Send mail to: mgnet@cs.yale.edu for the digests or bakeoff
mgnet-requests@cs.yale.edu for comments or help
Current editor: Craig Douglas douglas-craig@cs.yale.edu
Anonymous ftp repository: casper.cs.yale.edu (128.36.12.1)
World Wide Web: http://na.cs.yale.edu/mgnet/www/mgnet.html or
http://www.cerfacs.fr/~douglas/mgnet.html or
http://www.ccs.uky.edu/mgnet
Today's editor: Craig Douglas (douglas-craig@cs.yale.edu)
Volume 7, Number 4 (approximately April 30, 1997)
Today's topics:
New MGNet Site
FEATFLOW1.0 on the Internet
Query about Multi-grid Methods for Biharmonic Equation
Postcard from Copper Mountain
Multigrid Benchmarks Discussions
Planning for conferences
Publist Griebel
-------------------------------------------------------
Date: Wed, 30 Apr 1997 16:04:01 -0400
From: douglas@ccs.uky.edu (Craig Douglas)
Subject: New MGNet Site
I have put a duplicate of MGNet at the University of Kentucky. It can be
accessed through
htpp://www.ccs.uky.edu/mgnet
The web pages now include this site as well as Yale and CERFACS at the top.
-------------------------------------------------------
Date: Fri, 18 Apr 1997 15:35:45 +0200
From: Stefan Turek
Subject: FEATFLOW1.0 on the Internet
Dear colleagues,
Our FEM software for incompressible Navier-Stokes equations, FEATFLOW1.0,
including all sources, manuals and many (!) demos for nonstationary flows (as
MPEG movies), is "downloadable" via Internet, see
http://gaia.iwr.uni-heidelberg.de/~featflow
Stefan Turek
Institut fuer Angewandte Mathematik, Universitaet Heidelberg, Germany
ture@gaia.iwr.uni-heidelberg.de, http://gaia.iwr.uni-heidelberg.de/~ture
-------------------------------------------------------
Date: Wed, 23 Apr 1997 15:07:50 -0700 (PDT)
From: Matthew Cordery
Subject: Query about Multi-grid Methods for Biharmonic Equation
I am interested in multigrid methods for solving the biharmonic equation on
unstructured 2D triangular meshes and am wondering if anyone has any
experience in this problem that they might be willing to share. In
particular, I am interested in solutions to the biharmonic equation that
arises from the equations for creeping flow (Stoke's equations). The fluid
itself has a strongly temperature-dependent viscosity that may vary sharply
over short distances (relative to the size of the compuational domain). Thus,
my biharmonic equation would have a viscosity term embedded within it.
Thanks in advance for any help!
Dr. Matthew J. Cordery cordery1@llnl.gov
Environmental Computer Applications
Lawrence Livermore National Laboratory
L206
P.O. Box 808
Livermore, CA 94550
Editor's Note: Here is what I found on multigrid methods and Biharmonic
problems in the MGNet bibliography by searching on
biharmonic. Surely there is more that is not in the
bibliography or does not have the word in the title. If
you know of something, please e-mail both the inquirer and
MGNet. Thanks.
[1] R. N. Banerjee and M. W. Benson, An approximate inverse
based multigrid approach to the biharmonic problem, Int. J.
Comput. Math., 40 (1991), pp. 201-210.
[2] A. Brandt and J. Dym, Effective boundary treatment for the
biharmonic Dirichlet problem, in Seventh Copper Mountain
Conference on Multigrid Methods, N. D. Melson, T. A. Man-
teuffel, S. F. McCormick, and C. C. Douglas, eds., vol. CP
3339, Hampton, VA, 1996, NASA, pp. 97-107.
[3] S. C. Brenner, An optimal order nonconforming multigrid
method for the biharmonic equation, SIAM J. Numer. Anal.,
26 (1989), pp. 1124-1138.
[4] M. R. Hanisch, Multigrid Preconditioning for Mixed Finite
Element Methods, PhD thesis, Cornell, Ithaca, NY, 1991.
[5] ______, Multigrid preconditioning for the biharmonic Dirichlet
problem, SIAM J. Numer. Anal., 30 (1993), pp. 184-214.
[6] W. Heinrichs, A stabilized treatment of the biharmonic oper-
ator with spectral methods, SIAM J. Sci. Stat. Comput., 12
(1991), pp. 1162-1172.
[7] J. Linden, A multigrid method for solving the biharmonic equa-
tion on rectangular domains, in Advances in Multi-Grid
Methods, D. Braess, W. Hackbusch, and U. Trottenberg,
eds., vol. 11 of Notes on Numerical Fluid Mechanics, Braun-
schweig, 1984, Vieweg, pp. 64-76.
[8] P. Oswald, Hierarchical conforming finite element methods for
the biharmonic equation, SIAM J. Numer. Anal., 29 (1992),
pp. 1610-1625.
[9] P. Peisker, A multilevel algorithm for the biharmonic problem,
Numer. Math., 46 (1985), pp. 623-634.
[10] P. Peisker and D. Braess, A conjugate gradient method and
a multigrid method for Morley's finite element approxima-
tion of the biharmonic equation, Numer. Math., 50 (1987),
pp. 567-586.
[11] X. Zhang, Studies in domain decomposition: multilevel meth-
ods and the biharmonic Dirichlet problem, PhD thesis,
Courant Institute, New York University, New York City,
1991.
-------------------------------------------------------
Date: Thu, 1 May 1997 12:04:01 -0400
From: douglas@ccs.uky.edu (Craig Douglas)
Subject: Postcard from Copper Mountain
The Copper Mountain Multigrid Conference was held for the eighth time from
April 6-11, 1997. For the first time in years, there were no parallel
sessions for talks, giving the conference the type of intimacy found in the
GAMM parallel multigrid workshops held in Germany for many years and most
recently in Austria.
Two years ago there were many newcomers to the Copper Mountain conference.
Once again this was the case. In part this is due to the large number of
graduate students and fresh Ph.D.'s who have attended both conferences.
Ski conditions were the best in a generation at Copper Mountain, though
the conference attendees were much too busy to notice. Even when 7 inches, or
17.5 cm, of powder came down Thursday afternoon/evening, attendance was still
quite high. (Well, maybe a few went out on the slopes during the afternoon
breaks or before or after the conference.) However, with "parabolic" shaped
skis for rent, and this being a conference with a strong influence from the
PDE community, it was only a natural condition to assume that some of us tried
out this style of skis. There were reports that it was much easier to turn,
but harder to go straight on these skis. The conclusion drawn seemed to be
that the ease of use of and preference for the parabolic skis was clearly time
dependent.
One of the amusing moments occurred at the conference dinner. Steve
McCormick asked everyone to please stand up (quite a task at 9600 feet, or
3100 meters, above sea level in the evening after many lectures). People were
asked to sit down based on the number of conferences attended. Quite a number
sat down after one or two conferences. By 12 conferences (including the
iterative method conferences held on even numbered years) only Joel Dendy and
Steve were still standing.
The banquet ended with birthday cakes celebrating Seymour Parter's pending
seventieth birthday. One cake remained the next morning. The doors to the
conference building were locked until the conference participants finished the
cake off (Seymour did his part admirably).
Counting the conference circus and workshop nights, there were 60 talks.
As usual, the talks were held in the mornings and late afternoon/evenings.
Talks were 25 minutes long (at most) with the session chairs rigorously
enforcing the maximum time limits.
Monday evening was devoted to multilevel archaeology, a topic first
developed by Achi Brandt at the Seventh Copper Mountain Multigrid Conference
during the banquet speeches [1]. This branch was devoted to unearthing
fossils. However, the Boulder group insisted on misspelling the word as FOSLS
(or first order systems least-squares). This method adds a few variables to a
problem. This (usually trivial extra expense) is offset by the fact that it
allows you to measure the local and global error easily so that you know if
you have solved your problem or not (quite a neat trick).
The circus evening was quick due to the fact that almost everyone was
already speaking at the conference. The highlight was Michael Griebel's
daughter making it quite clear from outside of the conference room that she
wanted her daddy right away. Rarely has a talk been concluded with such
determination by the speaker. However, Michael made the point that using
extremely simple computer science data methods (hashing in particular),
accessing information about nonuniform grid data points could be done quite
cheaply in comparison to the more common tree data structures.
The workshop evening was devoted to discussing benchmarks. Bodo Parady
was the virtual speaker (he was in California on a telephone hooked up to the
conference microphone). As noted in the March MGNet digest (volume 7, number
3), the multigrid SPECmark is open to review. Bodo provided a number of clues
as to what he wants to see from the multigrid community for a new set of
benchmarks (see related digest article on benchmarks).
There were many, many topics covered at this conference. This has been
normal in the past conferences, which is why it still exists, and will be done
a ninth time in two years. There were numerous talks devoted to algorithms,
theory, applications, parallel computers, and problems not derived from PDE's.
There were quite a few interesting applications included in the talks.
Some of these included the following (in no particular order):
o Radon transfer (J. Dym)
o Material sciences (S. McKay)
o Linear elasticity (S. D. Kim)
o Sonic flow - sub/trans/super (B. Diskin)
o Magneto hydrodynamics (A. J. Meir)
o Image processing (K. Witsch, J. Dym)
o Point forces (K. Witsch)
o Reservoir simulation (H. Zhang)
o Electrostatic/circuit simulation (R. Kulke)
o Stress factors (S. Brenner)
o Structural analysis (M. Bittencourt)
o Multi-material heat transfer (W. Dai)
Numerous other people talked about small applications as part of their
presentations.
The talks themselves dealt with many topics. These included the
following, lengthy list:
o Survey (A. Brandt)
o Packaged codes (M. Bittencourt, R. Kulke, W. Mitchell)
o Black box multigrid (J. Dendy)
o Gray box multigrid (J. Dym)
o Implementation efficiency (M. Griebel, U. Ruede, C. Douglas)
o Sparse grids (H.-J. Bungartz, M. Griebel)
o Anisotropic problems (D. Mavriplis, X. Zhang)
o Convection diffusion problems (J. Kouatchou, W. Spotz)
o Mixed finite element multigrid methods (Z. Cai)
o Hierarchical bases (H.J. Bungartz)
o Mortar method (M. Sarkis)
o Exponential bases (M. Kuether, G. Starke)
o Nonconforming finite elements (Z. Chen, S. Maliassov)
o Coarsening strategies (D. Mavriplis, M. Bittencourt)
o Algebraic multigrid (J. Ruge, V. Henson, L. Dutto, C.A. Thole)
o Inter-grid operators (Z. Chen, W.-L. Wan)
o Domain decomposition methods (J. Jones, W. Mitchell, C. Douglas)
o Ficticious domains (S. Maliassov)
o Locally refined grids (Y. Shapira, M. Bittencourt, S. Maliassov)
o Multi-resolution, wavelets (A. Brandt, D. Gines, N. Coult, R. Lorentz)
o FOSLS (R. Hiptmair, S. McCormick, T. Manteuffel, M. Berndt, P. Bochev, S.
D. Kim, B. Lee)
o Newton-Krylov multigrid methods (D. Knoll, T. Washio)
o Helmholtz, wave problems (I. Livshits)
o Stokes problems (Z. Cai)
o Navier-Stokes problems (D. Mavriplis, E. Sterner, X. Vasseur, H. Oswald)
o Algorithm comparisons (S. Fulton, B. Diskin, E. Sterner, X. Vasseur,
G. Wade, B. Lee)
o Explicitly parallel multigrid (W. Mitchell, C. Douglas, L. Dutto,
V. Henson, H. Oswald, D. Xie)
o Smoother properties (J. Jones, J. Pasciak, Y. Yavneh)
o Well posedness, stability (A. Knyazev, J. Kouatchou, W. Spotz)
My apologies to all of the people that I have mislabeled or left out.
The next (number 9) Copper Mountain multigrid conference will be in April,
1999. Should there be a tenth, it will be in a famous year: 2001, which
seems appropriate somehow.
Many of us will re-appear at Copper Mountain next year for the iterative
method conference. It will be March 29 - April 3, 1998. Ski ya then.
Reference
[1] A. Brandt, Multigrid history, in Seventh Copper Mountain Conference on
Multigrid Methods, N. D. Melson, T. A. Manteuffel, S. F. McCormick, and C.
C. Douglas, eds., vol. CP 3339, Hampton, VA, 1996, NASA, p. ix.
Editor's Note: If I left anyone out of a category or misfiled anyone,
------------- please send me an update immediately. Thanks.
-------------------------------------------------------
Date: Thu, 1 May 1997 17:20:32 -0400
From: douglas@ccs.uky.edu (Craig Douglas)
Subject: Multigrid Benchmarks Discussions
Multigrid benchmarks were discussed at the Thursday evening (April 10)
workshop at Copper Mountain. The first half was devoted to finding out what
the new SPECmark for multigrid might be. Bodo Parady, who is on the SPEC
floating point benchmarks committee, offered some hints as to what is wanted
from the multigrid community.
The new multigrid benchmarks for SPEC must ...
o be hard, but not too difficult to optimize. C++ code has been
eliminated due to the complexity of optimization. Fortran
is considered ideal, but not 100% essential.
o be optimizable on cache based machines, but not be cache resident
o be optimizable on vector machines
o come with the correct answer so that a comparison can be made to
determine how close the optimized code is to the "correct"
solution.
The new multigrid benchmarks for SPEC must NOT ...
o be a kernel benchmark.
o be completely solvable by compiler writers.
o be a BLAS or LINPACK style benchmark.
What is wanted is a set of real world problems. Large (rather than small)
kernels are wanted. The bigger the code the better up to a point. Multiple
codes is wanted, not just a single one.
After we ended our phone conversation with Bo (funded by a grant from the
Douglas family), we turned to a general discussion of what might be useful to
users of multigrid methods. Here are some points made:
o We need a database of problems with solutions similar to the
very successful Boeing-Harwell collection of matrices.
o We need an index file of codes that work for each problem.
o We need a lot of problems in a lot of different areas. The
database should not be a mechanism to cancel lots of people's
grants because they only solve a small collection of problems.
o Two new mailing lists will be created for people interested in
benchmark discussions: one for people who just want to discuss
issues and one for contributors to either the SPECmark or the
database.
Not just the people at the conference will be included in this venture.
Anyone can get involved. In fact, certain people who were not present were
identified for contacting later.
If you are interested in joining the mailing lists, please send a note to
mgnet@ccs.uky.edu specifying whether you want to be on the discussion list
or the contributor list (the latter automatically is on the former). If you
signed up at the conference, you are already on the list(s).
-------------------------------------------------------
Date: Tue, 29 Apr 97 19:36:40 +0300
From: Alexander Trofimov
Subject: Planning for conferences
Dr. A.V. Trofimov
Dniepropetrovsk State University
Faculty of Mechanics and Mathematics
Theoretical and Applied Mechanics Chair
Dniepropetrovsk, Ukraine
I ask you to send me information about multigrid and domain decomposition
conferences that will take place this and next year.
E:mail for contacts: Alexander.Trofimov@p8.f25.n464.z2.fidonet.org
Editor's Note: Please send information about other conferences that I
------------- do not know about to both him and MGNet.
Summer School on Multilevel preconditioning methods with parallel
implementation aspects and applications in Scientific Computing,
University of Nijmegen (NL), May 19-26, 1997,
Conference on Preconditioned Iterative Solution Methods for Large
Scale Problems in Scientific Computations, University of Nijmegen (NL),
May 27-29, 1997
3rd IMACS Iterative Methods Conference, Jackson Hole, WY (USA), July
9-12, 1997
AFOSR International Conference on Direct Numerical Simulation and
Large Eddy Simulation, Louisiana Tech University, Ruston, LA (USA), August
4-8, 1997
10th Domain Decomposition Symposium, Boulder, CO (USA), August 10-14,
1997
Guangzhou International Symposium on Computational Mathematics,
Guangzhou (P.R. China), August 11-15, 1997
? -> GAMM Workshops, Germany and Austria, sometime in 1998
5th Copper Mountain Iterative Methods Conference, Copper Mountain, CO
(USA), March 29-April 3, 1998
? -> 11th Domain Decomposition Symposium, somewhere, sometime in 1998
-------------------------------------------------------
Date: Fri, 25 Apr 1997 11:55:05 +0200 (MSZ)
From: Michael Griebel
Subject: Publist Griebel
Attached you find the publication list of me for the MG-net archives and
publication data base
Best regards
Michael Griebel
REFERENCES
[1] M. Griebel. Multilevelmethoden als Iterationsverfahren u"ber
Erzeugendensystemen. Teubner Skripten zur Numerik,
Teubner Verlag, Stuttgart, 1994.
[2] M. Griebel und C. Zenger, Editoren. Numerical Simulation in
Science and Engineering, Proceedings of the FORTWIHR
Symposium on High Performance Scientific Computing in
Munich, June 17-18 1993, Notes on Numerical Fluid Me-
chanics 48, Vieweg-Verlag, Braunschweig, 1994.
[3] M. Griebel, T. Dornseifer und T. Neunhoeffer. Numerische
Simulation in der Str"omungsmechanik, eine praxisorientierte
Einf"uhrung, Vieweg-Verlag, Braunschweig, 1995.
[4] H.-J. Bungartz, M. Griebel und C. Zenger. Einf"uhrung in die
Computergraphik: Grundlagen, Geometrische Modellierung,
Algorithmen, Vieweg-Verlag, Braunschweig, 1996.
Editor:
REFERENCES
[1] M. Griebel, D .Keyes, R. Niemienen, T .Schlick, D. Roose.
Springer Lecture Notes in Computational Science and Engi-
neering. Eine neue Lecture Notes Reihe im Springer Verlag.
Zeitschriftenartikel:
REFERENCES
[1] I. Babuska, M. Griebel und J. Pitkaranta. The problem of
selecting the shape functions for a p-type finite element.
Int. J. Num. Meth. Engin., 28:1891-1908, 1989. also as
Report MD88-36-IB-MG-JP, TR88-36, University of Mary-
land, IPST, College Park, 1988.
[2] M. Griebel. The combination technique for the sparse grid solu-
tion of PDEs on multiprocessor machines. Parallel Process-
ing Letters, 2(1):61-70, 1992. also as SFB Bericht 342/14/91
A, Institut f"ur Informatik, TU M"unchen, 1991.
[3] M. Griebel und P. Oswald. On additive Schwarz preconditioners
for sparse grid discretization. Numer. Math., 66(4):449-464,
1994. also as Bericht Math/92/7, Institut f"ur angewandte
Mathematik, Friedrich-Schiller-Universit"at Jena, 1992.
[4] M. Griebel, C. Zenger und S. Zimmer. Multilevel Gauss-Seidel-
algorithms for full and sparse grid problems. Computing,
49:127-148, 1993.
[5] M. Griebel und V. Thurner. Solving CFD-problems efficiently
by the combination method. CFD-News, 3(4):19-31, 1993.
[6] M. Griebel. Multilevel algorithms considered as iterative meth-
ods on semidefinite systems. SIAM Int. J. Sci. Stat. Com-
put., 15(3):547-565, 1994.
[7] H. Bungartz, M. Griebel, D. R"oschke und C. Zenger. Pointwise
convergence of the combination technique for Laplace's equa-
tion. East-West Journal of Numerical Mathematics, 1(2):21-
45, 1994. also as SFB-Bericht 342/16/93A, Institut f"ur In-
formatik, TU M"unchen, 1993.
[8] H. Bungartz, M. Griebel und U. R"ude. Extrapolation, combina-
tion and sparse grid techniques for elliptic boundary value
problems. Computer Methods in Applied Mechanics and
Engineering, Vol. 116:243-252, 1994. also in C. Bernardi
und Y. Maday, Editoren, International conference on spec-
tral and high order methods, ICOSAHOM 92. Elsevier, 1992,
und als SFB Bericht, 342/10/92 A, Institut f"ur Informatik,
TU M"unchen, 1992.
[9] M. Griebel und V. Thurner. The efficient solution of fluid dy-
namics problems by the combination technique. Int. J. Num.
Meth. for Heat and Fluid Flow, 5(3):251-269, 1995. also
as SFB Bericht 342/1/93 A, Institut f"ur Informatik. TU
M"unchen, 1993.
[10] M. Griebel. Parallel domain-oriented multilevel methods, SIAM
Journal on Scientific Computing 16(5):1105-1125, 1995.
[11] M. Griebel und P. Oswald. On the abstract theory of addi-
tive and multiplicative Schwarz algorithms. Numer. Math.,
70:163-180, 1995.
[12] M. Griebel und P. Oswald. Tensor-product-type subspace split-
tings and multilevel iterative methods for anisotropic prob-
lems. Advances in Computational Mathematics, 4:171-206,
1995. also as SFB-Bericht 342/15/94A, Institut f"ur Infor-
matik, TU M"unchen, 1994.
[13] M. Griebel und T. Neunhoeffer. Parallel point- and domain-
oriented multilevel methods for elliptic PDE's on workstation
networks. J. Comp. Appl. Math., 66:267-268, 1996.
[14] H. Bungartz, M. Griebel, D. R"oschke und C. Zenger. A proof of
convergence for the combination technique for the Laplace
equation using tools of symbolic computation. Mathemat-
ics and Computers in Simulation, Vol. 42:595-605, 1996.
also in G. Jacob, N. Oussous und S. Steinberg, Editoren,
IMACS Symposium on Symbolic Computation, Lille, Juni
1993. IMACS/Universite des Sciences et Technologies de
Lille, Villeneuve d'Ascq, 1993 und als SFB Bericht, 342/4/93
A, Institut f"ur Informatik, TU M"unchen, 1993.
[15] T. Grauschopf, M. Griebel und H. Regler. Additive multilevel-
preconditioners based on bilinear interpolation, matrix de-
pendent geometric coarsening and algebraic multigrid coars-
ening for second order elliptic PDEs. Applied Numeri-
cal Mathematics, 23(1):63-96, 1997. also as SFB-Bericht
342/02/96A Institut f"ur Informatik, TU M"unchen, 1996.
[16] M. Griebel, T. Neunhoeffer und H. Regler. Algebraic multi-
grid methods for the solution of the Navier-Stokes equa-
tions in complicated domains. Int. J. Numer. Methods for
Heat and Fluid Flow, submitted, 1996. also as SFB Bericht
342/1/96A, Institut f"ur Informatik, TU M"unchen, 1996.
[17] M. Griebel und G. Starke. Multilevel preconditioning based on
discrete symmetrization for convection-diffusion equations.
Journal of Computational and Applied Mathematics, sub-
mitted, 1996.
Serien- und Konferenzbeitr"age:
REFERENCES
[1] M. Griebel. Baumartige Strukturierung linearer Gleichungssys-
teme mit d"unn besiedelter Matrix. In Berichte aus den
Informatikinstituten, 9. Jahrestagung der o"sterreichischen
Gesellschaft f"ur Informatik, S. 105-115. Fakult"at f"ur Math-
ematik und Informatik, Universit"at Passau, Bericht MIP-
8604, 1986.
[2] M. Griebel. Ein gemeinsamer Datentyp f"ur eine Baumstruk-
turierung bei der Methode der finiten Elemente und beim
geometrischen Modellieren. In VDI-Bericht 610.5 Daten-
verarbeitung in der Konstruktion '86, CAD und Informatik,
S. 543-557. VDI-Verlag, 1986.
[3] M. Griebel. A parallelizable and vectorizable multi-level algo-
rithm on sparse grids. In W. Hackbusch, Editor, Parallel
Algorithms for partial differential equations, Notes on Nu-
merical Fluid Mechanics, Volume 31, S. 94-100. Vieweg Ver-
lag, Braunschweig, 1991. also as SFB Bericht, 342/20/90 A,
Institut f"ur Informatik, TU M"unchen, 1990.
[4] M. Griebel. Parallel multigrid methods on sparse grids. In Multi-
grid Methods III, International Series of Numerical Mathe-
matics, Volume 98, S. 211-221. Birkh"auser Verlag, Basel,
1991. also as SFB Bericht, 342/30/90 A, Institut f"ur Infor-
matik, TU M"unchen, 1990.
[5] M. Griebel, M. Schneider und C. Zenger. A combination tech-
nique for the solution of sparse grid problems. In P. de Groen
und R. Beauwens, Editoren, Iterative Methods in Linear Al-
gebra, S. 263-281. IMACS, Elsevier, North Holland, 1992.
also as SFB Bericht, 342/19/90 A, Institut f"ur Informatik,
TU M"unchen, 1990.
[6] M. Griebel. Multilevel algorithms considered as iterative meth-
ods on indefinite systems. In T. Manteuffel, Editor, Pro-
ceedings of the 2nd Copper Mountain Conference on Itera-
tive Methods. University of Colorado at Denver, 1992. also
as SFB Bericht, 342/29/91 A, Institut f"ur Informatik, TU
M"unchen, 1991.
[7] M. Griebel. Eine Kombinationstechnik f"ur die L"osung von
D"unn-Gitter-Problemen auf Multiprozessor-Maschinen. In
H.G. Bock, W. Hackbusch und R. Rannacher, Editoren,
Numerische Algorithmen auf Transputer-Systemen, Teubner
Skripten zur Numerik. Teubner Verlag, Stuttgart, 1992.
[8] M. Griebel. Grid- and point-oriented multilevel algorithms.
In W. Hackbusch und G. Wittum, Editoren, Incomplete De-
compositions (ILU) - Algorithms, Theory, and Applications,
Notes on Numerical Fluid Mechanics, Volume 41, S. 32-46.
Vieweg Verlag, Braunschweig, 1993. also as SFB Bericht,
342/14/92 A, Institut f"ur Informatik, TU M"unchen, 1992.
[9] M. Griebel, W. Huber, U. R"ude und T. St"ortkuhl. The combi-
nation technique for parallel sparse-grid-preconditioning and
-solution of PDEs on multiprocessor machines and worksta-
tion networks. In L. Bouge, M. Cosnard, Y. Robert und
D. Trystram, Editoren, Lecture Notes in Computer Science
634, Parallel Processing: CONPAR92-VAPP V, S. 217-228.
Springer Verlag, 1992.
[10] M. Griebel, W. Huber und C. Zenger. A fast Poisson solver
for turbulence simulation on parallel computers using sparse
grids. In E.H. Hirschel, Editor, Flow Simulation with High-
Performance Computers I, Notes on Numerical Fluid Me-
chanics, Volume 38, S. 101-113. Vieweg Verlag, Braun-
schweig, 1993.
[11] M. Griebel. Sparse grid multilevel methods, their paralleliza-
tion, and their applications to CFD. In J. H"auser, Editor,
Parallel Computational Fluid Dynamics 92, S. 161-174. New
Brunswick, USA, Elsevier, 1993.
[12] M. Griebel. A domain decomposition method using sparse grids.
In A. Quarteroni, Editor, Contemporary Mathematics, Vol.
157, DDM6, S. 255-261. American Mathematical Society,
1994.
[13] M. Griebel, W. Huber, T. St"ortkuhl und C. Zenger. On the par-
allel solution of 3D PDEs on a network of workstations and
on vector computers. In A. Bode und M. Dal Cin, Editoren,
Lecture Notes in Computer Science 732, Parallel Computer
Architectures: Theory, Hardware, Software, Applications, S.
276-291. Springer Verlag, 1993.
[14] M. Griebel und S. Zimmer. Adaptive point block methods. In
W. Hackbusch und G. Wittum, Editoren, Adaptive Methods:
Algorithms, Theory and Applications, Notes on Numerical
Fluid Mechanics. Vieweg Verlag, Braunschweig, S. 142-157,
1993.
[15] M. Griebel. Parallel point-oriented multilevel methods. In P.
Hemker und P. Wesseling, Editoren, Multigrid Methods IV,
International Series of Numerical Mathematics, EMG93.
Birkh"auser Verlag, S. 215-232, 1994.
[16] M. Griebel. Domain-oriented multilevel methods. In D. Keyes
und J. Xu, Editoren, Contemporary Mathematics, Vol. 180,
DDM7, S. 223-229. American Mathematical Society, 1994.
[17] H. Bungartz, M. Griebel, D. R"oschke und C. Zenger. Two proofs
of convergence for the combination technique for the efficient
solution of sparse grid problems. In D. Keyes und J. Xu,
Editoren, Contemporary Mathematics, Vol. 180, DDM7, S.
15-20. American Mathematical Society, 1994.
[18] M. Griebel und W. Huber. Turbulence simulation on sparse grids
using the combination method. In N. Satofuka, J. Periaux,
A. Ecer Editoren, Parallel Computational Fluid Dynamics,
New Algorithms and Applications, S. 75-84. North-Holland,
Elsevier, 1995.
[19] N. R"osch, S. Kr"uger, M. Griebel und C. Zenger. Quanten-
chemie auf Parallelrechnern, Zur Perspektive der Dichte-
funktionaltheorie. Proceedings der BMWF-Tagung HPSC95,
Aachen, 1996.
[20] M. Griebel und S. Knapek. Matrix-dependent multigrid-
homogenization for diffusion problems. Proceedings of the
GAMM-Seminar "Modelling and Computation in Environ-
mental Sciences". Notes on Numerical Fluid Mechanics, to
appear. Vieweg-Verlag, Braunschweig, 1996.
[21] M. Griebel, W. Huber und C. Zenger. Numerical Turbulence
Simulation on a parallel computer using the combination
method. DFG-SPP "Flow Simulations with High Perfor-
mace Computers". Notes on Numerical Fluid Mechanics, to
appear. Vieweg-Verlag, Braunschweig, 1996.
Technische Berichte: (Soweit nicht als Zeitschrifte-
nartikel oder Konferenzbeitrag erschienen)
REFERENCES
[1] M. Griebel. On the combination of the ideas of multilevel solvers
using hierarchical bases and the substructuring technique for
the finite element method. Bericht I8709, Institut f"ur Infor-
matik, TU M"unchen, 1987.
[2] M. Griebel. Zur L"osung von Finite-Differenzen- und Finite-
Element-Gleichungen mittels der
Hierarchischen Transformations-Mehrgitter-Methode. SFB
Bericht 342/4/90 A, Institut f"ur Informatik, TU M"unchen,
1990.
[3] M. Griebel, C. Zenger und S. Zimmer. Improved multilevel al-
gorithms for full and sparse grid problems. SFB Bericht
342/15/92 A, Institut f"ur Informatik, TU M"unchen, 1992.
[4] U. G"artel, M. Griebel, W. Huber, H. Schwichtenberg,
T. St"ortkuhl, U. Trottenberg, G. Winter, C. Zenger. The
parallel ASMG algorithm for 3D Poisson-like equations
on multi-workstations. Arbeitspapiere der GMD 767,
Gesellschaft f"ur Mathematik und Datenverarbeitung, Sankt
Augustin, 1993.
[5] M. Griebel und P. Oswald. Remarks on the theory of addi-
tive and multiplicative Schwarz algorithms. SFB Bericht
342/6/93A, Institut f"ur Informatik, TU M"unchen, 1993.
[6] M. Griebel und T. Neunhoeffer. A domain-oriented multilevel
algorithm - implementation and parallelization. SFB Bericht
342/18/94A, Institut f"ur Informatik, TU M"unchen, 1994.
[7] M. Griebel und W. Huber. Turbulence simulation on sparse grids
using the combination method. SFB Bericht 342/19/94A,
Institut f"ur Informatik, TU M"unchen, 1994.
[8] T. Grauschopf und M. Griebel. Parallelization of a multigrid
algorithm on the KSR1. in LRZ Bericht 9401, Overview of
Research on the Parallel Computer SNI-KSR at the Leibnitz-
Rechenzentrum M"unchen, M. Brehm, C. Schaller, (eds).
Leibniz-Rechenzentrum der Bayerischen Akademie der Wis-
senschaften, M"unchen, S. 63-69, 1994.
[9] M. Griebel und W. Huber. Parallel turbulence simualtion on
the IBM SP2 using a sparse grid method. Contribution
Sup'Prize 1995, Sup'Eur User Group Organization, 1995.
[10] M. Griebel, R. Kreissl, M. Rykaschewski und C. Zenger. Re-
sults of Benchmark Computations for the DFG-SPP "Flow
Simulations with High Performace Computers", 1995.
Editor's Note: The bibliography will be revised with these included in
------------- early May.
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