A Multigrid Tutorial-William L. Briggs--second edition.pdf

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A Multigrid Tutoyial

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A Multigrid Tutorial Second Edition William L Briggs Department of Mathematics University of Colorado at Denver Denver, Colorado Van Emden Henson Center for Applied Scientific Computing Lawrence Livermore National Laboratory Livermore, California Steve F. McCormick Department of Applied Mathematics University of Colorado at Boulder Boulder, Colorado Society for Industrial and Applied Mathematics siam

Copyright ©2000 by the Society for Industrial and Applied Mathematics. 1 0 9 8 7 6 5 4 32 All rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 University City Science Center, Philadelphia, PA 19104-2688. Portions of this work were performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract W-7405-Eng-48. Library of Congress Cataloging-in-Publication Data Briggs, William L. A multigrid tutorial.—2nd. ed. / William L. Briggs, Van Emden Henson, Steve F. McCormick. p. cm. Includes bibliographical references and index. ISBN 0-89871-462-1 (pbk.) 1. Differential equations, Partial—Numerical solutions. 2. Multigrid methods (Numerical analysis) I. Henson, Van Emden. II. McCormick, S. F. III. Title. QA377.B75 2000 515'.353-dc21 00-024103 • Siam is a registered trademark.

To the ladies... Julie, Teri, Lynda, Katie, Jennifer

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Contents Preface to the Second Edition Preface to the First Edition 1 Model Problems Exercises 2 Basic Iterative Methods Exercises 3 Elements of Multigrid Exercises 4 Implementation Exercises 5 Some Theory Exercises 6 Nonlinear Problems Exercises 7 Selected Applications Exercises 8 Algebraic Multigrid (AMG) Exercises 9 Multilevel Adaptive Methods Exercises 10 Finite Elements Exercises Bibliography Index vii ix xi 1 4 7 27 31 43 45 68 73 91 95 109 113 133 137 159 163 174 177 186 189 191

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