Notes in €omputattonal -Lure -erne and Engineering Are Magnus Bruaset AsIak Tveito Editors Numerical Solution of Partial Differential Equations on Parallel Computers @ - springer Editors Timothy J. Barth Michael Griebel David E. Keyes Risto M. Nieminen Dirk Roose Tamar Schlick Are Magnus Bruaset Aslak Tveito (Eds.) Numerical Solution of Partial Differential Equations on Parallel Computers With 201 Figures and 42 Tables ABC Editors Are Magnus Bruaset Aslak Tveito Simula Research Laboratory P.O. Box 134 1325 Lysaker, Fornebu, Norway email:
[email protected] [email protected] The second editor of this book has received financial support from the NFF – Norsk faglitterær forfatter- og oversetterforening Library of Congress Control Number: 2005934453 Mathematics Subject Classification: Primary: 65M06, 65M50, 65M55, 65M60, 65Y05, 65Y10 Secondary: 65N06, 65N30, 65N50, 65N55, 65F10, 65F50 ISBN-10 3-540-29076-1 Springer Berlin Heidelberg New York ISBN-13 978-3-540-29076-6 Springer Berlin Heidelberg New York 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 for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2006 Printed in The Netherlands 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. Typesetting: by the authors and TechBooks using a Springer LATEX macro package Cover design: design & production GmbH, Heidelberg Printed on acid-free paper SPIN: 11548843 46/TechBooks 543210 Preface Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the supercomputing power of today. When trying to replicate Nature in the computer’s silicon test tube, there is need for precise and computable process descriptions. The scientific fields of Mathematics and Physics provide a powerful vehicle for such descriptions in terms of Partial Differential Equations (PDEs). Formulated