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Volume 9, Number 2 (approximately February 28, 1999)

Today's topics:

     Important Date
     Microsoft Word Documents
     EMG'99 home page
     Copper Mountain Preliminary Program Online
     PLTMG8.1 on MGNet
     Mathematical/Computational Techniques for Multilevel Adaptive Methods
     Paper on Global Hall Conductor in the Earth's Ionosphere
     Viscous Incompressible/Low-Mach-Number Flows on High Aspect Ratio Grids
     Paper on Stress Concentration Problems
     4 Copper Mountain Papers
     Two prints from Jun Zhang
     Teigland Bibliography Update
     International Conference on Preconditioning Techniques 


Date: Sun, 28 Feb 1999 11:23:22 +0500
From: Craig C. Douglas 
Subject: Important Date

March 11    Hotel reservations for the Copper Mountain Conference on Multigrid
            Methods.  See for a
            link to the conference.


Date: Sun, 28 Feb 1999 15:42:55 +0500
From: Craig C. Douglas 
Subject: Microsoft Word Documents

I am receiving more and more preprints or papers for virtual proceeding papers
produced using Microsoft Word.  Some I can look at on my laptop and some I
cannot.  There are several common themes that will make submission much

If your document uses special fonts, it will probably not be renderable by the
vast majority of MGNet readers.  Also, one of the options in Word2000 is to
save files in HTML format in a manner that is supposed to be lossless.  The
font problem still exists in this case.

If you use a different separator than the default , (Windows), you might save
the file once with the default separator.

A quick fix is to submit either an Adobe PDF file as well or to use "print to
file" using the Apple Laserwriter printer driver (the ancient printer, not a
PostScript level 3 driver).  The PDF file will be closer to what your document
looks like under Word.


Date: Tue, 09 Feb 1999 09:36:17 +0100
From: Kris Riemslagh 
Subject: EMG'99 home page

We forgot to include a reference to our home-page in the call for papers of
the EMG 99.  Please include the following link at your EMG99 page:

Dr. ir. Kris Riemslagh
Universiteit Gent
Vakgroep Werktuigkunde en Warmtetechniek
Dept. Mechanical and Thermal Engineering
Sint Pietersnieuwstraat 41
B-9000 GENT, Belgie
Tel: +32/9/264.33.13; Fax: +32/9/264.35.86


Date: Sun, 28 Feb 1999 11:25:21 +0500
From: Craig C. Douglas 
Subject: Copper Mountain Preliminary Program Online

The Copper Mountain preliminary program (still tentative) is at


Date: Mon, 08 Feb 1999 10:26:20 -0800
From: "Randolph E. Bank" 
Subject: PLTMG8.1 on MGNet

I would like to update pltmg8.0 with pltmg8.1.  Functionally, this version is
identical to pltmg8.0.  A few bugs have been fixed, and the driver program
routines have been reworked a bit.  In particular, xgraph.c should be more
compatible with default linux X-windows configurations.

Randolph E. Bank                         Tel: (619) 534-4204
Department of Mathematics                Fax: (619) 534-5273
University of California, San Diego      Email:
La Jolla, CA 92093-0112        

    Editor's Note: See


Date: Mon, 01 Mar 1999 12:20:48 -0500
From: "E. Bruce Pitman" 
Subject: MGCG

I am looking for papers and any code that might be available, using multigrid
as a preconditioner to a CG solver.  Any pointers will be greatly appreciated.

E. Bruce Pitman
Director of Graduate Studies
Department of Mathematics
106 Diefendorf Hall                     
State University of New York           
Buffalo, NY  14214-3093
(716)829-2144 voice      (716)829-2299 fax       Center for Computational Research


Date:          Mon, 1 Mar 1999 12:41:14 
Subject: Mathematical/Computational Techniques for Multilevel Adaptive Methods

Je suis etudiant tchadien.  Le tchad est un pays africain.  Je prepare une
these sur "mathematical and computational techniques for multilevel adaptive
methods".  Je voudrais avoir une documentation complete en anglais sur le
sujet.  Je veux aussi les travaux recents sur les multigrilles et les
multiniveaux adaptative.  mon adresse:  Djibet M'bainguesse enseignant et
chercheur faculte des sciences exactes et appliquees
Universite du Tchad
bp1027 N'djamena Tchad.


Date: Fri, 12 Feb 1999 10:43:34 +0700
From: "Valeri Denissenko" 
Subject: Paper on Global Hall Conductor in the Earth's Ionosphere

    Multigrid Method for a Global Hall Conductor in the Earth's Ionosphere

                             Valeri V. Denissenko
                     Institute of Computational Modelling
                         Krasnoyarsk, 660036, Russia


Since conductivity is an asymmetric tensor in the ionosphere the elliptical
operators of the boundary value problems are not selfadjoint.  To overcome
difficulties that arise in numerical solution of problems with not selfadjoint
operators it is proposed to replace the traditional statements with new ones
in which the operators are symmetrical and positive definite.  A narrow
boundary strip in that the coefficients are huge in comparing with those in
the interior of the domain is separated with a special boundary condition.
The finite element equations are obtained as a conditions of a minimum of the
energy functional with a special set of parameters to approximate the main
boundary conditions.  Positive definiteness of the matrix is proved.  A
multigrid method that is used to solve these equations and a numerical example
are presented.

Key words.  gyrotropic transfer, Hall conductivity, symmetrization, elliptic
equation, variational principle, finite elements, multigrid method

AMS subject classifications.  Primary 65N30, 35J50; Secondary 78A25

    Editor's Note: See or


Date: Thu, 25 Feb 1999 14:56:23 +0100
From: Jan Vierendeels 
Subject: Viscous Incompressible/Low-Mach-Number Flows on High Aspect Ratio Grids

      A Multigrid Semi-Implicit Line Method for Viscous Incompressible 
             and Low-Mach-Number Flows on High Aspect Ratio Grids

                Jan Vierendeels, Kris Riemslagh, and Erik Dick
               Department of Mechanical and Thermal Engineering
                          Universiteit Gent, Belgium


Discretization of viscous incompressible and viscous low-Mach-number flows
often leads to a system of equations, which is very difficult to solve.  There
are two reasons.  First, the use of high aspect ratio grids results in a very
numerically anisotropic behaviour of the diffusive and acoustic terms and
second, in low-Mach-number flow, the ratio of the convective and acoustic
eigenvalues of the inviscid system becomes very high.

We implemented an AUSM based discretization method, using an explicit
third-order discretization for the convective part, a line-implicit central
discretization for the acoustic part and for the diffusive part.  The lines
are chosen in the direction of the gridpoints with shortest connection.  The
preconditioned semi-implicit line method is used in multistage form because of
the explicit third-order discretization of the convective part.  Multigrid is
used as acceleration technique.

It is shown that the convergence is very good, independent of grid aspect
ratio and Mach number.

    Editor's Note: See or


Date: Mon, 1 Mar 1999 01:37:23 -0800 (PST)
From: Alexander Trofimov 
Subject: Paper on Stress Concentration Problems

             Multigrid Methods for Stress Concentration Problems

                            Alexander V. Trofimov
                   Dnepropetrovsk State University, Ukraine


Some aspects of the Multigrid Methods implementation to stress concentration
problems are discussed.  Convenient variational formulations for such problems
are proposed.  Computational aspects of Richardson's extrapolation methods
implementation and nonlinear iterations are investigated.  The efficiency of
multigrid and some other widespread algorithms is compared.

Warning:  The correct drawing of mathematical symbols depends on the Windows
tuning parameter "list separator."  You have to choose

    Control Panel -> Regional Settings -> Numbers -> List separator
    It must be set to ";" (semicolon)

    Editor's Note: See or


Date: Sun, 28 Feb 1999 16:18:20 +0500
From: Craig C. Douglas 
Subject: 4 Copper Mountain Papers

The Application of the Multigrid Method in a Nonhydrostatic Atmospheric Model

                                 Shu-Hua Chen
                 Department of Earth and Atmospheric Sciences
                              Purdue University
                        West Lafayette, IN 47907, USA


A nonhydrostatic atmospheric model is developed.  The use of the Semi-implicit
scheme in this model has relaxed the constraint of exceedingly small time
step, but it generates a huge sparse matrix (400,000 x 400,000) of the
Elliptic Partial Differential Equations (EPDEs).  This study attempts to apply
the Multigrid method to solve these EPDEs and to address the performance and
efflciency of the Multigrid method.  Two experiments are examined.  The model
results are in good agreement with those in historical papers and the
analytical solution.  Furthermore, the Multigrid solver, mud3cr, applied in
this model is very efflcient.  These indicate the success of the Muitigrid
method applied to nonhydrostatic atmospheric models.

    Editor's Note: See or

                                  * * * * *

                 Cache Based Multigrid on Unstructured Grids

                                 Jonathan Hu
                            Universityof Kentucky
                           Departmentof Mathematics
                          715 Patterson Offlce Tower
                        Lexington, KY 40506-0027, USA


High speed cache memory is commonly used to address the disparity between the
speed of a computer's central processing unitand the computer's main memory
speed.  It is advantageous to maximize the amount of time that data spends in
cache.  Tiling is a software technique which is often used to do just this.
Tiling is not able, however, to handle dynamically changing data structures,
such as are encountered in adaptively chosen, unstructured grids.  We develop
a variant of the Gauss-Seidel method which keeps data in cache memory for much
longer than non-cache implementations.  As a result, our method is
significantly faster than non-cache implementations.  Examples from the
structured grid case demonstrate the benefits of such a variant and provide
motiv ation for the more difflcult unstructured grid case.  For this case, an
O(n) algorithm is introduced that divides nodes into blocks whichf it into
cache.  This leads to a new ordering which allows significantly more
Gauss-Seidel updates and residual calculation to be done in cache than in
standard implementations.  Numerical experiments demonstrate the speedups
possible with the cache aware Gauss-Seidel method and with a multigrid V cycle
using the cache aware method.

    Editor's Note: See or

                                  * * * * *

   A Multigrid Strategy for Accelerating Steady-State Computations of Waves
                 Propagating with Curvature Dependent Speeds

                               Jonathan Rochez
                        Department of Applied Science
                       University of California, Davis
                                Davis, CA, USA


A multigrid strategy is developed for accelerating the steady state
computations of waves propagating with curvature dependent speeds.  This will
allow the rapid computation of a ``burn table.'' In a high explosive material,
the creation of a burn table will allow the elimination of solving chemical
reaction ODEs and feed in source terms to the reactive flow equations for
solution of the system of ignition of the high explosive material.  Standard
iterative methods show a quick reduction of the residual followed by a slow
final convergence to the solution at high iterations.  Such systems are
excellent choices for the use of multigrid methods to speed up convergence,
even on a nonlinear system such as this.  Numerical steady-state solutions to
the eikonal equationon on a rectangular grid are conducted.  Results are
presented for a square grid in 2D and a cubic grid in 3D using a Runge-Kutta
time iteration for the smoothing operator until steady-state is reached.

Editor's Note: See or ------------- * * * * * Fourier Analysis of GMRES(m) Preconditioned by Multigrid R. Wienands GMD Institute for Algorithms and Scientific Computing D-53754 St. Augustin, Germany Abstract This paper deals with convergence estimations of a preconditioned GMRES(m) method, where multigrid is used as the preconditioner. Fourier analysis is a well-known useful tool in the multigrid community for the prediction of two-grid convergence rates. This analysis is generalized to the situation where multigrid is a preconditioner. Editor's Note: See or ------------- ------------------------------------------------------- Date: Sun, 28 Feb 1999 11:55:54 -0500 (EST) From: Jun Zhang Subject: Two prints from Jun Zhang A Grid Based Multilevel Incomplete LU Factorization Preconditioning Technique for General Sparse Matrices Jun Zhang Department of Computer Science, University of Kentucky 773 Anderson Hall, Lexington, KY 40506--0046, USA ABSTRACT We design a grid based multilevel incomplete LU preconditioner (GILUM) for solving general sparse matrices. This preconditioner combines a high accuracy ILU factorization with an algebraic multilevel recursive reduction. The GILUM preconditioner is a compliment to the domain based multilevel block ILUT preconditioner. A major difference between these two preconditioners is the way that the coarse level nodes are chosen. In this sense the approach of GILUM is analogous to that of algebraic multigrid method. However, the GILUM construction is completely different from the algebraic multigrid construction. A partial ILUT factorization is applied to the reordered matrix and the coarse level system is obtained implicitly. The incomplete factorization process is repeated with the coarse level systems recursively. The GILUM approach avoids some controversial issues in algebraic multigrid method such as how to construct the interlevel transfer operators and how to compute the coarse level operator. Numerical experiments are conducted to compare GILUM with other ILU preconditioners. * * * * * RILUM: A General Framework for Robust Multilevel Recursive Incomplete LU Preconditioning Techniques Jun Zhang Department of Computer Science, University of Kentucky 773 Anderson Hall, Lexington, KY 40506--0046, USA ABSTRACT We introduce a general framework for constructing multilevel recursive incomplete LU preconditioning techniques (RILUM) for solving general sparse matrices. This technique is based on a recursive two by two block incomplete LU factorization on the coefficient matrix. The coarse level system is constructed as an (approximate) Schur complement. A dynamic preconditioner is obtained by solving the Schur complement matrix approximately. The novelty of the proposed techniques is to solve the Schur complement matrix by a preconditioned Krylov subspace method. The very preconditioner for this secondary iteration is constructed by considering the Schur complement matrix as a general sparse matrix and by applying to it the block ILU factorization process that was applied to the original matrix. This recursive procedure continues for a few times and results in a multilevel preconditioner. Different implementation strategies are discussed. We conduct numerical experiments with two particular RILUM implementations to show the performance of the proposed techniques and to demonstrate grid independent convergence rates of RILUM for solving certain problems. Editor's Note: See ------------- ------------------------------------------------------- Date: Mon, 15 Feb 1999 16:05:21 +0100 From: Rune Teigland Subject: Teigland Bibliography Update Please find attached a listing of my contributions related to multigrid/domain decomposition. @phdthesis{ author = "Teigland, R.", title = "On Multilevel Methods for Numerical Reservoir Simulation, Report No. 92, October 1991, ISSN 0084-778x", school = "University of Bergen, Norway", year = "1991", } @inproceedings{ author = "Teigland R. and Fladmark G.E.", title = "Cell-centered Multilevel Methods in Reservoir Simulation", booktitle = "International Series of Numerical Mathematics", volume = "98", year = "1991", pages = "365-376", publisher = "Birkhauser Verlag, Basel." } @article{ author = "Ersland B.G. and Teigland R.", title = "Comparison of Two Cell-Centered Multigrid Schemes for Problems with Discontinuous Coefficients", journal = "Numer. Meth. for PDE", volume = "9", year = "1993", pages = "265-283", } @inproceedings{ author = "Teigland, R.", title = "An Additive {S}chwarz Procedure for Complex Flows", editor = "Paul A. Thibault and Denis M. Bergeron", booktitle = "Proc. Third Annual Conference of the CFD Society of Canada", year = 1995, pages = "145-152" } @inproceedings{ author = "Gjesdal T., Lossius M.E.H., Teigland R.", title = "Multigrid Solution of Incompressible Flow Using Pressure Correction Smoothers", editor = "Paul A. Thibault and Denis M. Bergeron", booktitle = "Proc. Third Annual Conference of the CFD Society of Canada", year = 1995, pages = "145-152" } @article{ author = "Teigland R.", title = "On some variational acceleration techniques and related methods for local refinement", journal = "Int. J. Numer. Meth. Fluids", volume = "28", year = "1998", pages = "945-960", } @inproceedings{ author = "Teigland, R.", title = "A Domain Decomposition Strategy for Simulation of Complex Industrial Fluid Flows", booktitle = "Proc. Ninth Int. Conf. on Domain Decomposition", editors = "P.E. Bj{\o}rstad, M.S. Espedal, and D.E. Keyes", publisher = "Domain Decomposition Press, Bergen, Norway", year = "1998", pages = "817-825", } Rune Teigland | Tel:+47 55 99 68 97 (office)| | Norsk Hydro | Tel:+47 55 95 32 35 (home) | (((( | Research Center | E-mail: |(oooo)| N-5020 Bergen, Norway | | | Editor's Note: These will be integrated into the bibliography. See ------------- ------------------------------------------------------- Date: Feb 1999 From: Yousef Saad Subject: International Conference on Preconditioning Techniques SUBJECT: Intl. Conf. on preconditioning techniques FROM: Yousef Saad - U. of Minnesota * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * TITLE: 1999 INTERNATIONAL CONFERENCE ON PRECONDITIONING TECHNIQUES * * FOR LARGE SPARSE MATRIX PROBLEMS IN INDUSTRIAL APPLICATIONS * * * * DATE: June 10 - 12, 1999 * * * * PLACE: University of Minnesota, Hubert H. Humphrey Institute, * * Minneapolis, Minnesota * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Please consult the web-site for detailed information. CONFERENCE TOPICS: o Incomplete factorization preconditioners o Domain decomposition preconditioners o Approximate inverse preconditioners o Multi-level preconditoners o Preconditioning techniques in optimization problems o Preconditioning techniques in finite element problems o Preconditioning techniques in image processing o Applications in Computational Fluid Dynamics (CFD) o Applications in computational finance o Multiphase subsurface flow applications o Applications in petroleum industry o Applications in semiconductor device simulation IMPORTANT: * Deadline for submitting extended abstracts has been extended to March 5th, 1999. Extended abstracts should be 7 pages maximum. mail to: Sparse-99 MSI 1200 Washington ave. S Minneapolis, MN 55415 Electronic submission encouraged. Send papers (post-script) to Editor's Note: Deadline extended to MONDAY, MARCH 8 (so write fast :-) ------------- ------------------------------ End of MGNet Digest **************************