Continuation of Probability Density Functions using a Generalized Lyapunov Approach

Autor:	Baars, S., Viebahn, J. P., Mulder, T. E., Kuehn, C., Wubs, F. W., Dijkstra, H. A.
Rok vydání:	2020
Předmět:	Mathematics - Numerical Analysis Physics - Computational Physics Physics - Data Analysis Statistics and Probability Physics - Fluid Dynamics Physics - Geophysics
Zdroj:	Journal of Computational Physics 336 (2017) 627-643
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jcp.2017.02.021
Popis:	Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2011.05690 Zobrazit plný text záznamu View this record from Arxiv