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:    ftp.ccs.uky.edu (128.163.209.106)

World Wide Web:  http://www.mgnet.org or
                 http://www.cerfacs.fr/~douglas/mgnet.html or
                 http://phase.etl.go.jp/mgnet or
                 http://www.ccs.uky.edu/mgnet

Today's editor:  Craig Douglas (douglas-craig@cs.yale.edu)

Volume 8, Number 1 (approximately January 31, 1998)

Today's topics:

     Important Dates
     Parallel 2D/3D Multigrid Solver
     Learning Tool (SOR, Multigrid)
     GRUMMP
     Preprint available (Saad, Sosonkina, and Zhang)
     Two Fellowships at Sandia National Laboratories
     14th GAMM-Seminar Kiel on Concepts of Numerical Software
     [DD11] - EmailAddress
     4th International Conference on Numerical Methods and Applications
     Some of the new entries in the bibliography

-------------------------------------------------------

Date: Sat, 31 Jan 1998 12:14:52 +0500
From: Craig C. Douglas 
Subject: Important Dates

This is a busy month.  All of these conferences are listed in the web page
on conferences on MGNet.

February 15     Abstracts due for the Workshop on Practical Aspects of
                Algebraic Multigrid Methods (March 25 - 27 in Stuttgart,
                Germany).

February 15     Early registration due for the GAMM - Workshop on Multigrid
                Methods (October 5 - 8 in Bonn, Germany).

February 25     Guaranteed availability of rooms for the 5th Copper Mountain
                Conference on Iterative Methods (March 30 - April 3)

February 28     Submission of abstracts for the 11th Domain Decompostion
                Symposium (July 20 - 24 in Greenwich, England)

Februrary 28    Submission of abstracts for C3AD (August 17 - 22
                in Petropolis, Brazil)

-------------------------------------------------------

Date: Tue, 06 Jan 1998 11:58:08 -0500
From: bernard bunner 
Subject: Parallel 2D/3D Multigrid Solver

Hello Mr. Douglas,

A brief introduction of myself.  I am a Ph.D. student with Prof. Tryggvason
at the U. of Michigan and I'm working on DNS of multiphase flows using a
front-tracking method.  Our code requires the solution of elliptic problems
with variables coefficients on a rectangular, staggered, constant step grid
(we use a finite-difference formulation similar to the MAC method).

With our 2D and 3D serial codes, we typically use Mudpack.But we wanted to
parallellize the codes and run large 3D simulations.  Since I didn't find the
equivalent of Mudpack in parallel, I developed my own programs and would like
to know if you'd be interested in putting them on your site.  The main
features are:

    - MPI
    - staggered grid (unlike Mudpack), rectangular domain, constant dx, dy,
    (dz)
    - V or W cycling
    - full weighting for the restriction and bilinear interpolation for the
    correction
    - either vertex-centered or cell-centered operations
    - periodic, Neumann, or Dirichlet BCs

I don't make any claim other than the codes work (I only checked on IBM-SP2
and HP-EXEMPLAR).  They are fairly short and documentation is OK.

Bernard Bunner

    Editor's Note: in mgnet/Codes/bunner.
    -------------

-------------------------------------------------------

Date: Wed, 07 Jan 1998 16:48:08 -0200
From: Armando de Oliveira Fortuna 
Subject: Learning Tool (SOR, Multigrid)

        I wrote a solver for the Laplace/Poisson equations which 
allows the user to select between multigrid, Line-SOR or Point-SOR.
It is a nice tool to introduce multigrid to new students - they can 
see for themselves how multigrid compares to SOR.

        The program is fully configurable at run-time. The user can
choose whether he or she wants to use multigrid or SOR, and then 
select:

* if SOR:

        * the relaxation parameter
        * whether to use the Line or Point version

if Multigrid:

        * the type of cycle (F,V,W)
        * whether to start on the fine grid or on the coarsest grid

        As for output, the program prints the iteration or mg cycle number and
the residue. It also saves that information to a file, so it 
can be later plotted.

        I would like to make this program available through MGNet.

        Thank you very much,

Armando de Oliveira Fortuna, Ph.D              Av. Dr. Carlos Botelho,
1465
Inst. de Ciencias Matematicas de Sao Carlos    CEP 13560-970, CP 668
Depto. de Ciencias de Comp. e Estatistica      Sao Carlos, SP, Brasil
Universidade de Sao Paulo (USP)                FAX: +55 (0)16 274-9150
www.lcad.icmsc.sc.usp.br ======== ======
email:fortuna@lcad.icmsc.sc.usp.br

    Editor's Note: in mgnet/Codes/fortuna.
    -------------

-------------------------------------------------------

Date: Wed, 28 Jan 1998 12:48:15 -0800 (PST)
From: Carl Ollivier-Gooch 
Subject: New 2D/3D Unstructured Mesh Generator

GRUMMP
Generation and Refinement of Unstructured Mixed-Element Meshes in Parallel

The goal of the GRUMMP project is to develop automatic mesh generation
software for unstructured meshes with mixed element types. The software
will be able to produce high-quality meshes which meet user-defined mesh
density requirements, using elements appropriate for the geometry and
physics of a particular problem. We envision a system in which common
types of physical problems have pre-defined mesh sizing and element
aspect ratio functions, allowing easy generation of meshes for these
applications areas. For flexibility and generality, the user will also
be able to prescribe these functions (for totally different
applications) or modify the pre-defined behaviors (to provide a quality
mesh in the wake of an airplane wing, for example).

GRUMMP Features

The initial version of the GRUMMP libraries has been released, including
executables for two- and three-dimensional mesh generation and
improvement and for three-dimensional scattered data interpolation.

- Two-dimensional and three-dimensional simplicial mesh generation
- Automatic creation and use of geometric length scale based on input data
- Mesh quality assessment using numerous geometric quality measures
- Improvement of existing two- and three-dimensional meshes
- Complete set of mesh manipulation primitives:
+ Local reconnection --- face swapping and edge removal (latter in 3D only)
+ Optimization-based vertex smoothing --- guaranteed better than Laplacian
+ Point insertion and/or deletion to match local length scale
- Mesh generation and improvement use the same primitives and length
scale calculation, providing uniform results from both processes
- Flexible I/O format (available in 2D; soon to be available in 3D)

The software is available in source form via ftp at

ftp://tetra.mech.ubc.ca/pub/GRUMMP/GRUMMP-0.1.0.tar.gz

For more information, including an online copy of the User Guide, visit
the GRUMMP home page at

http://tetra.mech.ubc.ca/GRUMMP/index.html

or send email to the developer at cfog@mech.ubc.ca.

Carl Ollivier-Gooch cfog@mech.ubc.ca
Department of Mechanical Engineering Voice: +1-604-822-1854
University of British Columbia Fax: +1-604-822-2403
2324 Main Mall URL: http://www.mech.ubc.ca/~cfog
Vancouver, BC V6T 1Z4 Canada

    Editor's Note:  A hyperlink to this has been added to the Codes' web page.
    -------------

-------------------------------------------------------

Date: Mon, 19 Jan 1998 17:02:51 -0600 (CST)
From: JUN ZHANG 
Subject: Preprint available (Saad, Sosonkina, and Zhang)

We are happy to announce the following preprint.

         Domain Decomposition and Multi-Level Type
        Techniques for General Sparse Linear Systems

                      Yousef Saad 

        Department of Computer Science and Engineering
                 University of Minnesota
        200 Union Street S.E., Minneapolis, MN 55455
    E-mail:saad@cs.umn.edu, URL:http://www.cs.umn.edu/~saad


                      Maria Sosonkina

               Department of Computer Science 
              University of Minnesota, Duluth
 320 Heller Hall, 10 University Drive, Duluth, Minnesota 55812-2496
                     masha@d.umn.edu


                       Jun Zhang

        Department of Computer Science and Engineering
                  University of Minnesota
        200 Union Street S.E., Minneapolis, MN 55455
    E-mail:jzhang@cs.umn.edu, URL:http://www.cs.umn.edu/~jzhang

                        ABSTRACT

Domain-decomposition and multi-level  techniques  are often formulated
for those linear systems that arise from the solution of elliptic-type
Partial  Differential   Equations.  In this   paper, generalizations of
these techniques for  irregularly structured sparse linear systems are
considered.  An interesting common approach  used to derive successful
preconditioners is  to resort to Schur  complements.  In particular, we
discuss a     multi-level  domain decomposition-type     algorithm for
iterative solution of large sparse linear systems based on independent
subsets of nodes. We also discuss a Schur complement technique that
utilizes incomplete LU factorizations of local matrices.

Postscript file of the above preprint may be downloaded from the
following web pages:

  http://www.cs.umn.edu/~saad  or  http://www.cs.umn.edu/~jzhang

For those who do not have access to web facility, send an e-mail to
jzhang@cs.umn.edu for a postscript file or a hard copy.

-------------------------------------------------------

Date: Mon, 12 Jan 98 12:17:52 MST
From: tuminaro@siesta.cs.sandia.gov (Ray S. Tuminaro)
Subject: Two Fellowships at Sandia National Laboratories

I would like the following job postings to appear on the next 
MGNet newsletter.

            Two Fellowships at Sandia National Laboratories

The Computational Sciences and Mathematics Center at Sandia National
Laboratories (Albuquerque/NM and Livermore/CA) is seeking qualified candidates
for two post-doctoral fellowship positions.  These positions offers an
exceptional opportunity for innovative research in scientific computing.  The
successful candidates will hold a Ph.D. in a scientific computing discipline
and have significant experience in iterative linear equation solvers, high
performance computing, and numerical algorithms.

The Center maintains strong research programs in a variety of areas, including
numerical mathematics, discrete algorithms, computational physics/engineering,
and advanced systems software and tools.  A unique computing environment is
supported which includes a 4500-node Intel TFlops computer, a 1800-processor
Intel Paragon, a 192-processor SGI Origin system, an 84-processor DEC-8400
system, and experimental heterogeneous computer platforms.

The position includes a competitive salary, moving expenses, and a
professional travel allowance.

Interested persons should submit a complete resume with names and addresses of
three references to:

        Ray S. Tuminaro    
        Sandia National Laboratories
        Department 9222 / MS 9214
        P.O. Box 969
        Livermore, CA 94551-0969
        tuminaro@ca.sandia.gov
        (510) 294-2564

Applications will be accepted through March or until the position is awarded.

Sandia National Labs is a U.S.  Department of Energy multiprogram laboratory,
operated by Sandia Corporation, a wholly owned subsidiary Lockheed Martin
Corporation, with locations in Albuquerque, NM and Livermore, CA.

Equal Opportunity Employer.  Drug-free workplace.  U.S. Citizenship is
normally required.

-------------------------------------------------------

Date: Sat, 31 Jan 1998 12:14:52 +0500
From: Craig C. Douglas 
Subject: 14th GAMM-Seminar Kiel on Concepts of Numerical Software

The latest in the series of GAMM seminars at Kiel was held January 23rd to
25th with the topic being Concepts of Numerical Software.  Below is the list
of talks.

P. Bastian (Stuttgart):
Parallel unstructured grid computations

K. Johannsen (Stuttgart):
np - the Modular Numerical Subsystem of UG

R. Roitzsch, B. Erdmann, J. Lang (Berlin):
The benefits of modularization: From Kaskade to Kardos

J. Schoeberl, G. Haase (Linz):
Some Concepts of the Object Oriented Code FEPP

Ch. Weiss, H. Hellwagner, L. Stals, U. Ruede (Augsburg):
Data Locality Optimizations to Improve the Efficiency of
Multigrid Methods

Ch. Becker, S. Kilian, H. Oswald, St. Turek (Heidelberg):
Some software and algorithmic concepts of FEAST

J. Fuhrmann, H. Langmach, Th. Koprucki, M. Petzoldt,
I. Schmelzer (Berlin):
pdelib: An Open Modular Toolbox for the Numerical Solution
of Partial Differential Equations

K. Gerdes (Zurich):
HP90: A general and flexible Fortran 90 hp-FE code

K. Urban, T. Barsch (Aachen):
Software tools for using wavelets on the interval for the
numerical solution of operator equations

D. di Serafino, A. Murli (Napoli, Italy):
The PINEAPL Library: a Parallel Numerical Library
for Industrial Applications

M. Griebel, T. Schiekofer, G. Zumbusch (Bonn):
Software concepts of a sparse grid finite difference code

Ch. Lage (Zurich):
Concept-Oriented Design of Numerical Software

O. Steinbach (Stuttgart):
Implementation and Parallelization of Boundary Element Methods

M. Konik (Chemnitz):
Object-oriented implementation of multiscale methods for
boundary integral equations

C. C.Douglas (Lexington, USA):
Cache Based Multigrid on Structured/Unstructured Grids in 2D/3D

W. Hackbusch (Kiel):
Hierarchical structures and their representations

K. G. Siebert, A. Schmidt (Freiburg):
ALBERT: An adaptive hierarchical finite element toolbox

M. Weidmann  (Muenchen):
On the Object-Oriented Redesign of a Real-World CFD Program

H.-J. Bungartz, Ch. Zenger (Muenchen):
What we can learn from computer science for the design
of numerical programs

A. Langer (Dortmund):
LiMA - A generic class library for mesh representation in 2D/3D

M. Metscher (Bonn):
Efficient hierarchical Searching on arbitrary nested Grids,
Application to Particle Tracing

G. Bader, G. Berti (Cottbus):
Reusable software components for sequential and
distributed solution of PDE problems

K. Birken (Stuttgart):
Towards automatic parallelization of numerical
software based on formal specification concepts

L. Stals (Bath, UK):
Flexible Data Structure For the Adaptive Refinement
on Unstructured Grids in Parallel

Ch. Wieners (Stuttgart):
Parallel linear algebra and the application to multigrid methods

-------------------------------------------------------

From: 
Date: Wed, 4 Feb 1998 08:40:45 GMT
Subject: [DD11] - EmailAddress

As some of you pointed out that there could be a problem with the email
address D.Decomposition@gre.ac.uk
I suggest you to use dd11@gre.ac.uk which certainly works with no problems
while I am asking the system people to look at D.Decomposition@gre.ac.uk

I hope this will help during the crucial time when abstracts are on their
way.

DD11

-------------------------------------------------------

Date: Thu, 22 Jan 1998 11:41:14 +0000
From: Olivier Goyon 
Subject: 4th International Conference on Numerical Methods and Applications

Dear collegue

I am writing to you in connection with the mini symposium  entitled
"Multilevel methods for incompressible viscous flows" which will be
held in sofia from 19 to 23 August, 1998 during the 
4th International Conference on Numerical Methods and Applications.

As you can see the aim of this symposium is to bring together groups,
which are actively involved in the development of multilevel methods
for incompressible flows.

We would be very pleased if you express interest in attending this
symposium.

Sincerely yours,

        Dr Dimitris DRIKAKIS and Dr Olivier GOYON

  4th International Conference on Numerical Methods and Applications: 
                     NM\&A-O($h^4$)'98

       Bulgarian Academy of Sciences in Cooperation with SIAM

               Call for Papers for the Mini Symposium 
          "Multilevel methods for incompressible viscous flows"


The above mini symposium is organized during the 4th International Conference
on Numerical Methods and Applications: NM\&A-O($h^4$)'98, which will
be held in Sofia from 19 to 23 August, 1998.
The goal of this Symposium is to provide means for presenting both final
results of research and especially early informal communication of
research in progress, as well as
to encourage  discussion and interchange of ideas between diverse disciplines
interested in the topic of "Multilevel Methods for Incompressible
Viscous Flows".
The Symposium intentionally covers a wide range of algorithms and methods
including classical multigrid methods, nonlinear Galerkin methods,
adaptive mesh refinement, local solution techniques and
cyclic-like reduction methods.
Authors should send three copies of an extended abstract to the
Mini Symposium Organizers. Abstracts can also be sent as ASCII files via e-mail.
Contributions will be reviewed for relevancy
and technical content on the basis of the abstract.
Instructions for the preparation of the final manuscript will be sent
around May 1, 1998. Further information about the conference proceedings
can be provided by  Dr Oleg Iliev (Conference Organizer, see address below).

Deadline Schedule:
==================

Abstract Due:           15th of March, 1998.
Abstract Acceptance:    30th of April, 1998.

Mini Symposium Organizers:
==========================

Dr. D. Drikakis and Dr O. Goyon
UMIST
Department of Mechanical Engineering
PO Box 88, Manchetser M60 1QD
United Kingdom

Fax: (44) 161 200 3723
Email: mcjtsog@sgo.me.umist.ac.uk

Further information about the conference is available on the Web Page:
http://banmatpc.math.acad.bg/~nma98/ or
http://orca.st.usm.edu/marcin/mp/cfp/sofia.html. 
For any further enquiry
about the conference  you can also contact the conference organizer:

NMA'98, c/o Dr. Oleg Iliev
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
Acad. G. Bonchev Str., Bl.8, 1113 Sofia, BULGARIA
Fax-No. (++359 2) 971 36 49

-------------------------------------------------------

Date: Sat, 31 Jan 1998 14:42:12 -0400
From: Craig Douglas 
Subject: Some of the new entries in the bibliography

Here are some recent new entries.  As usual, please send additions and
corrections.

Many corrections and small changes occurred to the bibliography in late
January.  This was due to Professor Wolfgang Hackbusch allowing me to spend
time going through his extensive library.  Many more entries will go into
the bibliography thanks to his helpfulness.

  [1] O. Axelsson and B. Polman, A robust preconditioner based
          on  algebraic  substructurig  and  two-level  grids,  in  Robust
          Multi-Grid Methods, W. Hackbusch, ed., vol. 23 of Notes
          on Numerical Fluid Mechanics, Braunschweig, 1989, Vieweg,
          pp. 1-26.
  [2] A. Barker and B. Gervang, Relaxed ILU preconditioning for
          the CG solution of a singular boundary value problem, in In-
          complete Decompositions (ILU) - Algorithms, Theory, and
          Applications, W. Hackbusch and G. Wittum, eds., vol. 41 of
          Notes on Numerical Fluid Mechanics, Braunschweig, 1993,
          Vieweg, pp. 1-11.
  [3] P. Bastian,  J. H. Ferziger,  G. Horton,  and J. Volk-
          ert, Adaptive multigrid solution of the convection-diffusion
          equation on the DIRMU processor,  in Robust Multi-Grid
          Methods, W. Hackbusch, ed., vol. 23 of Notes on Numerical
          Fluid Mechanics, Braunschweig, 1989, Vieweg, pp. 27-36.
  [4] R. Beauwens, Incomplete factorizations with S/P and modi-
          fied S/P consistently ordered M-factors, in Incomplete De-
          compositions (ILU) - Algorithms, Theory, and Applications,
          W. Hackbusch and G. Wittum,  eds.,  vol. 41 of Notes on
          Numerical Fluid Mechanics,  Braunschweig,  1993,  Vieweg,
          pp. 22-31.
  [5] C. Becker, J. H. Ferziger, M. Peric, and G. Scheuerer,
          Finite volume multigrid solution of the two-dimensional in-
          compressible Navier-Stokes equations, in Robust Multi-Grid
          Methods, W. Hackbusch, ed., vol. 23 of Notes on Numerical
          Fluid Mechanics, Braunschweig, 1989, Vieweg, pp. 37-47.
  [6] J.  W.  Boerstoel,  A.  E.  P.  Veldman,  J.  Van  Der
          Vooren, and A. J. Van Der Wees, Trends in CFD for
          aeronautical 3-D steady applications:  the Dutch situation,
          in Research in Numerical Fluid Mechanics,  P. Wesseling,
          ed., vol. 17 of Notes on Numerical Fluid Mechanics, Braun-
          schweig, 1987, Vieweg, pp. 1-18.
  [7] F. Brezzi and JPit"aranta, On the stabilization of finite el-
          ement approximations of the Stokes equations, in Efficient
          Solution of Elliptic Systems, W. Hackbusch, ed., vol. 10 of
          Notes on Numerical Fluid Mechanics, Braunschweig, 1984,
          Vieweg, pp. 11-19.
  [8] P.  Conradi  and  D.  Schr"oder,  Concepts for a dimension
          independent application of multigrid algorithms to semicon-
          ductor device simulation, in Robust Multi-Grid Methods,
          W. Hackbusch,  ed.,  vol. 23 of Notes on Numerical Fluid
          Mechanics, Braunschweig, 1989, Vieweg, pp. 48-57.
  [9] C. Cuvelier, On the computation of free boundaries, in Re-
          search  in  Numerical  Fluid  Mechanics,  P.  Wesseling,  ed.,
          vol.  17  of  Notes  on  Numerical  Fluid  Mechanics,  Braun-
          schweig, 1987, Vieweg, pp. 18-29.
[10]  W.  Dahmen  and  L.  Elsner,  Algebraic  multigrid  methods
          and the Schur complement, in Robust Multi-Grid Methods,
          W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Me-
          chanics, Braunschweig, 1989, Vieweg, pp. 58-68.
[11]  E. Dick, A multigrid method for the steady Euler equations,
          based on flux-difference splitting with respect to primitive
          variables, in Robust Multi-Grid Methods, W. Hackbusch,
          ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braun-
          schweig, 1989, Vieweg, pp. 69-85.
[12]  J.  H.  D"orfer,  Treatment  of  singular  perturbation  problems
          with  multigrid  methods,  in  Robust  Multi-Grid  Methods,
          W. Hackbusch,  ed.,  vol. 23 of Notes on Numerical Fluid
          Mechanics, Braunschweig, 1989, Vieweg, pp. 86-95.
[13]  C. C. Douglas, Multigrid methods in science and engineering,
          IEEE Comput. Sci. Eng., 3 (1997), pp. 55-68.
[14]  C.  C.  Douglas,  A.  Ern,  and  M.  D.  Smooke,  Multigrid
          solution of flame sheet problems on serial and parallel com-
          puters, Paral. Alg. Appl., 10 (1997), pp. 225-236.
[15]  D.Van Essen, G. Kupers, and H. Mes, Thermal hydraulic
          modelling  studies  on  heat  exchanging  components,  in  Re-
          search  in  Numerical  Fluid  Mechanics,  P.  Wesseling,  ed.,
          vol.  17  of  Notes  on  Numerical  Fluid  Mechanics,  Braun-
          schweig, 1987, Vieweg, pp. 30-44.
[16]  B. Gustafsson and G. Lindskog, Parallelizing incomplete
          factoarization preconditioning methods,  in Incomplete De-
          compositions (ILU) - Algorithms, Theory, and Applications,
          W. Hackbusch and G. Wittum,  eds.,  vol. 41 of Notes on
          Numerical Fluid Mechanics,  Braunschweig,  1993,  Vieweg,
          pp. 47-56.
[17]  W.  Hackbusch,  The frequency decomposition multi-grid al-
          gorithm,  in  Robust  Multi-Grid  Methods,  W.  Hackbusch,
          ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braun-
          schweig, 1989, Vieweg, pp. 96-104.
[18]  W. Hackbusch and A. Reusken, On global multigrid conver-
          gence for nonlinear problems, in Robust Multi-Grid Meth-
          ods, W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid
          Mechanics, Braunschweig, 1989, Vieweg, pp. 105-113.
[19]  D. H"anel, W. Schr"oder, and G. Seider, Multigrid meth-
          ods for the solution of the compressible Navier-Stokes equa-
          tions, in Robust Multi-Grid Methods, W. Hackbusch, ed.,
          vol.  23  of  Notes  on  Numerical  Fluid  Mechanics,  Braun-
          schweig, 1989, Vieweg, pp. 114-127.
[20]  W. Heinrichs, Effective preconditioning for spectral multigrid
          methods,  in Robust Multi-Grid Methods,  W. Hackbusch,
          ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braun-
          schweig, 1989, Vieweg, pp. 139-144.
[21]  R.  Hiptmair, Multilevel Preconditioning for Mixed Problems
          in Three Dimensions, PhD thesis, Technischen Universit"at
          Augsburg, Augsburg, Germany, 1996.
[22]  M. Hoekstra, Computation of steady viscous flow near a ship's
          stern, in Research in Numerical Fluid Mechanics, P. Wessel-
          ing,  ed.,  vol. 17 of Notes on Numerical Fluid Mechanics,
          Braunschweig, 1987, Vieweg, pp. 45-57.
[23]  C.   J.   Hoogendoorn   and   Th.   H.Van   Der   Meer,
          Convection-diffusion phenomena and a Navier-Stokes pro-
          cessor, in Research in Numerical Fluid Mechanics, P. Wes-
          seling, ed., vol. 17 of Notes on Numerical Fluid Mechanics,
          Braunschweig, 1987, Vieweg, pp. 58-72.
[24]  G. Horton, R. Knirsch, and G. Wittum, Modification of
          the ILU-methd for enhanced parallel efficiency, in Incom-
          plete Decompositions (ILU) - Algorithms, Theory, and Ap-
          plications, W. Hackbusch and G. Wittum, eds., vol. 41 of
          Notes on Numerical Fluid Mechanics, Braunschweig, 1993,
          Vieweg, pp. 57-66.
[25]  M.  A.  Hulsen  and  J.Van  Der  Zanden, Problems, analy-
          ses and solutions of the equations for viscoelastic flow, in
          Research in Numerical Fluid Mechanics, P. Wesseling, ed.,
          vol.  17  of  Notes  on  Numerical  Fluid  Mechanics,  Braun-
          schweig, 1987, Vieweg, pp. 73-86.
[26]  M. Hunek, K. Kozel, and M. Vavrincova, Numerical so-
          lution of transonic potential flow in 2d compressor cascades
          using multi-grid techniques, in Robust Multi-Grid Methods,
          W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Me-
          chanics, Braunschweig, 1989, Vieweg, pp. 145-154.
[27]  B.  Koren,  Multigrid  and  defect  correction  for  the  steady
          Navier-Stokes  equations,  in  Robust  Multi-Grid  Methods,
          W. Hackbusch,  ed.,  vol. 23 of Notes on Numerical Fluid
          Mechanics, Braunschweig, 1989, Vieweg, pp. 165-177.
[28]  Y.  P.  Marx  and  J.  Piquet,  Towards  multigrid  accelera-
          tion of 2d compressible Navier-Stokes finite volume implicit
          schemes,  in Robust Multi-Grid Methods,  W. Hackbusch,
          ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braun-
          schweig, 1989, Vieweg, pp. 178-187.
[29]  P. Neittaanm"aki and M. Kr'izek, Conforming FE-method
          for obtaining the gradient of a solution to the Ppoisson equa-
          tion, in Efficient Solution of Elliptic Systems, W. Hackbusch,
          ed., vol. 10 of Notes on Numerical Fluid Mechanics, Braun-
          schweig, 1984, Vieweg, pp. 74-86.
[30]  A.  J.  Renkema,  R.  Verstappen,  R.  W.De  Vries,  and
          P. J. Zandbergen, Some experiences with spectral multi-
          grid, in Research in Numerical Fluid Mechanics, P. Wessel-
          ing,  ed.,  vol. 17 of Notes on Numerical Fluid Mechanics,
          Braunschweig, 1987, Vieweg, pp. 101-114.
[31]  H. Schippers, Multiple Grid Methods for Equations of the Sec-
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