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COMPUTATIONAL METHODS FOR ENGINEERING SCIENCE
Edited by: B.H.V. Topping
Proper Generalized Decomposition Based Model Reduction: First Steps Towards a Change of Paradigm in Computational Mechanics
F. Chinesta1, A. Leygue1, F. Bordeu1, E. Cueto2 and A. Ammar3
1GEM UMR CNRS - Ecole Centrale de Nantes, EADS Corporate Foundation International Chair, France
F. Chinesta, A. Leygue, F. Bordeu, E. Cueto, A. Ammar, "Proper Generalized Decomposition Based Model Reduction: First Steps Towards a Change of Paradigm in Computational Mechanics", in B.H.V. Topping, (Editor), "Computational Methods for Engineering Science", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 10, pp 237-264, 2012. doi:10.4203/csets.30.10
Keywords: model order reduction, proper generalised decomposition, parametric models, high dimensional models, curse of dimensionality.
This chapter focuses on the development of a new simulation paradigm enabling the solving of models until now never solved and on introducing spectacular CPU time savings (of the order of millions) that combined with supercomputing could revolutionise future ICT (information and communication technologies) at the heart of science and technology. A new paradigm is proposed for simulation-based engineering sciences called proper generalized decomposition (PGD) which has proved its tremendous possibilities in the context of some basic demonstrators. Its transfer for treating large-scale models will require further developments that are in progress.
Many problems in science and engineering today remain intractable, in spite of the impressive progress attained in mechanical modelling, numerical analysis, discretisation techniques and computer science during the last decade, because their numerical complexity, or the restrictions imposed by different requirements make them unaffordable for today’s technologies.
The following different challenging scenarios for efficient numerical simulations are enumerated:
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