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Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 30
COMPUTATIONAL METHODS FOR ENGINEERING SCIENCE Edited by: B.H.V. Topping
Chapter 10
Proper Generalized Decomposition Based Model Reduction: First Steps Towards a Change of Paradigm in Computational Mechanics F. Chinesta^{1}, A. Leygue^{1}, F. Bordeu^{1}, E. Cueto^{2} and A. Ammar^{3}
^{1}GEM 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", SaxeCoburg Publications, Stirlingshire, UK, Chapter 10, pp 237264, 2012. doi:10.4203/csets.30.10
Keywords: model order reduction, proper generalised decomposition, parametric models, high dimensional models, curse of dimensionality.
Summary
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 simulationbased engineering
sciences called proper generalized decomposition (PGD) which has proved
its tremendous possibilities in the context of some basic demonstrators. Its transfer
for treating largescale 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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