Scientific Computing and Numerics (SCAN) Seminar
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.
Joint work with S. Baars, J.P. Viebahn, T. E. Mulder, C. Kuehn, and F. W. Wubs