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Lyapunov inverse iteration for identifying Hopf bifurcations in models of incompressible flow


Reference:

Elman, H. C., Meerbergen, K., Spence, A. and Wu, M., 2012. Lyapunov inverse iteration for identifying Hopf bifurcations in models of incompressible flow. SIAM Journal on Scientific Computing, 34 (3), A1584-A1606.

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    Official URL:

    http://dx.doi.org/10.1137/110827600

    Abstract

    The identification of instability in large-scale dynamical systems caused by Hopf bifurcation is difficult because of the problem of identifying the rightmost pair of complex eigenvalues of large sparse generalized eigenvalue problems. A new method developed in [K. Meerbergen and A. Spence, SIAM J. Matrix Anal. Appl., 31 (2010), pp. 1982--1999] avoids this computation, instead performing an inverse iteration for a certain set of real eigenvalues that requires the solution of a large-scale Lyapunov equation at each iteration. In this study, we refine the Lyapunov inverse iteration method to make it more robust and efficient, and we examine its performance on challenging test problems arising from fluid dynamics. Various implementation issues are discussed, including the use of inexact inner iterations and the impact of the choice of iterative solution for the Lyapunov equations, and the effect of eigenvalue distribution on performance. Numerical experiments demonstrate the robustness of the algorithm. Read More: http://epubs.siam.org/doi/abs/10.1137/110827600

    Details

    Item Type Articles
    CreatorsElman, H. C., Meerbergen, K., Spence, A. and Wu, M.
    DOI10.1137/110827600
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher StatementSpence_SIAM_J_Sci_Comp_2012_34_3_A1584.pdf: © 2012 Society for Industrial and Applied Mathematics
    RefereedYes
    StatusPublished
    ID Code32341

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