Abstract
The Karhunen-Loève (K-L) analysis is widely used to generate low-dimensional dynamical systems, which have the same low-dimensional attractors as some large-scale simulations of PDEs. If the PDE is symmetric with respect to a symmetry group G, the dynamical system has to be equivariant under G to capture the full phase space. It is shown that symmetrizing the K-L eigenmodes instead of symmetrizing the data leads to considerable computational savings if the K-L analysis is done in the snapshot method. The feasibility of the approach is demonstrated with an analysis of Kolmogorov flow.
Original language | English (US) |
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Pages (from-to) | 1526-1532 |
Number of pages | 7 |
Journal | SIAM Journal on Scientific Computing |
Volume | 18 |
Issue number | 5 |
DOIs | |
State | Published - Sep 1997 |
Keywords
- Karhunen-Loève analysis
- Optimal eigenfunctions
- Symmetry
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics