The DNA Seminar
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Seminars during Spring 2013
| Date | Speaker and title |
|---|---|
| 10. April (Wednesday) 13:15-14:00 Room 734 | Claudio Marchi (Padova): Continuous dependence estimates for the ergodic problem with an application to homogenization. Abstract: We consider the ergodic problem for Hamilton-Jacobi-Bellman operators. Under periodicity and ellipticity conditions, we show some continuous dependence estimates, namely estimates of the distance between the solutions of two problems with different coefficients. Afterwards, this result will allow us to estimate the rate of convergence for the homogenization problem of some stationary HJB equations. |
| 21. Feb (Thursday) 15.15-16.00 Room 734 | Timo Eirola (Aalto): Particle trajectory computations in a fusion reactor |
| 14. Feb (Thursday) 15.15-16.00 Room 734 | Rinaldo Colombo (University of Brescia, Italy): Crowd Dynamics through Hyperbolic Conservation Laws Recent results on the modeling of crowd dynamics are presented. The basic analytical properties of local and non-local models are described, while numerical integrations show qualitative properties of the corresponding solutions. |
| 13. Feb (Wednesday) 13.15–14.00 Room 734 | Markus Grasmair (Wien): Variational Methods for Ill-Posed Problems The problem of solving an operator equation of the form \(F(u) = v\) can, equivalently, be approached by minimising the residual \(\|F(u)-v\|^p\) for some convenient norm and some \(p \ge 1\). With this formulation, it is also possible to treat equations with noisy right hand side or noisy operators, where no exact solution may exist, but only some kind of best approximation. If the operator \(F\), however, is ill-posed or ill-conditioned, then the minimiser of the residual will, in general, be unsatisfactory. In order to obtain a meaningful solution, it is then necessary to introduce some kind of regularisation, either in the form of additional penalty terms (Tikhonov regularisation) or by choosing a suitable iterative minimisation method and stopping the iteration well before convergence is reached (iterative regularisation). In this talk we will discuss these approaches with a particular emphasis on non-linear and non-smooth methods and also provide results concerning (semi-)convergence and convergence rates. |
| 01. Feb (Friday) 09.15–10.00 Room 734 | Michael Vynnycky: Mathematical modelling for energy applications, industrial processes and natural phenomena |
| 30. Jan (Wednesday) 13.15–14.00 Room 734 | Anton Evgrafov (DTU): Topology optimization in engineering design: present state and future challenges. |
| 30. Jan 14:15-15:00 Room 734 | Prof. Dr. Dietmar Hömberg (TU Berlin and Weierstrass Institute for Applied Analysis and Stochastics): Optimal control of multiphase steel production. Multiphase steels combine good formability properties with high strength and have therefore become important construction materials, especially in automotive industry. The standard process route is hot rolling with subsequent controlled cooling to adjust the desired phase mixture. In the first part of the talk a phenomenological model for the austenite ferrite phase transition is developed in terms of a nucleation and growth process, where the growth rate depends on the carbon concentration in austenite. The approach allows for further extensions, e.g., to account for a speed up of nucleation due to deformation of austenite grains. The model is coupled with an energy balance to describe the phase transitions on a run-out table after hot rolling. Here, the most important control parameters are the amount of water flowing per time and the feed velocity of the strip. The spatial flux profile of the water nozzles has been identified from experiments. Since the process window for the adjustment of the phase composition is very tight the computation of optimal process parameters is an important task also in practice. This is discussed in the second part of the talk using a classical optimal control approach, where a coefficient in the Robin boundary condition acts as the control. I will discuss necessary and sufficient optimality conditions, describe a SQP-approach for its numerical solution and conclude with some numerical results. (Joint work with K. Krumbiegel and N. Togobytska, WIAS). |