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Continuation of bifurcations of periodic orbits for large-scale systems

Author
Net, M.; Sanchez, J.
Type of activity
Journal article
Journal
SIAM journal on applied dynamical systems
Date of publication
2015-01-01
Volume
14
Number
2
First page
674
Last page
698
DOI
https://doi.org/10.1137/140981010 Open in new window
Project funding
Cálculo numérico de variedades invariantes en EDPS disipativas. Aplicaciones a la convección térmica
Numerical study of the mechanisms of transition to weak turbulence in rotating thermal convection in spherical geometry
Repository
http://hdl.handle.net/2117/76843 Open in new window
URL
http://epubs.siam.org/doi/abs/10.1137/140981010 Open in new window
Abstract
A methodology to track bifurcations of periodic orbits in large-scale dissipative systems depending on two parameters is presented. It is based on the application of iterative Newton-Krylov techniques to extended systems. To evaluate the action of the Jacobian it is necessary to integrate variational equations up to second order. It is shown that this is possible by integrating systems of dimension at most four times that of the original equations. In order to check the robustness of the method,...
Citation
Net, M., Sanchez, J. Continuation of bifurcations of periodic orbits for large-scale systems. "SIAM journal on applied dynamical systems", 01 Gener 2015, núm. 2, p. 674-698.
Keywords
ALGORITHM, COMPUTATION, FLOWS, GMRES, KRYLOV METHODS, NAVIER-STOKES EQUATIONS, Newton-Krylov methods, ODES, POINTS, bifurcation tracking, continuation methods, extended systems, numerical computation of invariant objects, periodic orbits, variational equations
Group of research
DF - Dinàmica de Fluids: formació d'estructures i aplicacions geofísiques

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