Multigrid Methods III

394 Pages·1991·16.175 MB·English

by  Erik Dick (auth.), W. Hackbusch, U. Trottenberg (eds.)

ISNM98:
International Series of Numerical Mathematics
Internationale Schriftenreihe zur Numerischen Mathematik
Serie Internationale d'Analyse Numerique
Vol. 98
Edited by
K.-H. HolTmann, Augsburg; H. D. Mittelmann, Tempe;
J. Todd, Pasadena
Springer Basel AG
Multigrid Methods III
Edited by
w.
Hackbusch
U. Trottenberg
1991
Springer Basel AG
Editors
W. Hackbusch ^
T T
Universität Kiel ^TTf'ß *, u -,
Institut für Informatik Gesellschaft fur Mathematik
und Praktische Mathematik ™d patenverarbeitung mbH
Olshausenstrasse 40 Postfach 1240
D-2300Kiell ^ S^irlmgh ° Ven - ,
A
D-5205 Sankt Augustin 1
Deutsche Bibliothek Cataloging-in-Publication Data
Multigrid methods III / ed. by W. Hackbusch; U. Trottenberg.
- Basel ; Boston ; Berlin : Birkhäuser, 1991
(International series of numerical mathematics ; Vol. 98)
NE: Hackbusch, Wolfgang [Hrsg.]; European Multigrid Conference <03,1990, Bonn>; GT
This work is subject to copyright. All rights are reserved, whether the whole or part
of the material is concerned, specifically those of translation, reprinting, re-use of
illustrations, broadcasting, reproduction by photocopying machine or similar means,
and storage in data banks. Under § 54 of the German Copyright Law where copies are
made for other than private use a fee is payable to »Verwertungsgesellschaft Wort«, Munich.
© Springer Basel AG 1991
Originally published by Birkhäuser Verlag Basel in 1991
Softcover reprint of the hardcover 1st edition 1991
ISBN 978-3-0348-5714-7 ISBN 978-3-0348-5712-3 (eBook)
DOI 10.1007/978-3-0348-5712-3
v
PREFACE
These proceedings contain a selection of papers presented at the
Third European Conference on Multigrid Methods
which was held in Bonn on October 1-4, 1990.
Following conferences in 1981 and 1985, a platform for the presentation of new Multigrid
results was provided for a third time. Multigrid methods no longer have problems being
accepted by numerical analysts and users of numerical methods; on the contrary, they have
been further developed in such a successful way that they have penetrated a variety of new
fields of application. The high number of 154 participants from 18 countries and 76 presented
papers show the need to continue the series of the European Multigrid Conferences.
The papers of this volume give a survey on the current Multigrid situation; in particular,
they correspond to those fields where new developments can be observed. For example, se
veral papers study the appropriate treatment of time dependent problems. Improvements can
also be noticed in the Multigrid approach for semiconductor equations. The field of parallel
Multigrid variants, having been started at the second European Multigrid Conference, is now
at the centre of interest.
Whereas the papers of this volume are assumed to be of general interest for a large number of
scientists in academic as well as industrial research, those more specialized papers presented
at the conference will be published in the series GMD-Studien, volume no. 189: Multigrid
Methods: Special Topics and Applications II. (These papers are listed at the end of this
volume.)
At this point, we would like to thank again all participants and especially the lecturers and
those having presented posters for their contributions to the success of the conference.
The conference was initiated by
• Gesellschaft fiir Mathematik und Datenverarbeitung mbH (GMD),
St. Augustin,
• GAMM-Fachausschull 'Effiziente numerische Verfahren fiir partielle
Differentialgleichungen' .
The scientific organization was excellently conceived by Dr. Ute Giirtel, Institut fiir Metho
dische Grundlagen of the GMD. Together with Christine Harms, Conference Secretariat of
VI
the GMD, she was also responsible for the practical realization. Furthermore, several co
workers, the secretary and the students of the Institut fur Methodische Grundlagen provided
substantial assistance to the organization of the conference. We thank all persons involved.
We would like to express our gratitude to the Executive Board of the GMD for their support
of the conference. Furthermore, we thank the industrial sponsors (Bayer AG, Dornier GmbH,
Krupp Atlas Elektronik GmbH, Stardent Computer GmbH, Sun Microsystems GmbH, SU
PRENUM GmbH) for their interest in the topics of the conference.
Finally, we would like to thank Birkhauser Verlag for their friendly cooperation.
Kiel / St. Augustin, March 1991
Wolfgang Hackbusch
Ulrich Trottenberg
VII
CONTENTS
PART I: INVITED PAPERS
Multigrid methods for steady Euler-and Navier-Stokes equations based on polynomial
flux-difference splitting
Dick, E. .......................................... 1
Recent developments for the PSMG multi scale method
Frederickson, P.O.; McBryan, OA. ......... . 21
An adaptive multigrid approach for the solution of the 2D semiconductor equations
Hemker, P.w.; Molenaar, 1. . ........................... . 41
Multiscale Monte Carlo algorithms in statistical mechanics and quantum field theory
Lauwers, P.G. . ............................. . 61
Two fast solvers based on the multi-level splitting of finite element spaces
Leinen, P.; Yserentant, H. ........................ . 83
Multigrid methods for turbulent flow problems
Ruge, 1.; Brandt, A.; McWilliams, I.; Mil/iff, R. 91
A survey of Fourier smoothing analysis results
Wesseling, P. . ......................................... 105
PART II: CONTRffiUTED PAPERS
Multilevel methods for fast solution of N-body and hybrid systems
Balsara, D.S.; Brandt, A. . ................................. 131
Parabolic multigrid revisited
Brandt, A.; Greenwald, 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
VIII
Time-parallel multigrid solution of the Navier-Stokes equations
Burmeister, f.; Horton, G. . ................. . . ......... 155
Solution of 3-D problems using overlapping grids and multi-grid methods
Fuchs,L. . ................................ . ..... 167
A multigrid method for the solution of a convection-diffusion equation with rapidly
varying coefficients
Fuhrmann, 1.; Gartner, K. . ... 179
Parallel multigrid solution of 2D and 3D anisotropic elliptic equations: Standard and
nonstandard smoothing
Gartel, U.; Krechel, A.; Niestegge, A.; Plum, H.-f. ...................... 191
Parallel multigrid methods on sparse grids
Griebel, M. . ............. . . ................. 211
Analysis of multigrid methods for general systems of PDE
Gustafsson, B.; LOtstedt, P. ............... . . ...... 223
On the convergence of the nonlinear multigrid algorithm for potential operators
Hengst, S.; Telschow, G. .................................... 235
A multigrid algorithm with time-dependent, locally refined grids for solving the
nonlinear diffusion equation on a nonrectangular geometry
foppich, W .......................................... 241
Multigrid methods for hyperbolic equations
Katzer, E. ................ . ...... 253
Low-diffusion rotated upwind schemes, multigrid and defect correction for steady,
multi-dimensional Euler flows
Koren, B. ...... 265
Multigrid convergence acceleration for complex flow including turbulence
Lien, F.-S.; Leschziner, MA ................... . . . . . . . . . . 277
Time accurate multigrid solutions of the Navier-Stokes equations
Meinke, M.; Hanel, D. ................. . . . . . . . . . . . . . . . 289
Mesh-adaptive solution of the Navier-Stokes equations
Michelsen,!A ................... . . 301
A two-grid analysis of the combination of mixed finite elements and Vanka-type relaxation
Molenaar, f. .......................................... 313
IX
Multigrid applied to mixed fmite element schemes for current continuity equations
Reusken, A. ........................................... 325
Adaptive higher order multigrid methods
RUde, U. . .............. . . ................... 339
Shape from shading using parallel multigrid relaxation
Sweidens, W; Roose, D. ............... .................... 353
Cell-centered multigrid methods in porous media flow
Teigiand, R.; Fladmark, G.E. . .......... . . ..... 365
Multigrid waveform relaxation for solving parabolic partial differential equations
Vandewalle, St.; Piessens, R. .... 377
Contents of the GMD-Study No. 189 389
Participants 391