Numerical Analysis and Scientific Computing Seminar

Lyapunov Inverse Iteration for Identifying Hopf Bifurcations in Models of Incompressible Flow

Speaker: Howard Elman, University of Maryland

Location: Warren Weaver Hall 1302

Date: March 2, 2012, 10 a.m.

Synopsis:

Identification of instability caused by Hopf bifurcation requires computing the rightmost pair of complex eigenvalues of large eigenvalue problems. A new method replaces this computation with inverse iteration for a certain set of real eigenvalues. We enhance the robustness and efficiency of this approach and demonstrate its utility on examples from fluid dynamics. We explore inexact inner iterations, the impact of solution strategy for a subsidiary Lyapunov system, and effects of eigenvalue distribution on performance.

Joint work with

Karl Meerbergen, Katholieke Universiteit Leuven, Belgium Alastair Spence, University of Bath, United Kingdom Minghao Wu, University of Maryland