Kein Folientitel

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Industrial Mathematics Institute Kepler
Universität Linz MathConsult GmbH o.Univ.-Prof.
Dipl.-Ing. Dr. Heinz W. Engl http//www.indmath.
uni-linz.ac.at http//imcc.indmath.uni-linz.ac.at
http//www.mathconsult.co.at
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• The Industrial Mathematics Institute
• includes the Industrial Mathematics Competence
  Center
• participates in
• the SFB013 Numerical and Symbolic Scientific
  Computing
• the Software Competence Center Hagenberg
• ECMI (European Consortium for Mathematics in
  Industry)

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• Basic Research Inverse Problems
• Main application areas
• Shape optimization
• Process engineering (direct - inverse problems)
• Continuum mechanics
• Image processing
• Identification of parameters

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MathConsult GmbH

• Main fields of expertise
• Numerical Simulation
• Optimization
• Parameter Identification
• Mathematical Finance

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Optimal Cooling Strategies in Continuous Casting

• In the soft-reduction zone strand thickness is
  reduced by compression
• in order to counter segregation defects arising
  during solidification.
• Effective soft reduction requires
• that the point of complete solidification
  remains within a prescribed zone
• control of the location of this point by water
  cooling with the additional
• difficulty of varying casting speeds
• Mathematical model Reformulation as a nonlinear
  optimization problem
• combined with regularization

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Results
optimal cooling with increasing casting speed
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Numerical Simulation of the COREX- Process

• Industrial partner VOEST Alpine
  Industrieanlagenbau, Linz
• new technology to produce metallic iron
• two reactors reduction shaft and melter gasifier
• Mathematical modelling and numerical simulation
  of
• the flow of the solid material (iron ore, sponge
  iron) and of the reduction,
• the chemical reactions,
• the temperature distribution, and
• the deposition of dust contained in the reduction
  gas
• 3-dimensional model leads to a coupled system of
  about 40 nonlinear PDEs

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Material composition - mass fractions of CO and
Fe
Temperature distribution
Solid material flow
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Structural Optimization

• Industrial partner AVL List GmbH, Graz
• The aims in the area of structural optimization
  are
• weight reduction,
• increasing component lifetime by reducing high
  stress areas, and
• to obtain uniform stress distribution in the
  optimal design
• ? numerical solution of nonlinear optimization
  problems coupled with nonlinear field equations

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Results
Minimum weight Uniform stress distribution
original Design
optimal Design
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Compression of 3D Ultrasound Data
Industrial partner Kretztechnik AG,
Redl-Zipf Transfer of 3-dimensional medical
ultrasound data sets via electronic
networks Problem typical data size 2-16
MByte Solution data compression with wavelets
without loss of relevant information !
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Results
Comparison of different methods
IndMath method
MPEG
original data
3D-Bitmap, 3.2 MByte
Reconstruction from a 401 compression
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Pricing of Financial Derivatives
Vega (derivative of the value w.r.t. the
volatility) of a European up-and-out-call option
on an equity paying two discrete dividends. Vega
is plotted against the spot price of the
underlying and the time in days.
American call option on the dirty value of a
coupon bearing bond as a function of the spot
rate and the days till expiry of the option.