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-
ond Kind with Applications in Fluid Mechanics, PhD thesis,
Mathematisch Centrum, Amsterdam, 1983.
[32] V. V. Shaidurov, Multigrid Methods for Finite Elements,
vol. 318 of Mathematics and Its Applications, Kluwer Aca-
demic Publishers, Dordrecht, Boston, London, 1995.
[33] G. K. Verboom and A. Segal, Weakly-reflective boundary
conditions for shallow water equations, in Research in Nu-
merical Fluid Mechanics, P. Wesseling, ed., vol. 17 of Notes
on Numerical Fluid Mechanics, Braunschweig, 1987, Vieweg,
pp. 115-129.
[34] R. Verf"urth, A Review of A Posteriori Error Estimation
and Adaptive Mesh-Refinement Techniques, Wiley Teubner,
New York, Stuttgart, 1996. ISBN 0-471-96795-5.
[35] P. Wesseling, Research in Numerical Fluid Mechanics, vol. 17
of Notes on Numerical Fluid Mechanics, Vieweg, Braun-
schweig, 1987.
[36] G. Wittum, Distributive Iterationen f"ur Indefinite Systeme,
PhD thesis, Christian-Albrechts-Universt"at, Kiel, Ger-
many, 1986.
[37] ______, On the robustness of ILU-smoothing, in Robust Multi-
Grid Methods, W. Hackbusch, ed., vol. 23 of Notes on
Numerical Fluid Mechanics, Braunschweig, 1989, Vieweg,
pp. 217-239.
[38] B. Wohlmuth, Adaptive Multilevel-Finite-Elemente Meth-
ode zur L"osung elliptischer Randwertprobleme, PhD thesis,
Technischen Universit"at M"unchen, Mathematisches Institut,
1995.
[39] H. Yserentant, Ober die Aufspaltung von Finite-Element-
R"aumen in Teilr"aume Verschiedener Verfeinerungsstufen,
PhD thesis, Rheinisch-Westf"alischen Technischen
Hochschule Aachen, Aachen, Germany, 1984.
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End of MGNet Digest
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