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Volume 7, Number 1 (approximately January 31, 1997)

Today's topics:

     Short Issue
     Deadlines for Copper Mountain Conference on Multigrid Methods
     Paper (Diskin)
     Paper (Kouatchou)
     Paper (Kuether)
     Paper (Oswald)
     Paper (Sterner)
     Paper (Vasseur)
     Paper (W. L. Wan)
     New bib entry (J. Zhang)
     4 Conference/Workshop Announcements (Abridged)


Date: Fri, 31 Jan 1997 11:10:01 -0500 (EST)
From: Craig Douglas 
Subject: Short Issue

Due to my moving, this issue is shorter than normal.  My apologies; next month
I ought to be able to pester more people for material.  Many papers were due
today or shortly thanks to the European and Copper Mountain multigrid
conferences recently held or soon to be held.  As always, I am looking for
more material.


From: Steve McCormick 
Date: Sun, 19 Jan 1997 22:29:38 -0700 (MST)
Subject: Deadlines for Copper Mountain Conference on Multigrid Methods

For the 8th Copper Mountain Conference on Multigrid Methods (April 6-11),
we have extended the deadline for submission of abstracts to February 6th.
This is also the deadline for early registration and guaranteed availability
of lodging. Please access
for information on how to submit an abstract, register, or reserve a room.
There you will also find a bulletin board for sharing rooms, and later in
February you will find the schedule.

Steve McCormick: Appl. Math, C.B. 526, U. of CO, Boulder, CO 80309-0526
        -4066 fax


Date: Wed, 29 Jan 1997 11:59:57 +0200
From: Diskin Boris 
Subject: Paper (Diskin)

Multigrid Algorithm with Conditional Coarsening
for the Non-aligned Sonic Flow

Boris Diskin

Department of Applied Mathematics
and Computer Science
The Weizmann Institute of Science
Rehovot, Israel


A multigrid approach using conditional coarsening in constructing solvers for
non-elliptic equations on a rectangular grid is presented.  Such an approach
permits to achieve a full multigrid efficiency even in the case where the
equation characteristics do not align with the grid.  The 2D sonic-flow
equation linearized over a constant velocity field have been chosen as model
problem.  Efficient FMG solver for the problem is demonstrated.

    Editor's Note: in Conferences/CopperMtn97/


Date: Wed, 29 Jan 1997 14:15:57 +0100
From: "Marc Kuether" 
Subject: Paper (Kuether)

Exponentially fitted hierarchical bases multigrid for the
convection-diffusion equation


In this paper we construct hierarchical bases for an exponentially fitted
finite element discretisation of the one-dimensional stationary
convection-diffusion equation.  Then we prove the approximation and smoothing
property of the corresponding Hierarchical Bases twogrid method.

Key words:  Hierarchical Bases Multigrid method, exponentially fitted schemes,
convection-diffusion equation.

    Editor's Note: in Conferences/CopperMtn97/


Date: Wed, 29 Jan 1997 10:46:57 -0500
From: Jules Kouatchou 
Subject: Paper (Kouatchou)

Asymptotic Stability of a 9-point Multigrid Algorithm for the
Convection-Diffusion Equations

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


We consider the solution of the convection-diffusion equation in two dimension
by a 9-point discretization formula combined with multigrid algorithm .  We
analytically prove the epsilon-asymptotic stability of the coarse-grid
operators.  Two strategies are examined.  A method to compute the asymptotic
convergence is described and applied to the multigrid algorithm.

    Editor's Note: in Conferences/CopperMtn97/


From: Hubertus.Oswald 
Subject: Paper (Oswald)

Parallel multilevel algorithms for solving the incompressible Navier-Stokes
equations with nonconforming finite elements in three dimensions

H. Oswald
Institut fur Angewandte Mathematik
Universitat Heidelberg
Im Neuenheimer Feld 294
69120 Heidelberg, Germany


This paper presents results of a numerical study for unsteady three-
dimensional, incompressible flow.  A finite element multigrid method is used
in combination with a operator splitting techniqueand upwind discretization
for the convective term.  A nonconforming element pair, living on hexahedrons,
which is of order O(h^2/h) for velocity and pressure, is used for the spatial
discretization.  The second order \theta fractional step scheme is employed
for the time discretization.

For this approach we present the parallel implementation of a multigrid code
for MIMD computers with message passing and distributed memory .
Multiplicative multigrid methods as stand-alone iterations are considered.  We
present a very efflcient implementation of Gauss-Seidel resp. SOR smoothers,
which have the same amount of communication as a Jacobi smoother.

    Editor's Note: in Conferences/CopperMtn97/


Date: Wed, 29 Jan 1997 14:04:04 +0100 (MET)
From: Erik Sterner 
Subject: Paper (Sterner)

A multigrid smoother for high Reynolds number flows


The linearized Navier-Stokes equations are solved in 2D using a multigrid
method where a semi-implicit Runge-Kutta scheme is the smoother.  With this
smoother the stiffness of the equations due to the disparate scales in the
boundary layer is removed and Reynolds number independent convergence is

    Editor's Note: in Conferences/CopperMtn97/


Date: Wed, 29 Jan 1997 10:43:35 +0000
From: "VASSEUR" 
Subject: Paper (Vasseur)

A FMG-FAS procedure for the fully coupled resolution 
of the Navier-Stokes equations on cell-centered colocated grids

X. Vasseur
Ecole Centrale de Nantes 
CFD Group, LMF UA1217 CNRS
1, rue de la No\"e, B.P. 92101 
F-44321 Nantes cedex 3, FRANCE


These last twenty years, the search of robust and efficient strategies for the
numerical resolution of the steady or unsteady incompressible Navier-Stokes
equations has been a crucial task giving rise to numerous methods.  The major
obstacle of these equations lies in the absence of pressure terms in the
incompressibility constraint.

Several ways have been suggested to overcome this difficulty.  The first trend
is represented by pressure correction methods like SIMPLE or PISO procedures.
The main drawback of such techniques lies in the slowing down of convergence
when the number of grid points or the clustering ratios over curvilinear grids
increase.  A possible cure consists in using non-linear multigrid with
sequential pressure correction methods as basis solvers (or smoothers).  The
second trend is to solve the incompressible Navier-Stokes equations in a
locally or fully coupled manner, where momentum and continuity equations are
solved simultaneously.  Coupled strategies for the resolution of the
Navier-Stokes equations in primitive variables allow to develop robust solvers
and subsequently to understand the limitations of segregated methods.

A fully coupled method for the resolution of the incompressible Navier-Stokes
equations is presented.  This method previously used by Deng et al.  (1991)
employs a cell-centered colocated grid, standard linearization of convection
terms, central difference discretization for both convective and diffusive
terms and a pressure Poisson equation approach, leading to deduce from the
incompressibility constraint an equation for the pressure variable.  The
originality of this present work is to introduce auxiliary variables --the
so-called pseudo-velocities-- to make easier the flux reconstruction step.
The resulting structure of the nodal unknowns matrix consists in seven or
nineteen bands of sparse blocks.  Direct solvers have been used to solve
coupled systems but their use for three-dimensional applications is penalized
by strong storage limitations.  In order to improve the global efficiency of
the algorithm by seeking grid independent convergence rates, a non-linear
multigrid approach is chosen by implementing a FMG-FAS (Full Multigrid-Full
Approximation Scheme) procedure for the resolution of the coupled system.
Numerical treatments and implementation aspects of this non-linear procedure
are detailed.

Steady laminar lid-driven cavity flows calculations have been performed on
three-dimensional geometries to discuss the performances of this approach.
The retained test-problems were the three-dimensional versions of the ones
investigated by Demirdzic et al.  (1992) and Oosterlee et al.  (1993) :
regular, skewed and L-shaped lid-driven cavities.  The non-linear multigrid
approach (MGC) is compared with the single grid coupled method (SGC) and
decoupled methods based on the sequential PISO algorithm (DC, DC-MG) with
different pressure linear solvers respectively Krylov subspace solver and a
linear multigrid solver.  Computations were performed on cartesian, orthogonal
and stretched grids for the regular cubic cavity, cartesian and non-orthogonal
grids for the skewed lid-driven cavity (skewness angle :  30 degrees) and
finally curvilinear grids for the L-shaped cavity.  The chosen Reynolds
numbers (Re) are equal to 100 or 400.  From the whole numerical results, the
main conclusion is that the non-linear multigrid approach seems quite
powerful, at least more efficient than decoupled or single grid coupled

    Editor's Note: in Conferences/CopperMtn97/


Date: Wed, 29 Jan 1997 17:21:19 -0800 (PST)
From: Wing-Lok Wan 
Subject: Paper (W. L. Wan)

An Energy-Minimizing Interpolation for Multigrid Methods

We shall study multigrid methods from energy minimizations and approximations.
Through the analysis of an multigrid method in 1D, we introduce the concepts
of stability and the approximation property in the classical theory.  Based on
them, we derive an energy-minimizing interpolation and present a two level
analysis for it.  Issues on coarsening are also addressed.  Finally, we
demonstrate the effectiveness of the multigrid method by applying it to
unstructured grids computations and discontinuous coefficient problems.

    Editor's Note: in Conferences/CopperMtn97/


Date: Fri, 17 Jan 1997 21:09:51 -0500
From: Jun Zhang 
Subject: New bib entry (J. Zhang)

  author =      "J. Zhang",
  title  =      "A cost-effective multigrid projection operator",
  year   =      "1996",
  journal=      "J. Comput. Appl. Math.",
  month  =      "December",
  volume =      "76",
  number =      "1",
  pages  =      "325-333",


Date: Fri, 31 Jan 1997 10:23:01 -0500 (EST)
From: Craig Douglas 
Subject: 4 Conference/Workshop Announcements (Abridged)

I condensed these radically.  The full texts are on the indicated web pages
and MGNet's conference page.

    From: Maya Neytcheva 
    Date: Thu, 23 Jan 1997 08:41:45 +0100 (MET)
    Subject: PRISM'97

Preconditioned Iterative Solution Methods 
for Large Scale Problems in Scientific Computations 
May 27-29, 1997, University of Nijmegen, The Netherlands

The purpose of the conference is to provide a forum for the presentation and
the discussion of recent progress in the analysis and implementation of of
preconditioned iterative solution methods.  This includes their implementation
on parallel computer architectures.  A stress will be put on applications in
various fields where a strong demand of efficient solution of large scale
problems exists.

attn. O. Axelsson or M. Neytcheva
Department of Mathematics
Toernooiveld 1, NL-6525 ED Nijmegen, The Netherlands
e-mail:     fax: +31 (0)24 3652140

                                  * * * * *

    Date: Thu, 23 Jan 1997 08:42:53 +0100 (MET)
    From: Maya Neytcheva 
    Subject: Summer school

Multilevel preconditioning methods 
with parallel implementation aspects and
applications in Scientific Computing
May 19--26, 1997, University of Nijmegen, The Netherlands

The summer school will concentrate on methods, concepts, techniques for
solving large scale Scientific Computation problems.  The methods in focus are
iterative methods with multilevel preconditioning, which offer rates of
convergence, (almost) independent of the size of the problems (a crucial issue
for very large scale real-life applications) and optimal computational
complexity.  Two important issues are specially emphasized:  - efficient
parallel implementations of methods of the above type, and - applicability of
the methods to practical problems in which large scale linear and nonlinear
systems have to be solved, especially for problems originating from material
sciences, biomedical computations, and computational mechanics.

Summer School'97
Attn. Maya Neytcheva
Department of Mathematics
Toernooiveld 1, NL-6525 ED Nijmegen, The Netherlands
e-mail:     fax: +31 (0)24 3652140

                                  * * * * *

    Date: Sun, 26 Jan 1997 21:46:12 -0800 (PST)
    From: "Scott B. Baden" 
    Subject: Structured Adaptive mesh refinement workshop

Workshop on Structured Adaptive Mesh Refinement Grid Methods    
                            March 12-13, 1997
           Institute for Mathematics and Its Applications 
                         University of Minnesota 

Workshop Goals:
    This workshop will bring together experts in applications, numerical
    methods, and software development from academia, the national labs, and
    industry. The goal of the workshop is to identify common ground in
    the application and implementation of SAMR, as well as issues requiring 
    specialization. The specific objectives of the workshop are: 

         (i) to improve the general understanding of the application of
             SAMR to practical problems, 
        (ii) to identify issues critical to efficient and effective 
             implementation on high performance computers, 
       (iii) to stimulate the development of a  community code
             repository for  software including benchmarks to assist 
             in the evaluation of software and compiler technologies.

Logistics:  Further information on registration, accommodations, and travel 
            is available at the following Web site: 

                                  * * * * *

    Date: Sun, 19 Jan 1997 20:56:38 GMT
    From: Chaoqun Liu 

                         August 4-8, 1997
           Louisiana Tech University, Ruston, Louisiana, USA

by the US Air Force Office of Scientific Research (AFOSR), will be hosted 
by Louisiana Tech University, Ruston, Louisiana, USA on August 4-8, 1997. 
As computers become more powerful, direct numerical simulation (DNS) and 
large eddy simulation (LES) become more viable for
the prediction and control of transitional and turbulent flows on complex
configurations.  The conference encourages participants to make presentations
on any topics related to DNS and LES.


Prof. Chaoqun Liu, FAICDL Chairman 
Department of Mathematics and Statistics
Louisiana Tech University
P.O. Box 3189
Ruston, LA 71272-0001, USA
Tel : (318) 257-2257
Fax : (318) 257-2437
email :\~cliu


End of MGNet Digest