Multi-Grid Methods and Applications
Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. The reader finds here an elementary introduction to multi-grid algorithms as well as a comprehensive convergence analysis. One section describes special applicat
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Springer-Verlag Berlin Heidelberg GmbH
Wolfgang Hackbusch
Multi-Grid Methods and Applications
With 43 Figures and 48 Tables
i
Springer
Wolfgang Hackbusch MPI für Mathematik in den Naturwissenschaften Inselstr. 22-26 04103 Leipzig, Germany e-mail: [email protected]
Cataloging-in-Publication Data applied for A catalog record for this book is available from the Library of Congress. Bibliographie information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographie data is available in the Internet at http://dnb.ddb.de
Second Printing 2003
Mathematics Subject Classification (2000): 65 N 55
ISSN 0179-3632 ISBN 978-3-642-05722-9 ISBN 978-3-662-02427-0 (eBook) DOI 10.1007/978-3-662-02427-0 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifieally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on mierofilm 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 Spnnger-Verlag Berlin Heidelberg GmbH, Violations are liable for prosecution under the German Copyright Law.
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Springer-Verlag Berlin Heidelberg 1985
Ongmally pubhshed by Spnnger-Verlag Berlm Heidelberg New York m 1985 Softcover reprint of the hardcover 1st edition 1985 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specifie statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: design&production, Heidelberg Printed on acid-free paper
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Preface
Although multi-grid methods had already been described in the early 1960's, it was not until the mid-seventies that they were realised to be very efficient methods of solution with a broad area of application. Over the past ten years, the number of publications on this topic has grown rapidly with the result that in searching for information about multi-grid methods at the present time, one is confronted with an abundance of articles scattered in a wide range of periodicals and proceedings. This mono graph is an attempt to describe the basic concepts of multi-grid methods. Different groups of readers may be interested in different parts of the book. The first part, which concentrates on the algorithmic details, is intended for readers interested in the theory and practice of multi-grid methods. The second part is devoted to the mathematical analysis, and is especially intended for mathematicians. Readers interested in engineering and technical applications will find numerous chapters on specific multi-grid applications and additional techniques: the primary emphasis is on applications in the fi
