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The Proper Generalized Decomposition for Advanced Numerical Simulations

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Abstract

This chapter summarizes several recurrent issues related to efficient numerical simulations of problems encountered in engineering sciences. In order to alleviate such issues, model reduction techniques constitute an appealing alternative to standard discretization techniques. First, reduction techniques based on Proper Orthogonal Decompositions are revisited. Their use is illustrated and discussed, suggesting the interest of a priori separated representations which are at the heart of the Proper Generalized Decomposition (PGD). The main ideas behind the PGD are described, underlying its potential for addressing standard computational mechanics models in a non-standard way, within a new computational engineering paradigm. The chapter ends with a brief overview of some recent PGD applications in different areas, proving the potentiality of this novel technique.

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Authors and Affiliations

  1. GeM UMR CNRS, Ecole Centrale de Nantes, Nantes Cedex 3, France

    Francisco Chinesta & Adrien Leygue

  2. Applied Mathematics, Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Roland Keunings

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  1. Francisco Chinesta
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Correspondence to Francisco Chinesta .

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Chinesta, F., Keunings, R., Leygue, A. (2014). Introduction. In: The Proper Generalized Decomposition for Advanced Numerical Simulations. SpringerBriefs in Applied Sciences and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-02865-1_1

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