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 Current editor:  Craig Douglas       
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Volume 7, Number 10 (approximately October 31, 1997)

Today's topics:
     Multigrid Positions
     Kaskade 3.x Tutorial
     Paper from Jun Zhang
     Dissertation: Robust Iterative Methods on Unstructured Meshes (Brezina)
     Bibliography Update (P. Deuflhard)
     Some of the new entries in the bibliography


Date: Fri, 24 Oct 1997 13:43:49 -0600 (MDT)
From: Jan Mandel 

Would you consider registering your own domain name?  I am getting tired of
trying to remember the URL... and my bookmarks are so large they are no
help... :-)

    Editor's Note: After receiving one too many of these complaints lately,
    -------------  I registered as a domain.  You can now just
                   use to go to a MGNet site.  This defaults
                   currently to the University of Kentucky.  The mirror
                   sites are still in operation and can still be accessed
                   either directly or through URL's built into the pages.

                   If you have a link to MGNet with (or
          as the machine part of the URL, please
                   change the address.


Date: Mon, 06 Oct 1997 16:05:47 -0700
From: "Robert D. Falgout" 
Subject: Multigrid Positions

                 Multilevel Methods Experts
           Center for Applied Scientific Computing
           Lawrence Livermore National Laboratory

The  Center for Applied Scientific Computing (CASC)  at  LLNL
has  openings  at  all  levels for outstanding  computational
scientists  with  expertise  in multilevel  methods  for  the
solution  of partial differential equations.  The  successful
candidate  will work with other computational  scientists  in
CASC to develop parallel multilevel algorithms and codes  for
solving the large linear and nonlinear systems that arise  in
a  variety  of  simulation codes of interest to the  defense,
energy, environmental, and  biomedical sciences.

Applicants should have a Ph.D. (or equivalent experience)  in
computational  mathematics.  A strong  background  in  large-
scale scientific computing is desirable.  Salary and benefits
are  competitive, and there is a generous budget  for  travel
and equipment.  Applicants should send a resume and statement
of   research  interests  to:  Ms.  Molly  Dougan,   Lawrence
Livermore   National  Laboratory,  P.O.   Box   808,   L-155,
Livermore,  CA 94551 (email:  For  further
information,    contact   Steven   Ashby,    CASC    Director

The  Center  for  Applied  Scientific  Computing  (CASC)  was
established in March 1996 to conduct collaborative scientific
investigations  which require the power of  high  performance
computers and the efficiency of modern computational methods.
LLNL is home to the ASCI Blue Pacific massively parallel  IBM
SP-2,  as  well as a cluster of DEC Alpha 8400s  and  an  SGI
Infinite  Reality visualization platform.  Please  visit  our
Web site at

LLNL  is an M/F/D/V employer located in the Livermore  Valley
of Northern California.  Minorities and women are  especially
encouraged to applied.  U.S. citizenship is preferred.


Date: Wed, 08 Oct 1997 16:52:19 +0200
Subject: Kaskade 3.x Tutorial

We prepared an internet tutorial ( ) on our

        Adaptive Multilevel Code 
                KASKADE 3.x

It includes informations on installing and using the software package.

Sincerely yours,
Bodo Erdmann

PS : Is it a good idea to make a link on this tutorial in your webside

    Editor's Note: Now included in the tutorials web page.

Bodo Erdmann
Konrad-Zuse-Zentrum fuer Informationstechnik (ZIB)
e-mail:        | Abt. Scientific Software     |
Telefon: (030) 84185 - 315    | Takustr. 7
Fax:     (030) 84185 - 125    | D-14195 Berlin - Dahlem


Date: Wed, 22 Oct 1997 11:51:02 -0500 (CDT)
Subject: Paper from Jun Zhang

I just uploaded a paper to; the abstract is

     VML: A Class of Virtual Multi-Level Iterative Methods
         for Solving Partial Differential Equations
        (to appear in Applied Mathematics and Computation)

                         Jun Zhang

     Department of Mathematics, The George Washington University, 
                     Washington, DC 20052

     (    Department of Computer Science and Engineering
          University of Minnesota, Minneapolis, MN 55455  )


We introduce virtual multi-level iterative methods (VML) which attempt 
to remove low frequency errors by conducting some special smoothing 
(residual norm minimization) procedure with respect to the coarse 
grids. However, there is no coarse grid formed explicitly, no
inter-grid transfer operator is needed, and even the smoothing
procedure can be done almost locally. These properties are attractive 
to parallel computers. VML with different relaxation schemes and 
different smoothing techniques constitutes a class of VML iterative 
methods. They may be used to accelerate general (single-level) 
iterative methods or be used with the standard (real) multigrid 
method to alleviate the inherent lack of parallelism. Numerical 
experiments with some relaxation and smoothing techniques are
used to show how the VML iterative methods work.
Key words: Virtual multi-level iterative method, multigrid method,
residual norm minimization, relaxation.ard)

    Editor's Note: in mgnet/papers/Zhang/


Date: Mon, 27 Oct 1997 01:22:19 -0700 (MST)
Subject: Dissertation: Robust Iterative Methods on Unstructured Meshes (Brezina)

               Robust Iterative Methods on Unstructured Meshes
                                Marian Brezina

We propose and analyze three multilevel iterative solvers of both domain
decomposition and multigrid type.  All of these methods are algebraic,
allowing almost or fully black-box implementation.  Their development was
motivated by the need to solve large algebraic systems of equations resulting
from finite element discretizations of self-adjoint, second order uniformly
elliptic problems on unstructured three-dimensional meshes.  Two of the
methods discussed perform a simple, but effective domain decomposition as a
part of the solving process.  This allows for a remarkable adaptivity, where
the decomposition is generated depending on the difficulty of the problem
without requiring an input of a different decomposition.  We focus on
achieving robustness features that allow using the new methods as a
replacement of direct solvers for solving these systems.  The new methods are
superior in terms of computational complexity and storage requirements.  On
serial architectures, the asymptotic computational complexity of these methods
for solving 3D problems is shown to be in the range of $O(n^{7/6})$ and
$O(n^{49/33})$.  The methods all benefit from implementation on modern
parallel architectures which can reduce the computational complexity to
$O(n^{7/6})$ for all three methods.  The theoretical results are accompanied
by computational experiments confirming the theoretically predicted
convergence properties and suggesting the potential of the methods for solving
a wider variety of problems than those covered by the current theory.

    Editor's Note: in mgnet/papers/Brezina/


Date: Tue, 14 Oct 1997 12:07:50 +0200
Subject: Bibliography Update (P. Deuflhard)

Three bibtex references for the mgnet.bib file:

  author =      "F. A. Bornemann and P. Deuflhard",
  title =       "Cascadic multigrid methods",
  booktitle =   "Domain Decomposition Methods in Science and Engineering:
                 Proceedings of the Eighth International Conference on Domain
                 Decomposition, Beijing, P.R. China",
  editors =     "R. Glowinski and J. Periaux and Z.-C. Shi and O. Widlund",
  publisher =   "John Wiley \& Sons",
  address =     "New York",
  year =        "1997",
  pages =       "205--212",
  author =      "P. Deuflhard and M. Weiser",
  title =       "Local Inexact Newton Multilevel FEM for Nonlinear Elliptic
  booktitle =   "Computational Science for the 21st Century",
  editors =     "M-O. Bristeau and G. Etgen and W. Fitzigibbon and J-L. Lions
                 and J. Periaux and M. Wheeler",
  publisher =   "John Wiley \& Sons",
  address =     "New York",
  year =        "1997",
  pages =       "129--138",
  author =      "F. A. Bornemann and P. Deuflhard",
  title =       "The cascadic multigrid method for elliptic problems",
  journal =     "Numer. Math.",
  volume =      "75",
  year =        "1996",
  pages =       "135--152",


Date: Fri, 31 Oct 1997 11:53:16 -0500
From: Craig Douglas 
Subject: Some of the new entries in the bibliography

After a very long hiatus, I am finally finding time to work on the MGNet
bibliography again.  The backlog of updates should be done this week.

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

  author =      "E. Brakkee and A. Segal and C. G. M. Kassels",
  title =       "Parallel domain decomposition algorithm for the
                 incompressible {N}avier--{S}tokes equations",
  journal =     "Simul. Pract. Theory",
  volume =      "3",
  year =        "1995",
  pages =       "185--205",
  author =      "V. Debeda and J. P. Caltagirone and P. Watremez",
  title =       "Local multigrid refinement method for natural convection in
                 fissured porous media",
  journal =     "Numer. Heat Transf. B, Fundam.",
  volume =      "28",
  year =        "1995",
  pages =       "455--467",
  author =      "G. Globisch",
  title =       "On an automatically parallel generation technique for
                 tetrahedral meshes",
  journal =     "Parallel Comput.",
  volume =      "21",
  year =        "1995",
  pages =       "1979--1995",
  author =      "E. {D.~de} Goede and J. Groeneweg and K. H. Tan",
  title =       "Domain decomposition method for the three-dimensional shallow
                 water equations",
  journal =     "Simul. Pract. Theory",
  volume =      "3",
  year =        "1995",
  pages =       "307--325",
  author =      "J. Hoffren and T. Siikonen and S. Laine",
  title =       "Conservative multiblock {N}avier--{S}tokes solver for
                 arbitrarily deforming geometries",
  journal =     "J. Aircraft",
  volume =      "32",
  year =        "1995",
  pages =       "1342--1350",
  author =      "Z. Huang",
  title =       "A multi grid algorithm for {S}tokes problem",
  journal =     "J. Comput. Math.",
  volume =      "13",
  year =        "1995",
  pages =       "291--305",
  author =      "H. G. Joo and T. J. Downar",
  title =       "Incomplete domain decomposition preconditioning for coarse
                 mesh neutron diffusion problems",
  booktitle =   "Proceedings of the International Conference, Mathematics and
                 Computations, Reactor Physics, and Environmental Analyses
  editors =     "",
  series =      "",
  volume =      "2",
  publisher =   "American Nuclear Society
  address =     "La Grange Park, IL",
  year =        "1995",
  pages =       "1584--1594",
  author =      "H. X. Lin and H. {H.~ten} Cate and L. Dekker and A. W.
                 Heeminkand M. R. T. Roest and E. A. H. Vollebregt and
                 {Th.~L.~van} Stijn and J. B. Berlamont",
  title =       "Parallel simulation of {3-D} flow and transport models within
                 the {NOWESP} project",
  journal =     "Simul. Pract. Theory",
  volume =      "3",
  year =        "1995",
  pages =       "257--271",
  author =      "H. X. Lin and H. J. Sips",
  title =       "Domain decomposition for parallel finite element simulations",
  booktitle =   "Proceedings of European Simulation Symposium Delft,
                 Netherlands, 25-28 October 1993",
  editors =     "",
  series =      "",
  volume =      "",
  publisher =   "SCS",
  address =     "Ghent, Belgium",
  year =        "1993",
  pages =       "353--358",
  author =      "W. K. Liu and Y. Chen",
  title =       "Wavelet and multiple scale reproducing kernel methods",
  journal =     "Int. J. Numer. Methods Fluids",
  volume =      "21",
  year =        "1995",
  pages =       "901--931",
  author =      "I. G. Mamedova and V. A. Serebryakov",
  title =       "Parallel programming of boundary valued problems for the
                 {P}oisson and {H}elmholtz equations by a multigrid
  journal =     "Programmirovanie",
  volume =      "21",
  year =        "1995",
  pages =       "",
  author =      "E. Memin and P. Perez",
  title =       "Multiresolution Markov random field and multigrid algorithm
                 for discontinuity preserving estimation of the optical flow",
  journal =     "Proc. SPIE - Int. Soc. Opt. Eng.",
  volume =      "2568",
  year =        "1995",
  pages =       "30--41",
  author =      "P. Monk and S. Zhang",
  title =       "Multigrid computation of vector potentials",
  journal =     "J. Comput. Appl. Math.",
  volume =      "62",
  year =        "1995",
  pages =       "301--320",
  author =      "C. R. {E.~de} Oliveira and C. C. Pain and A. J. H. Goddard",
  title =       "Parallel domain decomposition methods for large scale finite
                 element transport modelling",
  booktitle =   "Proceedings of the International Conference, Mathematics and
                 Computations, Reactor Physics, and Environmental Analyses
  editors =     "",
  series =      "",
  volume =      "12",
  publisher =   "American Nuclear Society
  address =     "La Grange Park, IL",
  year =        "1995",
  pages =       "490--498",
  author =      "C. W. Oosterlee",
  title =       "The convergence of parallel multiblock multigrid methods",
  journal =     "Appl. Numer. Math.",
  volume =      "19",
  year =        "1995",
  pages =       "115--128",
  author =      "V. Sass and H. C. Kuhlmann and H. J. Rath",
  title =       "Investigation of three-dimensional thermocapillary convection
                 in a cubic container by a multi-grid method",
  journal =     "Int. J. Heat Mass Transf.",
  volume =      "39",
  year =        "1996",
  pages =       "603--613",
  author =      "C. Sheng and L. K. Taylor and D. L. Whitfield",
  title =       "Multigrid algorithm for three dimensional incompressible high
                 {R}eynolds number turbulent flows",
  journal =     "AIAA J.",
  volume =      "33",
  year =        "1995",
  pages =       "2073--2079",
  author =      "G. Wang",
  title =       "On the use of orthogonal wavelets on the interval in the
                 moment method {EM} scattering",
  journal =     "Microw. Opt. Technol. Lett.",
  volume =      "11",
  year =        "1996",
  pages =       "10--13",
  author =      "M. F. Wehner and A. A. Mirin and P. G. Eltgroth and
                 W. P. Dannevik and C. R. Mechoso and J. D. Farrara and
                 J. A. Spahr",
  title =       "Performance of a distributed memory finite difference
                 atmospheric general circulation model",
  journal =     "Parallel Comput.",
  volume =      "21",
  year =        "1995",
  pages =       "1655--1675",
  author =      "G. Xu and F. Sadeghi",
  title =       "Thermal {EHL} analysis of circular contacts with measured
                 surface roughness",
  booktitle =   "Proceedings of the 1995 Joint ASME/STLE Tribology Conference",
  editors =     "",
  series =      "",
  volume =      "",
  publisher =   "American Society of Mechanical Engineers",
  address =     "New York",
  year =        "1995",
  pages =       "10pp",


End of MGNet Digest