Oberseminar Numerical Mathematics / Scientific Computing
Grigorios A. Pavliotis
Imperial College London
Analysis and numerics for SPDEs with multiple scales
Abstract:
In this talk we will present analytical and numerical techniques for studying stochastic partial differential equations with multiple scales. After showing a rigorous homogenization theorem for SPDEs with quadratic nonlinearities, we present a numerical method for solving efficiently SPDEs with multiple scales. We then apply these analytical and numerical techniques to the stochastic Kuramoto-Shivashinsky equation for which we show that noise induced intermittent behavior and noise induced stabilization of solutions can occur. Finally, we show how ideas from parameter estimation for diffusion processes can be used in order to obtain low dimensional coarse-grained models from time series of the SPDE (projected onto the dominant modes). This is joint work with D. Blomker and M. Hairer (analysis), A. Abdulle (numerical analysis), M. Pradas Gene, D. Tseluiko, S. Kalliadasis, D.T. Papageorgiou (stochastic Kuramoto-Shivashinsky equation), S. Krmuscheid, S. Kalliadasis (data-driven derivation of coarse-grained models).
| Date: | 25.06.12 | Time: | 17:00 Uhr | Location: | FU Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin. | Room: | 031 Basement |