On the use of POD-based ROMs to analyze bifurcations in some dissipative systems Articles
Overview
published in
- PHYSICA D-NONLINEAR PHENOMENA Journal
publication date
- September 2012
start page
- 1393
end page
- 1405
issue
- 17
volume
- 24
Digital Object Identifier (DOI)
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.