Regensburg 2007 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 24: Poster I

DY 24.57: Poster

Mittwoch, 28. März 2007, 16:00–18:00, Poster D

Blocking method in model reduction for nonlinear dynamics — •Thorsten Bogner — Condensed Matter Theory, Fakutät für Physik,* Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany

In many fields where nonlinear dynamical systems arise, e.g. fluid dynamics, already advanced numerical methods are known. Unfortunately, these methods often lead to a very high dimensional description if an acceptable error bound is desired. In these cases model reduction can simplify the numerical description significantly. It can also make new applications possible, where speed is necessary or computational power is limited.

An established method in model reduction is the Proper Orthogonal Decomposition (POD) that aims on finding a subspace of the phase space that can reproduce the dynamics ’optimally’. This is based on the spatial correlation matrix, which is numerically approximated from sample trajectories. It has the disadvantage, that the large system has to be solved to perform the POD.

Instead of treating the large system directly, we use a blocking method to get an approximate POD of the full system. Also an iteration is possible to increase the accuracy. For our method only calculations on small systems are necessary. This leads to a significant reduction of work load and memory size for the POD itself.

We test our method on the linear 1D diffusion equation as a toy modell with is also accessible analytically. Further we introduce nonlinearities resulting in the Burgers equations and the KPZ equation.