%0 Report %1 cliffe1992iterative %A Cliffe, K. %A Garratt, T. %A Spence, A. %C Harwell, United Kingdom %D 1992 %K 76e09-stability-and-instability-of-nonparallel-flows 76m10-finite-element-methods-in-fluid-mechanics %N AEA-D&R--0324 %T Iterative methods for the detection of Hopf bifurcations in finite element discretisation of incompressible flow problems %X This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalised eigenvalue problems arising from mixed finite element discretisations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and can be used in a scheme to determine the stability of steady state solutions and to detect Hopf bifurcations. We introduce a modified Cayley transform of the generalised eigenvalue problem which overcomes a drawback of the usual Cayley transform applied to such problems. Standard iterative methods are then applied to the transformed eigenvalue problem to compute approximations to the eigenvalue of smallest real part. Numerical experiments are performed using a model of double diffusive convection.

@techreport{cliffe1992iterative, abstract = {This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalised eigenvalue problems arising from mixed finite element discretisations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and can be used in a scheme to determine the stability of steady state solutions and to detect Hopf bifurcations. We introduce a modified Cayley transform of the generalised eigenvalue problem which overcomes a drawback of the usual Cayley transform applied to such problems. Standard iterative methods are then applied to the transformed eigenvalue problem to compute approximations to the eigenvalue of smallest real part. Numerical experiments are performed using a model of double diffusive convection.}, added-at = {2020-11-13T00:56:31.000+0100}, address = {Harwell, United Kingdom}, author = {Cliffe, K. and Garratt, T. and Spence, A.}, biburl = {https://www.bibsonomy.org/bibtex/2fb121f7435320ca74040b63121569cbf/gdmcbain}, institution = {AEA Technology Decommissioning and Radwaste, . Radwaste Disposal Div.}, interhash = {76b6c4bb56cb4c782191b04b53f93462}, intrahash = {fb121f7435320ca74040b63121569cbf}, keywords = {76e09-stability-and-instability-of-nonparallel-flows 76m10-finite-element-methods-in-fluid-mechanics}, number = { AEA-D&R--0324 }, timestamp = {2020-11-13T01:06:21.000+0100}, title = {Iterative methods for the detection of Hopf bifurcations in finite element discretisation of incompressible flow problems}, year = 1992 }