The Proper Generalized Decomposition for Advanced Numerical Simulations
Many problems in scientific computing are intractable with classical numerical techniques. These fail, for example, in the solution of high-dimensional models due to the exponential increase of the number of degrees of freedom.Recently, the authors of thi
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Francisco Chinesta Roland Keunings Adrien Leygue
The Proper Generalized Decomposition for Advanced Numerical Simulations A Primer
SpringerBriefs in Applied Sciences and Technology
For further volumes: http://www.springer.com/series/8884
Francisco Chinesta Roland Keunings Adrien Leygue •
The Proper Generalized Decomposition for Advanced Numerical Simulations A Primer
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Roland Keunings Applied Mathematics Université catholique de Louvain Louvain-la-Neuve Belgium
Francisco Chinesta Adrien Leygue GeM UMR CNRS Ecole Centrale de Nantes Nantes France
ISSN 2191-530X ISBN 978-3-319-02864-4 DOI 10.1007/978-3-319-02865-1
ISSN 2191-5318 (electronic) ISBN 978-3-319-02865-1 (eBook)
Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2013951633 Ó The Author(s) 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Ofelia, Françoise and Samantha
Preface
In spite of the impressive progress made during the last decades in mathematical modelling and techniques of scientific computing, many problems in science and engineering remain intractable. Among them, we can cite those related to highdimensional models (i.e., in dynamics of complex fluids, quantum chemistry), for which classical mesh-based approaches fail due to the exponen
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