Numerical Modeling in Materials Science and Engineering (Springer Series in Computational Mathematics)

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Michel Bellet Michel Deville SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS

Numerical Modeling in Materials Science

and Engineering

Springer

32

Springer Series in Computational Mathematics Editorial Board R. Bank R.L. Graham J. Stoer R. Varga H. Yserentant

32

Michel Rappaz Michel Bellet Michel Deville

Numerical M odeling in M aterials Science and Engineering T ranslated by R ay Snyder

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Michel Rappaz Computational Materials Laboratory Polytechnique Fédérale de Lausanne 1015 Lausanne, Switzerland [email protected] Michel Bellet Mines-ParisTech – CEMEF – UMR CNRS 7635 Centre de Mise en Forme des Matériaux (Materials Processing) BP 207 06904 Sophia Antipolis, France [email protected] Michel Deville Computational Engineering Laboratory Polytechnique Fédérale de Lausanne 1015 Lausanne, Switzerland [email protected] Translator Ray Snyder Originally published in French under the title Modélisation numérique en science et génie des matériaux (TM vol. 10)” ©1998 Presses polytechniques et universitaires romandes, Lausanne, Switzerland All rights reserved

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ISSN 0179-3632 ISBN 978-3-540-42676-9 (hardcover) ISBN 978-3-642-11820-3 (softcover) DOI 10.1007/978-3-642-11821-0

e-ISBN 978-3-642-11821-0

Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010922315 Mathematics Subject Classification (2000): 65M06, 65M60, 65N06, 65N30 © Springer-Verlag Berlin Heidelberg 2003, First softcover printing 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, 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. Cover design: SPi Publisher Services Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

M. Rappaz et al., Numerical Modeling in Materials Science and Engineering, Springer Series in Computational Mathematics 32, DOI 10.1007/978-3-642-11821-0_1, © Springer-Verlag Berlin Heidelberg 2010

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