Send mail to:             for the digests or bakeoff
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 Current editor:  Craig Douglas       
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Today's editor:  Craig Douglas (

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: (Craig Douglas)
Subject: New MGNet Site

I have put a duplicate of MGNet at the University of Kentucky.  It can be
accessed through


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

Stefan Turek
Institut fuer Angewandte Mathematik, Universitaet Heidelberg, Germany,


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           
Environmental Computer Applications
Lawrence Livermore National Laboratory
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,


Date: Thu, 1 May 1997 12:04:01 -0400
From: (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

    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

    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.


[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: (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"

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

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 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:

    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,
        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


[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.



[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.



[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:


[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,
[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,
[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)


  [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,
  [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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