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Volume 5, Number 10 (approximately October 31, 1995)

Today's topics:

     Are you keeping a shadow or have an active multigrid WWW site?
     ~/.mailcap file for web access to MGNet
     Kaskade Code Update
     5 Papers (Y. Shapira)
     Preprint: Multigrid Method for Convection-Diffusion Equation
     Boundary Value ODE book
     Algebraic MG Conference (revised paper due date)
     Workshop in Bulgaria


Date: Tue, 31 Oct 1995 13:25:18 -0500 (EST)
From: Craig Douglas 
Subject: Are you keeping a shadow or have an active multigrid WWW site?

I am aware of at least one partial and one complete shadow of the contents of
MGNet.  As any of you know who regualrly use the Internet, the world wide web
is rapidly reducing the data transfer rate on the Internet to zero.  If you
are running a shadow and are willing to admit it, please let me know so that I
can put a pointer to your machine into the MGNet web pages (for either WWW or
anonymous ftp access).

While I am updating the web pages for MGNet, if you have a WWW page of
interest to the multigrid or domain decomposition communities, please let me
know so I can add a hypertext link to it.



Date: Tue, 31 Oct 1995 10:05:28 -0500 (EST)
From: Craig Douglas 
Subject: ~/.mailcap file for web access to MGNet

Many people send messages to me asking how to avoid having to store the
gzipped files before viewing them when accessing MGNet with a web browser.  I
have no idea if you are using a Mac, OS/2, or Windows.  On the UNIX systems
that I use, however, I have a file in my home directory called .mailcap.  Mine
contains the following lines:

audio/*; audiotool %s
image/*; xv %s
video/mpeg; mpeg_play  %s
video/gl; xgl %s
video/dl; xdl %s
application/postscript; ghostview %s
application/x-dvi; xdvi %s


Date: Thu, 12 Oct 1995 09:37:55 +0100
From: erdmann@ZIB-Berlin.DE (Erdmann)
To: mgnet
Subject: Kaskade Code Update

                        Adaptive multilevel-code
               for linear scalar elliptic and parabolic problems 
                     in 1, 2, 3 space dimensions.
               We included example algorithms for nonlinear methods
               used in obstacle, porous media or stefan problems.

                           --- a C++ toolbox  ----

    Authors: Rudolf Beck
             Rainer Roitzsch
             Bodo Erdmann

    Last update: 10th October 1995

    1. P. Deuflhard, P. Leinen, H. Yserentant:
       Concepts of an Adaptive Hierarchical Finite Element Code.
       IMPACT, 1, 1989.

    2. F. Bornemann:
       An Adaptive Multilevel Approach to Parabolic Equations in Two
       Space Dimensions. Dissertation, Freie Universitaet Berlin, 1991.

    3. F. Bornemann, B. Erdmann, R. Kornhuber:
       Adaptive Multilevel Methods in Three Space Dimensions.
       Int. J. Numer. Meths. in Eng., 36, 1993.

    4. R. Kornhuber:
       Monotone Multigrid Methods for Nonlinear Variational Problems.
       Habilitationsschrift, Freie Universitaet Berlin, 1995.

    5. R. Beck, B. Erdmann, R. Roitzsch:
       Kaskade 3.0, An Object-Oriented Adaptive Finite Element Code
       Techn. Report TR 95-4, 1995.

    5. R. Beck, B. Erdmann, R. Roitzsch:
       Kaskade 3.0, User's Guide
       Techn. Report TR 95-11, 1995.


The KASKADE 3.0 software package solves 
linear scalar elliptic and parabolic problems in 1, 2, 3 space dimensions
with adaptive finite element methods.

Furthermore, the toolbox includes extensions for handling systems of 
equations and example algorithms for nonlinear methods
used in obstacle, porous media or Stefan problems.

Core of the program is a variety og multilevel/multigrid preconditioners
for the arising linear systems.

This object-oriented code is written in C++ and can
be compiled with Gnu g++, version 2.6.3, and some other compilers.

It solves the same mathematical problem classes as its predecessor
KASKADE 2.x, which is written in C.

The code, a programmer's manual describing the software design, 
and a user's guide are available by anonymous ftp 

from the MGNet or from the eLib at the Konrad-Zuse-Zentrum in Berlin.


   in the subdirectories

   /pub/kaskade/3.0  and   /pub/kaskade/Manuals/3.0


   in the subdirectories


How to use the code?

1. uncompress 3.0.tar.Z
   - or -
   gunzip 3.0.tgz

2. tar -xf 3.0.tar
   (Creates a directory 3.0  with the sources)

3. cd 3.0

4. make 
   (Uses the make-file 'makefile' to compile and link the executable 'k6' 
    handling  1D-, 2D-, and 3D-problems.
    In the make-file there are four targets (k1,k2,k3,k6 (default)) to 
    obtain seperate versions for different space dimensions ( - and one 
    that comprises all of them).
    You find some more information about this in the short documentation 
    in the main file or in the user's guide. 
    The file kaskade.make is a copy of the makefile. You should use it to
    define new dependencies of files.)

5. k6 cmd=unit2 
   (Starts the program, the command file unit2 defines a 2D problem)

How to use the Programmer's Manual?

1. uncompress
   - or -

2. output on a postscript printer

How to use the User's Guide?

1. uncompress
   - or -

2. output on a postscript printer

We are extending the User's Guide (tutorial) continously.

  Address:    Konrad-Zuse-Zentrum Berlin (ZIB)
              Heilbronnerstrasse 10
              10711 Berlin 
  Telefon:    0049+30+89604-215


For questions and remarks, please use the  e-mail addresses. 



    You may use or modify this code for your own non-commercial
    purposes for an unlimited time. 
    In any case you should not deliver this code without a special 
    permission of ZIB.
    In case you intend to use the code commercially, we oblige you
    to sign an according licence agreement with ZIB.


Bodo Erdmann
Rainer Roitzsch

Bodo Erdman                 | Konrad-Zuse-Zentrum fuer Informationstechnik (ZIB)    | Abt. Numerische Software-Entwicklung
Telefon: (030) 89604-215    | Heilbronner Str.10
Fax: -125                   | D-10711 Berlin - Wilmersdorf


Date: Thu, 19 Oct 1995 14:15:31 -0600
From: Yair Shapira 
Subject: 5 Papers

I put 5 papers on mgnet...  My new email address is

Best regards
Yair Shapira.

                    Towards Automatic Multigrid Algorithms
                for SPD, Nonsymmetric and Indefinite Problems

                  Yair Shapira, Moshe Israeli and Avram Sidi

                   Computer Science Department, Technion, 
                            Haifa $32000$, Israel


A new multigrid algorithm is constructed for the solution of linear systems of
equations which arise from the discretization of elliptic PDEs.  It is defined
in terms of the difference scheme on the fine grid only, and no
rediscretization of the PDE is required.  Numerical experiments show that this
algorithm gives high convergence rates for several classes of problems:
symmetric, nonsymmetric and problems with discontinuous coefficients,
non-uniform grids and non-rectangular domains.  When supplemented with an
acceleration method, good convergence is achieved also for pure convection
problems and indefinite Helmholtz equations.

    Editor's Note: in mgnet/papers/Shapira/ and
    -------------     mgnet/papers/Shapira/automg.abs

                             * * * * * * * * * *

                         Multigrid Techniques for 3-D
                       Definite and Indefinite Problems
                       with Discontinuous Coefficients

                                 Yair Shapira
                   Computer Science Department, Technion --
             Israel Institute of Technology, Haifa 32000, Israel


A multigrid method for the solution of finite difference approximations of
elliptic PDEs is introduced.  A parallelizable version of it, suitable for two
and multi level analysis, is also defined, and serves as a theoretical tool
for deriving an optimal implementation for the main version.  For indefinite
Helmholtz equations, this analysis provides a prediction of the optimal mesh
size for the coarsest grid used.  Numerical experiments show the applicability
of the method to 3-d diffusion problems with discontinuous coefficients and
highly indefinite Helmholtz equations.

    Editor's Note: in mgnet/papers/Shapira/ and
    -------------     mgnet/papers/Shapira/automgD3.abs

                             * * * * * * * * * *

                           Coloring Update Methods

                                 Yair Shapira
                   Computer Science Department, Technion --
              Israel Institute of Technology, Haifa 32000, Israel


For linear update methods with nonsingular iteration matrices, a coloring
method is introduced for which the multicolor iteration matrix is similar to
the original one.  It is general in the sense that its definition is
independent of grids and stencils.  A method for transforming eigenvectors of
the original iteration matrix to those of the multicolor one is introduced.
Applications to unstructured grids and multigrid solution of three-dimensional
problems are presented.

    Editor's Note: in mgnet/papers/Shapira/ and
    -------------     mgnet/papers/Shapira/colors.abs

                             * * * * * * * * * *

                      Parallelizable Approximate Solvers
                  for Recursions Arising in Preconditioning

                                 Yair Shapira
                   Computer Science Department, Technion --
              Israel Institute of Technology, Haifa 32000, Israel


For the recursions used in the Modified Incomplete LU (MILU) preconditioner,
namely, the incomplete decomposition, forward elimination and back
substitution processes, a parallelizable approximate solver is presented.  The
present analysis shows that the solutions of the recursions depend only weakly
on their initial conditions and may be interpreted to indicate that the
inexact solution is close, in some sense, to the exact one.  The method is
based on a domain decomposition approach, suitable for parallel
implementations with message passing architectures.  It requires a fixed
number of communication steps per preconditioned iteration, independently of
the number of subdomains or the size of the problem.  The overlapping
subdomains are either cubes (suitable for mesh-connected arrays of processors)
or constructed by the data-flow rule of the recursions (suitable for
line-connected arrays with possibly SIMD or vector processors).  Numerical
examples show that, in both cases, the overhead in the number of iterations
required for convergence of the preconditioned iteration is small relatively
to the speed-up gained.

    Editor's Note: in mgnet/papers/Shapira/ and
    -------------     mgnet/papers/Shapira/iluparallel.abs

                             * * * * * * * * * *

                   Two-Level Analysis and Multigrid Methods
                 for SPD, Non-Normal and Indefinite Problems

                                 Yair Shapira
                   Computer Science Department, Technion --
              Israel Institute of Technology, Haifa 32000, Israel


A convergence theory for Black-Box Multigrid for a class of SPD problems is
presented.  Improved versions of Black-Box Multigrid for diffusion problems
with discontinuous coefficients are defined.  A two-level analysis method for
several automatic multigrid methods for certain separable problems is
introduced.  Unlike standard two-level analysis methods, based on Fourier
analysis, it is based on spectral analysis, hence applicable to non-normal
problems and to certain problems with variable coefficients.  For indefinite
problems, it provides a way to choose an optimal mesh size for the coarsest
grid used and motivates the definition of an improved version of Black-Box
Multigrid.  Numerical experiments confirming the analysis are reported.

    Editor's Note: in mgnet/papers/Shapira/ and
    -------------     mgnet/papers/Shapira/tlanalysis.abs

Date: Tue, 24 Oct 1995 12:26:38 -0400
From: Jun Zhang 
Subject: Preprint: Multigrid Method for Convection-Diffusion Equation

                   An Accurate and Stable Multigrid Method 
                    for Convection-Diffusion Equations   

                Murli M. Gupta, Jules Kouatchou and Jun Zhang
                          Department of Mathematics 
                       The George Washington University
                          Washington, DC 20052, USA

We introduce a high-order compact difference scheme with multigrid algorithm
to solve the convection-diffusion equations with constant coefficients.  This
high-order discretization scheme is shown to be more accurate and stable than
the usual five-point discretization scheme.  It solves the convection-
diffusion equations directly without using any preconditioner or adding any
artificial dissipation terms.  This method is shown to converge faster than
some of the existing methods and to achieve higher accuracy.  Numerical
experiments are presented to validate the conclusions.

Please send your comments to:

    Editor's Note: in mgnet/papers/Gupta-Kouatchou-Zhang/ and
    -------------     mgnet/papers/Gupta-Kouatchou-Zhang/con_diff.abs.


Date: Thu, 12 Oct 95 09:48:54 BST
From: "M. Ainsworth" 
Subject: Article for MGNet


                    LEICESTER UNIVERSITY, UK

                       8th-19th July 1996

The Programme
The meeting will comprise two one-week modules, each of which can "stand
alone", although it is expected that many participants and speakers will stay
for the full two weeks.

From Monday to Friday each week there will be three five-lecture courses given
by the invited lecturers as follows:

                    Week 1, 8th-12th July 1996

    G. Cybenko (Dartmouth) "Neural Networks"

    M. Plum (Clausthal) "Eigenvalue Problems for Differential Equations"

    G. Strang (MIT) "Wavelets" 

                   Week 2, 15th-19th July 1996

    L. Greengard (NYU) "Multipole Methods" 

    C. Schwab (ETH, Zurich) "Hierarchical Modelling" 

    J. Xu (Penn State) "Multilevel and Domain Decomposition Methods" 

The principal aim of the meeting is to gather together numerical analysts and
a team of internationally renowned experts for a period of intensive study and
research.  It is intended that the lectures should be accessible to people
(particularly research students) for whom the material is new, to enable them
to acquire reasonable competence in it, thus broadening their research
horizons.  Those with greater initial knowledge should end up being able to
work on significant problems in the area.

There will be a substantial amount of time available for research and
discussion with the assembled experts, who will make themselves available for
consultation in "office hours".  Typeset lecture notes will be provided by
most of the speakers.

In addition, there will be an opportunity for participants to present research
seminars on their own work.  It is anticipated that there will also be book
exhibitions and displays of computer software.

Registration forms and further details are available (electronically or by
surface mail) from:

    Dr M. Ainsworth (, Mathematics and Computer Science, 
    Leicester University, Leicester LE1 7RH, United Kingdom. 


Date: Wed,  4 Oct 1995 11:49:49 UTC-0700
From: Uri Ascher 
Subject: Boundary Value ODE book

Dear Colleagues,

  Our book,
            Numerical Solution of Boundary Value Problems 
                for Ordinary Differential Equations

has recently been published with SIAM in the Classics series and is now
available.  The first edition of this book, published in 1988 by
Prentice-Hall, became unavailable in 1993.  The current edition contains many
small corrections but no major ones.  Also, it's in a softcover volume and is
significantly cheaper than the original edition.  Those of you who are
interested in this field may find the book very helpful.

Please feel free to contact SIAM for further information:

ISBN 0-89871-354-4

                          Uri Ascher, Bob Mattheij and Bob Russell


Date: Fri, 20 Oct 1995 17:37:28 +0100
From: Maya Neytcheva 
Subject: Algebraic MG Conference (revised paper due date)

               Announcement and call for papers

                       CONFERENCE ON
   June 13-15, 1996, University of Nijmegen, The Netherlands

Owe Axelsson, Nijmegen, The Netherlands
Dietrich Braess, Bochum, Germany
Tony F. Chan, Los Angeles, California
Richard E. Ewing, College Station, Texas
Wolfgang Hackbusch, Kiel, Germany
Piet Hemker, Amsterdam, The Netherlands
Yuri A. Kuznetsov, Moscow, Russia
Ulrich Langer, Linz, Austria
Jean-Francois Maitre, Lyon, France
Panayot S. Vassilevski, Sofia, Bulgaria
David M. Young, Austin, Texas, honorary member
Harry Yserentant, Tubingen, Germany

Prof. Owe Axelsson 
Faculty of Mathematics and Informatics
Toernooiveld 1, NL-6525 ED Nijmegen
The Netherlands
fax: +31 (0)24 3652140

Owe Axelsson, Ben Polman, Rob Stevenson, Maya Neytcheva, Mariana Nikolova

The purpose of the conference is to provide a forum for the presentation and
the discussion of recent progress in the analysis, implementation and
applications in various fields of algebraic multilevel iteration methods in a
broad sense.  This includes their implementation on massively parallel

TOPICS covered include Algebraic Multilevel Iteration methods for
* second and fourth order elliptic scalar equations and systems of equations
* mixed variable variational problems
* nonselfadjoint problems and indefinite matrix problems
* inner-outer iteration methods
* parallel implementations, efficiency measures, scalability
* robust implementations, i.e. convergence uniform with respect to meshsize
  parameter and  singular perturbation parameters 
* applications for Navier's equations and Stokes problem
* applications outside partial differential equation problems
* applications for nonlinear problems, such as electromagnetic field, 
  plastic flow, Navier-Stokes, and Miscible displacement problems.

Papers intended for presentation at the conference should be submitted to Owe
Axelsson.  All papers should be up to 12 pages delivered in a plain LaTeX
format preferably as


and submitted either by electronic mail or on a floppy disk.  The submission
should be accompanied by a printout sent by ordinary mail.  The papers
accepted for presentation at the conference are planned to appear in a
proceedings volume ready for the conference.  Authors who are unable to
produce a paper in LaTeX or TeX format are requested to contact the
organizers.  All papers will be refereed.

Deadline for submission of contribution papers: December 15, 1995.
Notification of acceptance:                     March    15, 1996.

The registration fee will be DFL 600,- (currently $350) and includes a copy of
the conference proceedings, two lunches and coffee and tea during breaks.  The
conference language will be English.


Date: Mon, 4 Sep 95 11:22:22 +0300
From: (Plamen Yalamov)
Subject: Workshop in Bulgaria

                   RUSSE, BULGARIA, JUNE 24-27, 1996
Organizers:     University of Russe, Association of Bulgarian 
                Mathematicians - Russe
Co-organizers:  Institute of Mathematics and Center for Informatics 
                and Information Technologies of the Bulgarian Academy 
                of Sciences, Technical University of Gabrovo, Technical
                University of Sofia
Traditionally every 4 years a Conference on Numerical Analysis and
Applications is organized in Bulgaria.  The present workshop is meant to
support this tradition and to serve as an intermediate meeting between these
conferences.  We would like to give an opportunity for mathematicians and
applied scientists to discuss topics of common interest.
The workshop will have three tracks:
                1. Numerical linear algebra.
                2. Numerical methods for differential equations.
                3. Numerical modelling.
Preliminary list of Invited Speakers:
R. Bisseling (Netherlands), L. Brugnano (Italy), 
S. K. Godunov (Russia), A. Griewank (Germany), A. Hadjidimos (USA), 
S. Hammarling (UK), W. Hofmann (Germany), A. Karageorghis (Cyprus), 
Yu. A. Kuznetsov (Russia), R. Maerz (Germany), W. T. Pickering (UK), 
R. Plemmons (USA), I. V. Puzynin (Russia), G. I. Shishkin (Russia), 
T. Szulc (Poland), E. E. Tyrtyshnikov (Russia), W. Varnhorn (Germany), 
V. V. Voevodin (Russia), Z. Zlatev (Denmark).
Organizing committee:
L. Vulkov (Chair), P. Yalamov (co-Chair), A. Andreev, S. Chernev,
P. Ivanova, I. Lirkov, M. Paprzycki, V. Pavlov, S. Romanova, 
N. Strateva,T. Todorov, Z. Zlatev, K. Zlateva.
We would like to invite all interested individuals to ORGANIZE a MINISYMPOSIUM
related to one or more of the conference tracks.  Please send a minisymposium
abstract (approximately one page) and a list of 4-8 speakers to one of the
addresses listed below.  The deadline for proposals is December 1, 1995.
A general call for papers and more details about the meeting will be provided
in the future announcements.
For more information, please, contact:
Plamen Yalamov                  Marcin Paprzycki
Dept. of Mathematics            Dept. of Mathematics and CS
University of Russe             UTPB
7017 Russe                      Odessa, TX 79762
BULGARIA                        USA 


End of MGNet Digest