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Contemporary Mathematics 180 CONTEMPORARY MATHEMATICS 180 Domain Decomposition Methods in Scientific and Engineering Computing Proceedings of the Seventh International Conference on Domain Decomposition October 27-30, 1993 The Pennsylvania State University David E. Keyes Jinchao Xu Editors http://dx.doi.org/10.1090/conm/180 Recent Titles in This Series 180 David E. Keyes and Jinchao Xu, Editors, Domain decomposition methods in scientific and engineering computing, 1994 179 Yoshiaki Maeda, Hideki Omoro, and Alan Weinstein, Editors, Symplectic geometry and quantization, 1994 178 Helene Barcelo and Gil Kalai, Editors, Jerusalem Combinatorics '93, 1994 177 Simon Gindikin, Roe Goodman, Frederick P. Greenleaf, and Paul J. Sally, Jr., Editors, Representation theory and analysis on homogeneous spaces, 1994 176 David Ballard, Foundational aspects of "non"standard mathematics, 1994 175 Paul J. Sally, Jr., Moshe Flato, James Lepowsky, Nicolai Reshetikhin, and Gregg J. Zuckerman, Editors, Mathematical aspects of conformal and topological field theories and quantum groups, 1994 174 Nancy Childress and John W. Jones, Editors, Arithmetic geometry, 1994 173 Robert Brooks, Carolyn Gordon, and Peter Perry, Editors, Geometry of the spectrum, 1994 172 Peter E. Kloeden and Kenneth J. Palmer, Editors, Chaotic numerics, 1994 171 Rudiger GObel, Paul Hill, and Wolfgang Liebert, Editors, Abelian group theory and related topics, 1994 170 John K. Deem and Krishan L. Duggal, Editors, Differential geometry and mathematical physics, 1994 169 William Abikoff, Joan S. Birman, and Kathryn Kuiken, Editors, The mathematical legacy of Wilhelm Magnus, 1994 168 Gary L. Mullen and Peter Jau-Shyong Shiue, Editors, Finite fields: Theory, applications, and algorithms, 1994 167 RobertS. Doran, Editor, C*-algebras: 1943-1993, 1994 166 George E. Andrews, David M. Bressoud, and L. Alayne Parson, Editors, The Rademacher legacy to mathematics, 1994 165 Barry Mazur and Glenn Stevens, Editors, p-adic monodromy and the Birch and Swinnerton-Dyer conjecture, 1994 164 Cameron Gordon, Yoav Moriah, and Bronislaw Wajnryb, Editors, Geometric topology, 1994 163 Zhong-Ci Shi and Chung-Chun Yang, Editors, Computational mathematics in China, 1994 162 Ciro Ciliberto, E. Laura Livomi, and Andrew J. Sommese, Editors, Classification of algebraic varieties, 1994 161 Paul A. Schweitzer, S. J., Steven Hurder, Nathan Moreira dos Santos, and Jose Luis Arrant, Editors, Differential topology, foliations, and group actions, 1994 160 Niky Kamran and Peter J. Olver, Editors, Lie algebras, cohomology, and new applications to quantum mechanics, 1994 159 William J. Heinzer, Craig L. Huneke, and Judith D. Sally, Editors, Commutative algebra: Syzygies, multiplicities, and birational algebra, 1994 158 Eric M. Friedlander and Mark E. Mahowald, Editors, Topology and representation theory, 1994 157 Alfio Quarteroni, Jacques Periaux, Yuri A. Kuznetsov, and Olof B. Widlund, Editors, Domain decomposition methods in science and engineering, 1994 156 Steven R. Givant, The structure of relation algebras generated by relativizations, 1994 155 William B. Jacob, Tsit-Yuen Lam, and Robert 0. Robson, Editors, Recent advances in real algebraic geometry and quadratic forms, 1994 154 Michael Eastwood, Joseph Wolf, and Roger Zierau, Editors, The Penrose transform and analytic cohomology in representation theory, 1993 (Continued in the back of this publication) CoNTEMPORARY MATHEMATICS 180 Domain Decomposition Methods in Scientific and Engineering Computing Proceedings of the Seventh International Conference on Domain Decomposition October 27-30, 1993 The Pennsylvania State University David E. Keyes Jinchao Xu Editors American Mathematical Society Providence, Rhode Island Editorial Board Craig Huneke, managing editor Clark Robinson J. T. Stafford Linda Preiss Rothschild Peter M. Winkler The Seventh International Conference on Domain Decomposition was held at the Pennsylvania State University, from October 27~30, 1993, with support from the National Science Foundation, Grant No. DMS-9301980; Department of Energy, Grant No. DE-FG0293ER25184; Institute for Mathematics and its Applications (Minneapolis); GAMNI (France); IBM Corporation; Cray Research Corporation; and Pennsylvania State University. 1991 Mathematics Subject Classification. Primary 65M55, 65N55; Secondary 65F10, 65N30, 65N35, 65Y05. Library of Congress Cataloging-in-Publication Data International Conference on Domain Decomposition (7th : 1993 : Pennsylvania State University) Domain decomposition methods in scientific and engineering computing: proceedings of the Seventh International Conference on Domain Decomposition, October 27-30, 1993, the Pennsyl- vania State University / David E. Keyes, Jinchao Xu, editors. p. em. -(Contemporary mathematics, ISSN 0271-4132; v. 180) Includes bibliographical references. ISBN 0-8218-5171-3 (alk. paper) l. Decomposition method-Congresses. 2. Differential equations, Parital-Congresses. I. Keyes, David E. II. Xu, Jinchao, 1961-. III. Title. IV. Series: Contemporary mathematics (American Mathematical Sodety); v. 180. QA402.2.155 1993 515'.353--dc20 94-41503 CIP Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy an article for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication (including abstracts) is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Manager of Editorial Services, American Mathematical Society, P.O. Box 6248, Providence, Rhode Island 02940-6248. Requests can also be made by e-mail to reprint-permissionOmath. ams. org. The appearance of the code on the first page of an article in this publication (including ab- stracts) indicates the copyright owner's consent for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law, provided that the fee of $1.00 plus $.25 per page for each copy be paid directly to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, Massachusetts 01923. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. © Copyright 1994 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. § The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. 0 Printed on recycled paper. This volume was printed from copy prepared by the authors. Some of the articles in this volume were typeset by the authors using ANJS-'IEX or A;VfS-IJ\'IEX, the American Mathematical Society's TFX macro systems. 10 9 8 7 6 54 3 2 l 99 98 97 96 95 94 Contents Preface xi List of participants XlX Part I. Theory Interpolation spaces and optimal multilevel preconditioners FOLKMAR A. BORNEMANN 3 Two-level additive Schwarz preconditioners for nonconforming finite elements SUSANNE C. BRENNER 9 Two proofs of convergence for the combination technique for the efficient solution of sparse grid problems H.-J. BUNGARTZ, M. GRIEBEL, D. ROSCHKE, AND C. ZENGER 15 Domain decomposition methods for monotone nonlinear elliptic problems XIAO-CHUAN CAl AND MAKSYMILIAN DRYJA 21 Cascadic conjugate gradient methods for elliptic partial differential equations: Algorithm and numerical results PETERDEUFLHARD 29 Multilevel methods for elliptic problems with discontinuous coefficients in three dimensions MAKSYMILIAN DRYJA 43 Multilevel methods for elliptic problems on domains not resolved by the coarse grid RALF KORNHUBER AND HARRY YSERENTANT 49 Three-dimensional domain decomposition methods with nonmatching grids and unstructured coarse solvers P. LE TALLEC, T. SASSI, AND M. VIDRASCU 61 Domain decomposition for elliptic problems with large condition numbers S. V. NEPOMNYASCHIKH 75 v vi CONTENTS Stable subspace splittings for Sobolev spaces and domain decomposition algorithms P. OSWALD 87 A wire basket based method for spectral elements in three dimensions LUCA F. PAVARINO 99 An analysis of spectral graph partitioning via quadratic assignment problems ALEX POTHEN 105 Error estimators based on stable splittings u. RUDE 111 Multilevel methods for P1 nonconforming finite elements and discontinuous coefficients in three dimensions MARCUS SARKIS 119 On generalized Schwarz coupling applied to advection-dominated problems K. H. TAN AND M. J. A. BORSBOOM 125 Exotic coarse spaces for Schwarz methods for lower order and spectral finite elements 0LOF B. WID LUND 131 Part II. Algorithms Preconditioning via asymptotically-defined domain decomposition S. F. AsHBY, C. T. KELLEY, P. E. SAYLOR, AND J. S. ScROGGs 139 A spectral Stokes solver in domain decomposition methods M. AZAIEZ AND A. QUARTERONI 151 Preconditioned iterative methods in a subspace for linear algebraic equations with large jumps in the coefficients NIKOLAI S. BAKHVALOV AND ANDREW V. KNYAZEV 157 The hierarchical basis multigrid method and incomplete LU decomposition RANDOLPH E. BANK AND JINCHAO Xu 163 Domain decomposition and multigrid algorithms for elliptic problems on unstructured meshes TONY F. CHAN AND BARRY F. SMITH 175 Two-grid methods for mixed finite
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