vs. out-of-service cost)optimal resource assignment(capacity constraint, resource leveling)
Time-Cost-Tradeoff Problem combined with resource-leveling
Turnaround Scheduling: Resource planning for large-scale maintenance projects during shutdown of chemical plants
DFG Research Center Matheon 41
B14: Combinatorial Aspects of Logistics
Task: online/offline control of logistics systems
Practice: nothing like the logistics problem (specific aspects in each application)
Wanted: identify and tackle core models/approaches,e.g. reoptimization for online problems
Applications: vehicle dispatching, elevator control,automated transportation systems, ...
DFG Research Center Matheon 42
B14: Some Applications
Scheduling of laser welding robots in car body manufacturing (Volkswagen):
During welding each robot is fed by a laser source
Goal: minimize number of required laser sources
Control of destination-call elevator systems (Kollmorgen Steuerungstechnik):
Passenger specifies destination already when calling an elevator
Goal: small average/maximal waiting and journey times
DFG Research Center Matheon 43
B15: Service Design in Public Transport
Line Planning
two objectives: minimizing traveling times and costs
multi-commodity flow model
column generation approach
cooperation with ViP (Potsdam)
Timetabling
based on periodic event scheduling model
minimum cycle basis approach
cooperation with BVG (Berlin)
DFG Research Center Matheon 44
B15: Service Design in Public Transport
Fare Planning
maximizing revenue, profit, demand
discrete choice demand function
nonlinear optimization approach
Integrated Service Planning
complex interdependencies between individual problems
analyses of variable demand
Goal: decision support tool
SERVICE
DEMAND
DFG Research Center Matheon 45
B16: Mechansims for Network Design Problems
solve a combinatorial optimization problem
distribute the resulting cost among the users
establish fairness although users act selfishly (i.e. try to manipulate the algorithm) machine scheduling
DFG Research Center Matheon 46
Outline
MATHEON Introduction
A: Life Sciences
B: Logistics, Traffic, Telecommunication Networks
C: Production
D: Circuit Simulation and Opto-Electronic Devices
E: Finance
F: Visualization
Z: Education, Outreach, Administration
DFG Research Center Matheon 47
C: Production
Topics:
phase transitions in steels and solder alloys
production of semiconductor crystals
modeling of active and passive behavior of functional materials
online production planning
growth of thin films
Domains of Expertise
Automotive
Energy
Phase Transitions
DFG Research Center Matheon 48
C7: Application Background
Optimal planning of electricity production and trading:
Several uncertainty factors and risks must be taken into account.
Mean-risk optimization of electricity production in liberalized markets
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C7: Models and Results
Suitable Framework: Risk-averse stochastic programming
Challenges:
1. Justified finite approximations of stochastic parameters (energy demands, market prices)
2. Risk-aversion strategies
such that the resulting problems are numerically tractable
Results:
1. Scenario tree approximation methods based on stability theorems
2. Probabilistic constraints, polyhedral risk measures
Concrete Application: Medium-term optimization model for a municipal power company
DFG Research Center Matheon 50
C9: Applications of Semiconductor Crystals
Light-emitting diodes:Lifetime: ≈ 10 years
Light extraction efficiency > 32%(light bulb: ≈10%)
Blue laser:
Its use in DVD players admits up to 10-fold capacity of disc
SiC-based electronics still works at 600°C; SiC sensors placed close to car
engines save resources and costs
DFG Research Center Matheon 51
C9: Physical Vapor Transport Method
polycrystalline SiC powder sublimates inside induction-heated graphite crucible at 2000 – 3000 K and ≈20 hPa
a gas mixture consisting of Ar (inert gas), Si, SiC2, Si2C, ... is created
an SiC single crystal grows on a cooled seed
SiC seed crystal
2000-3000 K
SiC source powder
coil for induction heating
insulated graphite crucible
DFG Research Center Matheon 52
C10: Drag-out Problem for Rotating Disks
Industrial application: Fluid dynamical of PET polymer production
Steady-state solutions for angular velocities Ω=0.277, 1.0, 3.0
Comparison of FEM results to solutions of the asymptotic meniscus model (left, at constant radius r=9) and characteristics of
hyperbolic regime (right, at constant Ω=0.277).
Researchers: K. Afanasiev, A. Münch, B. Wagner, Appl. Math. Mod., 2007.
DFG Research Center Matheon 53
C11: Phase Transitions in Steel
Thermomechanical modelling of phase transitions in steelphysical properties of steel can be modified by heat treatmentwe consider three physical quantities which are associated by coupled partial and ordinary differential equationstemperature stress/displacement phase distributiondistribution of (metallurgical) phases corresponds to different degrees of hardness and ductilityphases exhibit different densities, thereby hardening may lead to distortion, i.e. undesired alterations in size and shape
Inhomogeneous cooling of a hot slab leads to a corresponding formation of the hard steel phase martensite which causes distortion.
DFG Research Center Matheon 54
C11: Heat Treatment — Simulation and Optimization
Challenges
thermomechanical modelling
adaptive numerical simulation
optimal control of hardening subject to distortion
laser welding and remelting
Adaptive simulation of laser surface hardening.
DFG Research Center Matheon 55
C14: Precipitation in GaAs Crystals
GaAs has a broad range of applications e.g. in micro- and optoelectronic devices
Heat treatment of GaAs wafer at ≈ 950 °C induces unwanted liquid As-rich precipitates
Can we prevent precipitation? Can we limit it to a homogeneous distribution?
Industrial partners:
DFG Research Center Matheon 56
C15: Magnetic Thin Films
A prime example of a pattern forming system with multiple scales and omnipresent in modern information technologies MRAMs, Spintronics
Non-Convexity & Non-Locality Pattern-Formation
Micromagnetic model: (director field)
DFG Research Center Matheon 57
C17: Separation Problems in Solders
Technological challenge: lead-free solder alloys
joint reliability: thermomechanically induced phase separation
First two images: Böhme/Müller, Lehrstuhl für Kontinuumsmechanik und Materialtheorie, TU Berlin
Goal: robust and reliable numerical simulation
coupled systems of PDEs: anisotropic phase-field models with logarithmic potential + linear elasticity [Dreyer (WIAS) & Müller (TUB)]
fast solvers: adaptive monotone multigrid methods
DFG Research Center Matheon 58
C18: Shape-memory Alloys
Shape-memory alloys and other multifunctional materials react on exterior stimuli like
temperature changes, electric or magnetic fields, light
viaelastic deformations and phase transformations (shape changes)polarization, magnetization, ...
Hysteretic behavior has its origin in time-dependent microstructures
Applicationsmedical area: superelastic grippers, dental wires, stents
MEMS: micro grippers, --valves and --pumps
DFG Research Center Matheon 59
C20: Modelling Car Frames
Aim: To model frames of automobiles with as a structure made of flexible beams connected together by rigid joints.
Challenge:
Modelling of compression, elongation and bending of the beams together and computation of the state energy from only the positions and orientations of the end points of the beams.
Optimize the structure through economic use of material while maintaining the static and dynamic properties under various load scenarios.
DFG Research Center Matheon 60
Outline
MATHEON Introduction
A: Life Sciences
B: Logistics, Traffic, Telecommunication Networks
C: Production
D: Circuit Simulation and Opto-Electronic Devices
E: Finance
F: Visualization
Z: Education, Outreach, Administration
DFG Research Center Matheon 61
D: Circuit Simulation and Opto-Electronic Devices
Topics:
shape memory alloys in airfoils
production of semiconductor crystals
methanole fuel cell optimization
metamaterials
Domains of Expertise
Electronic devices
Photonic devices
DFG Research Center Matheon 62
D1: Switched Systems of DAEs
Complex dynamical systems switching in time and frequency:
Electronic circuits: different device models used for different frequencies
Mechanical systems: robot manipulators or automatic gear-boxes (with DaimlerChrysler)
Biological systems: act differently depending on day cycles or on the nutrition
Traffic systems: operate differently depending on delays
DFG Research Center Matheon 63
D7: Numerical Simulation of Integrated Circuits
Coupling between circuits and components
Required by technological progress, miniaturization, detailed physical modeling
Mathematical Challenges
Stable computation of tractability index
Consistent initialization
Stable treatment of high order derivatives
Project focus
Apply algorithmic differentiation instead of numerical differentiation
Improve algorithms for index computation
Improve algorithms for consistent initialization
DFG Research Center Matheon 64
D13: Coupled Systems
Goals
Efficient numerical methods for coupled systemscoupling of different simulatorserror estimators step-size and convergence controller for coupled simulators
Model reduction for coupled systemspreservation of interconnection structure preservation of subsystem properties error estimates for the entire system
DFG Research Center Matheon 65
D14: Nonlinear and Dispersive Effects in Fiber Optics
Generalized Nonlinear Schrödinger Equation (GNLS)
Soliton Propagation Modulation Instability Supercontinuum Generation
DFG Research Center Matheon 66
D15: Photonic Crystal Fibers
Eigenvalue problems for Maxwell’s equations
Goal: Optimization of Geometry High order edge elementsAdaptive finite elements
Visualization of an PhC-eigenmode
courtesy Crystal Fibre, S.A.
PhC-fiber
DFG Research Center Matheon 67
Outline
MATHEON Introduction
A: Life Sciences
B: Logistics, Traffic, Telecommunication Networks
C: Production
D: Circuit Simulation and Opto-Electronic Devices
E: Finance
F: Visualization
Z: Education, Outreach, Administration
DFG Research Center Matheon 68
E: Finance
Topics:
measurement and hedging of risks
interaction models for asset price fluctuation
Domains of Expertise
Risk management and hedging
Simulation and calibration
DFG Research Center Matheon 69
E1: Motivation
Understanding statistical properties of price processes is of paramount importance for financial industry
Statistical models reproduce observed data, but do not give insight into casual connections
Agent based models are an attempt to understand fundamental mechanisms driving financial markets
Project E1 investigates an agent based model on the level of order book dynamics
More information and an applet version of the simulation tool are available on the project's homepage:www.wias-berlin.de/research-groups/stochsys/dfg.html
DFG Research Center Matheon 70
E2: Project Aims
Aim: Improve means of controlling financial risk due to climateRelevance: 20—30% of world wide economy affected by weather
Difficulty: Climate is a complex system
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E2: Hedging
Hedging of weather dependent income fluctuationsAim: Dynamic hedging with exchange-traded climate securities
Relevant and practical suggestions allowing to mitigate weather risk
Case Study: Weather derivatives based on Heating Degree Days
Result: The optimal investment in HDD derivatives is given by
DFG Research Center Matheon 72
E5: Main Problem and Goals
DFG Research Center Matheon 73
Outline
MATHEON Introduction
A: Life Sciences
B: Logistics, Traffic, Telecommunication Networks
C: Production
D: Circuit Simulation and Opto-Electronic Devices
E: Finance
F: Visualization
Z: Education, Outreach, Administration
DFG Research Center Matheon 74
F: Visualization
Topics:
discrete differential geometry
geometry processing
image processing
virtual reality PORTAL
Domains of Expertise
Geometry Processing
Image Processing
Interactive Graphics
DFG Research Center Matheon 75
F1: Discrete Surface Parametrizations
In computer graphics and numerics, surfaces in space are represented by surface meshes
Our aim: Develop theory and applications for surface meshes by discretizing the notions and methods of classical differential geometry
This is the paradigm of discrete differential geometry
Leads to “smart” discretizations
Examples of discrete minimal surfaces. They are discrete analogs of classical minimal surfaces
DFG Research Center Matheon 76
F2: Atlas-based 3D Image Segmentation
Applications
Geometry Reconstructionfrom 2D and 3d image data
Analysis of Shape Variability based on statistical shape models
Clinical Therapy and Surgery Planning
DFG Research Center Matheon 77
F4: Geometric Shape Optimization
Reverse engineeringClass-A surfaces for automotive design
Industry cooperation: Tebis AG
Thin shell simulationEfficient simulation of cloth dynamics
Cooperation: Columbia University, USA
Surface reconstructionReconstruction from 3D laser scans
Industry cooperation: Tube Experts
DFG Research Center Matheon 78
F4: Geometric Shape Optimization
3D mesh compression
Efficient storage of huge geometries with millions of triangles
Fast online transfer of 3D data sets
Goal: new industry standards such as Java 3D and MPEG-4
Industry cooperation: mental images GmbH
DFG Research Center Matheon 79
F4: Geometric Shape Optimization
Multimedia & Outreach: The award-winning video MESH
A journey through the geometry of polyhedral meshes
From Plato to contemporary geometry processing
Cooperation: Beau Janzen, Zipheron Design Labs
DFG Research Center Matheon 80
F5: Mathematics in Virtual Reality
Real-time Simulation of Fluid Motionbased on the discrete smoke ring flow.
Non-Euclidean Spaces:Interactive visualization and navigation.
Interactive Visualization and Modelingof integrable systems, e.g. K-surfaces.
Applications
DFG Research Center Matheon 81
F5: Mathematics in Virtual Reality
Cooperations & Outreach
Portal:Frequent demos for VIPs
3D-Lab at TU Berlin (EFRE):3D printer and scanner
Interactive navigation through scanned construction sites
DFG Research Center Matheon 82
F6: Multilevel Methods on Manifold Meshes
Surface Parameterization
permits high-quality regular remeshing
gives rise to subdivision hierarchies
New Quad-Cover algorithm generates regular surface parameterizations automatically[Eurographics, 2007]
1. Irregular scan data
2. Parameterization
3. Multi-resolution mesh
DFG Research Center Matheon 83
Outline
MATHEON Introduction
A: Life Sciences
B: Logistics, Traffic, Telecommunication Networks
C: Production
D: Circuit Simulation and Opto-Electronic Devices
E: Finance
F: Visualization
Z: Education, Outreach, Administration
DFG Research Center Matheon 84
Z: Education, Outreach, Administration
Topics:
modern mathematics at school
school teachers at universities
network of math-science oriented schools
public awareness of Mathematics
media presence
Domains of Expertise
Education
Training
Course Design
DFG Research Center Matheon 85
Z1.1: Current Mathematics at Schools
Aim: Enlarging the impact of Matheon with respect to the mathematical education at Berlin schools
Concept of the seminar courseBased on the new school law in Berlin
Introduce modelling problems at schools in cooperation with Matheon scientists
Didactic support by the delegated teachers
"Facharbeit" at the end of the course
School mathematics
Seminar course
University mathematics
Analysis
Linearalgebra/
Analyticalgeometry
Stochastic
MatheonModelling, simulation and optimization
of real-world processes
Mathematical modelling
DFG Research Center Matheon 86
Z1.2: Teachers at Universities
Aim: Solidifying and extending the cooperation between schools and universities
School teachers at universityStrengthening the teachers’/teacher students’ competence with respect to practical needs through a close cooperation among delegated teachers, scientists and students in:
Lectures
Seminars
Exercises
Practical courses in schools
Examinations
Financial and organizational support through the delegation of teachers by the Senatsverwaltung für Bildung, Wissenschaft und Forschung
DFG Research Center Matheon 87
Refreshing and completing the teachers’ mathematical and didactical knowledge
Promotion of mathematically talented students of the “Network Schools” and acquisition of university credits before entering the university
Advising and influencing the designof new curricula
Developing concepts for furtherance of highly talented pupils starting in grade 5
Z1.2: Teachers at Universities
Network of math-science oriented schools
Further development of mathematical education in schools by:
Foto: Heike Zappe, Humboldt-Universität zu Berlin
DFG Research Center Matheon 88
Z1.2: Teachers at Universities
Public awareness of mathematics
Improvement of the image of mathematics in the public at large by:
Didactical advice concerning organization and implementation of the online competition “Digitaler Adventskalender”
Support in organizing and carrying out the “Berliner Tag der Mathematik” and “Mathematikolympiade”
Organization and didactical support of activities at the intersection of school and university such as
“Rent the Center”
Summer School “Lust auf Mathematik”
DFG Research Center Matheon 89
Z1.3: Visualization of Algorithms
Visage Software for education
Based on the interactive geometry software Cinderella a software package for teaching graph algorithms is developed.
Features:
Free experimentation environment for graphs and algorithms
Creation of internet-based, interactive tutoring systems
Providing ready-to-use teaching material
DFG Research Center Matheon 90
Z1.3: Visualization of Algorithms
Experiences in school
Proving the software in school
Development of new didactic concepts
Evaluation of material and methods in everyday school life
Free experimentation environment for graphs and algorithms
Film
DFG Research Center MATHEONMathematics for key technologies
DFG Research Center MATHEON
Mathematics for key technologies:Modelling, simulation, and optimization
of real-world processes
Martin GrötschelThe End