On the use of POD-based ROMs to analyze bifurcations in some dissipative systems Articles uri icon

publication date

  • September 2012

start page

  • 1393

end page

  • 1405

issue

  • 17

volume

  • 24

international standard serial number (ISSN)

  • 0167-2789

electronic international standard serial number (EISSN)

  • 1872-8022

abstract

  • This paper deals with the use of POD-based reduced order models to construct bifurcation diagrams (which requires calculating steady and time-dependent attractors) in complex bifurcation problems involving dissipative systems. The method proposed in the paper relies on the observation that POD manifolds resulting from snapshots calculated in time-dependent runs for specific values of the parameters of the problem also contain the attractors for other values of the parameters. The reason for this property is explained for a general class of dissipative systems, which includes many problems of scientific/industrial interest. The consequence is that appropriate POD manifolds can be calculated in a quite computationally efficient way. The method is illustrated considering both a simple bifurcation problem for a Fisher-like equation and a fairly complex bifurcation problem for the complex Ginzburg&-Landau equation.