%0 Book Section %1 statphys23_0290 %A Bogner, T. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K decomposition density dynamics matrix model nonlinear orthogonal proper reduction renormalisation statphys23 topic-5 %T Density Matrix Renormalisation for model reduction in nonlinear dynamics %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=290 %X A new approach for calculating effective models for nonlinear dynamical systems is presented. This is accomplished by combining the Density Matrix Renormalisation Group(DMRG), a numerical precision method in the field of strongly correlated quantum systems, and the Proper Orthogonal Decomposition(POD), a widely used method in the numerics of Partial Differential Equations(PDEs). Our method allows to find a reduction without ever performing a calculation on the full system. We apply our method to several nonlinear PDEs. An analysis of the errors and a comparison to existing model reduction methods is made. Also the stability of the algorithm will be discussed. The results of our approach are comparable or even superior to standard POD. This holds for both, accuracy and computational costs.

@incollection{statphys23_0290, abstract = {A new approach for calculating effective models for nonlinear dynamical systems is presented. This is accomplished by combining the Density Matrix Renormalisation Group(DMRG), a numerical precision method in the field of strongly correlated quantum systems, and the Proper Orthogonal Decomposition(POD), a widely used method in the numerics of Partial Differential Equations(PDEs). Our method allows to find a reduction without ever performing a calculation on the full system. We apply our method to several nonlinear PDEs. An analysis of the errors and a comparison to existing model reduction methods is made. Also the stability of the algorithm will be discussed. The results of our approach are comparable or even superior to standard POD. This holds for both, accuracy and computational costs.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Bogner, T.}, biburl = {https://www.bibsonomy.org/bibtex/279fb63d0d08094ef8cd9d125eb1480c6/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {7014ec58342e50d7d21c13249c91c537}, intrahash = {79fb63d0d08094ef8cd9d125eb1480c6}, keywords = {decomposition density dynamics matrix model nonlinear orthogonal proper reduction renormalisation statphys23 topic-5}, month = {9-13 July}, timestamp = {2007-06-20T10:16:16.000+0200}, title = {Density Matrix Renormalisation for model reduction in nonlinear dynamics}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=290}, year = 2007 }