Industrial Mathematics Institute Kepler Universität Linz MathConsult GmbH

1. 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

2. 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)

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

4. MathConsult GmbH Main fields of expertise: • Numerical Simulation • Optimization • Parameter Identification • Mathematical Finance

5. 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

6. Results optimal cooling with increasing casting speed

7. 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

8. Material composition - mass fractions of CO and Fe Temperature distribution Solid material flow

9. 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

10. Results Minimum weight Uniform stress distribution original Design optimal Design

11. 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 !

12. Results Comparison of different methods MPEG IndMath method original data 3D-Bitmap, 3.2 MByte Reconstruction from a 40:1 compression

13. 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.