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Reduced‐order modelling for solving linear and non‐linear equations
Author(s) -
Verdon N.,
Allery C.,
Béghein C.,
Hamdouni A.,
Ryckelynck D.
Publication year - 2011
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1286
Subject(s) - a priori and a posteriori , computation , mathematics , burgers' equation , reduction (mathematics) , term (time) , mathematical analysis , partial differential equation , algorithm , physics , geometry , philosophy , epistemology , quantum mechanics
In this article, we present some investigations about the solving of transfer equations by reduced‐order models (ROM). We introduce a ROM, the a priori reduction (APR), and we present the results obtained for the 2D unsteady convection–diffusion equation and the 1D Burgers equation. The APR approach is then compared with the Karhunen–Loève decomposition and some properties of this method are emphasized. We show that the computation time necessary for solving these transfer equations is reduced, whereas the accuracy is of the same order of magnitude, in comparison with the solution obtained for the full model with classical methods. At last it is noticed that the APR method is an efficient way to correct the long term behavior of low order dynamical systems. Copyright © 2009 John Wiley & Sons, Ltd.