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:    casper.cs.yale.edu (128.36.12.1)

World Wide Web:  http://na.cs.yale.edu/mgnet/www/mgnet.html or
                 http://www.cerfacs.fr/~douglas/mgnet.html

Today's editor:  Craig Douglas (ccd@ms.uky.edu)

Volume 6, Number 12 (approximately December 31, 1996)

Today's topics:

     The Editor Is Moving
     1995 Copper Mountain Multigrid Proceedings Mailed !!!
     A new paper on biharmonic equation
     Dissertation on multigrid methods
     Updated algebraic multigrid code
     Multigrid in Numerical Linear Algebra with Applications
     Assistant Professorship at Tufts
     13th GAMM-Seminar Kiel
     Multiscale Phenomena, Modelling and Computation Workshop 
     Various Conferences
     New bib entry (Jun Zhang)
     Some of the new entries in the bibliography (> 3,000 entries warning)

-------------------------------------------------------

Date: Wed, 1 Jan 1996 00:00:01 -0500
From: Craig Douglas 
Subject: The Editor Is Moving

There will be another MGNet site added in the next month.  I have left IBM for
University of Kentucky, where I am now a professor in both the mathematics and
mechanical engineering departments, and am the associate directory of the
center for computational sciences.  I will still be at Yale one day a week and
spending my weekends in Connecticut.

Nine of the readers of this list wrote letters in support of my move.  I know
who several of you are, but do not have a clue who the rest are; many thanks
to the all of you.

As has been noted before in this digest, there are faculty positions open in
mathematics and computer science (1 each) that are appropriate to the readers
of MGNet.  Applications are due in writing about 10 January.

-------------------------------------------------------

Date: Thu, 19 Dec 1996 21:45:11 GMT
From: Duane Melson 
Subject: 1995 Copper Mountain Multigrid Proceedings Mailed !!!

The proceedings are back from the printers.  Most of the copies have been
mailed.

    Editor's Note: My copies arrived at my house on December 24th.
    -------------

-------------------------------------------------------

Date: Wed, 4 Dec 96 12:30:24 EST
From: Murli Gupta 
Subject: A new paper on biharmonic equation

I have placed in mgnet/incoming two files marked gupta.ps and gupta.txt
containing .ps file of our new paper with abstract in gupta.txt.  The abstract
is given below.  The paper will appear in SIAM J. Sci. Computing.

           Multigrid Solution of Automatically Generated High Order
                 Discretizations for the Biharmonic Equation 

                                 Irfan Altas
                       School of Information Studies, 
          Charles Sturt University, Wagga Wagga, NSW 2678 Australia 
                             ialtas@csu.edu.au; 
                                       
                                Jonathan Dym  
                          Department of Mathematics,
           University of Southern California, Los Angeles, CA 90089
                              jdym@cams.usc.edu;
                                       
                               Murli M. Gupta 
                          Department of Mathematics,
           The George Washington University, Washington, DC 20052 
                            mmg@math.gwu.edu; and

                                Ram P. Manohar
                          Department of Mathematics,
           University of Saskatchewan, Saskatchewan, S7N OWO Canada
                            manohar@sask.usask.ca

                                   Abstract

In this work, we use a symbolic algebra package to derive a family of finite
difference approximations for the biharmonic equation on a 9 point compact
stencil.  The solution and its first derivatives are carried as unknowns at
the grid points.  Dirichlet boundary conditions are thus incorporated
naturally.  Since the approximations use the 9 point compact stencil, no
special formulas are needed near the boundaries.  Both second order and fourth
order discretizations are derived.

The fourth order approximations produce more accurate results than the 13
point classical stencil or the commonly used system of two second order
equations coupled by the boundary condition.

The method suffers from slow convergence when classical iteration methods such
as Gauss-Seidel or SOR are employed.  In order to alleviate this problem we
propose several multigrid techniques which exhibit grid- independent
convergence and solve the biharmonic equation in a small amount of computer
time.  Test results from three different problems, including Stokes flow in a
driven cavity, are reported.

    Editor's Note: in mgnet/papers/Altas-Dym-Gupta-Manohar/high-order.ps.gz.
    -------------

-------------------------------------------------------

Date: Mon, 09 Dec 96 14:06:59 -0500
From: Sachit Malhotra 
Subject: Dissertation on multigrid methods

                         Topics in Multigrid Methods

                               Sachit Malhotra
                         Computer Science Department
                               Yale University

                                   Abstract

Multigrid methods are often used for the solution of systems of equations
arising from the discretization of elliptic partial differential equations.
Such problems are often the compute intensive kernels for many numerical
problems arising in science and engineering.  The solution of
three--dimensional problems, which lead to very large systems of equations, is
particulary well suited to solution by multigrid methods.

The large size of the problems to be solved has led to the increasing use of
parallel computers, for example clusters or LANs of workstations.  However, in
practice, most workstations are connected by relatively slow connections such
as ethernet.

In this dissertation, we investigate some of the issues involved in the
solution of elliptic problems using multigrid methods.  We shall focus on the
solution of these problems on clusters of workstations.  We shall define a
class of algorithms to accelerate the multigrid smoother on such clusters.
These methods subsume the latency inherent in the communication by using
redundant computation to combine a large number of small messages.

Alternating direction methods, which are often used as smoothers in the serial
case, suffer from a high parallel overhead because of the need to transpose
data in each smoothing iteration.  We suggest modifications of these methods
which are parallelizable and maintain the rate of convergence.  These
modifications are also applicable to alternating direction line SOR iterative
methods.

Lastly, we shall deal with the theoretical issues involved in transferring the
error in multigrid algorithms from one grid to another, possibly unrelated,
grid.  We derive sharp upper and lower bounds on the condition number of this
procedure.

    Editor's Note: in mgnet/papers/Malhotra.
    -------------

-------------------------------------------------------

Date: Sun, 8 Dec 1996 21:44:00 -0700
From: pvanek@tiger.cudenver.edu (Petr Vanek)
Subject: Updated algebraic multigrid code

I am just releasing the new version of the amg code.

Differences compare to the older one are:
1. It is significantly more robust
2. It runs in parallel on SGI-PC.
For the sake of portability, the only parallel construct which has been used
is the C$DOACROSS directive, so the code can be ported to other shared-memory
machines very easily.

The diasadvantage of the new version is sligtly lower performance in the case
of very simple problems.

    Editor's Note: in mgnet/codes/vanek.
    -------------

-------------------------------------------------------

Date: Fri, 06 Dec 1996 14:57:28 +0100
From neytchev@sci.kun.nl Fri Dec  6 09:00 EST 1996
Subject: Multigrid in Numerical Linear Algebra with Applications

Volume 3, Issue 4, 1996

    P. Vanek and J. Krizkova
    Two-Level Method with Small Coarse Grid Appropriate for 
    Unstructured Meshes (255--274)

    P. Amestoy, I.S. Duff and C. Puglisi
    Multifrontal QR Factorization in a Multiprocessor Environment (275--300)

    M. Berry and R. Fierro
    Low-rank Orthogonal Decompositions for Information Retrieval
    Applications   (301--327)

    Y. Saad and K. Wu
    DQGMRES: A Direct Quasi-minimal Residual Algorithm Based on
    Incomplete Orthogonalization  (329--343)

Volume 3, Issue 5, 1996
Speciall issue on Algebraic Multilevel Iteration Methods

    G. Starke (351--367)
    Multilevel Minimal Residual Methods for Nonsymmetric Elliptic Problems

    A. Reusken
    A Multigrid Method Based on Incomplete Gaussian Elimination (369--390)

    P.J. Ferket
    The Finite Difference Based Fast Adaptive Composite Grid Method (391--411)

    V. Migallon, J. Penades and D. Szyld
    Block Two-stage Methods for Singular Systems and Markov Chains (413--426)

    Z. Chen, R. Ewing, R. Lazarov, S. Malyasov and Y.A. Kuznetsov
    Multilevel Preconditioners for Mixed Methods for Second  (427--453)
    Order Elliptic Problems

Maya Neytcheva             
Faculty of Mathematics and Informatics,  University of Nijmegen     
Toernooiveld, 6525 ED Nijmegen, The Netherlands            
tel: +31-24-3652485
e-mail: neytchev@sci.kun.nl

-------------------------------------------------------

Date: Tue, 3 Dec 1996 13:08:31 -0500
From: borgers@math.tufts.edu (Christoph Borgers)
Subject: Assistant Professorship at Tufts

Tufts University
Department of Mathematics
Medford, MA 02155

Applications are invited for an Assistant Professorship to begin September 1,
1997.  Initial one-year contract, renewable to a maximum of three years.
Ph.D., promise of strong research and evidence of strong teaching ability
required.  Research interests preferred:  numerical linear algebra or
numerical elliptic PDE's or mathematical biology.  Candidates with the ability
to be successful at teaching students from underrepresented groups are
encouraged to apply.  Send application and three letters of recommendation to
Christoph Borgers, Hiring Committee Chair.  Review of applications will begin
January 31, 1997 and continue until the position is filled.

Tufts University is an Equal Opportunity/Affirmative Action employer.  Members
of underrepresented groups (including people of color, persons with
disabilities, Vietnam veterans and women) are strongly encouraged to apply.

-------------------------------------------------------

Date: Mon, 23 Dec 1996 11:00:38 +0100 (MET)
From: Jens Burmeister 
Subject: 13th GAMM-Seminar Kiel

The prelimanary programme of the
 
                       13th GAMM-Seminar Kiel
                               on 
            Numerical Treatment of Multi-Scale Problems
 
                     January 24th to 26th, 1997.
                           Kiel, Germany
 
is now available on the web. Please visit our webpage
 
            http://www.numerik.uni-kiel.de/gamm.html
 
With best regards
Jens Burmeister

-------------------------------------------------------

Date: Thu, 2 Jan 1997 11:26:17 +0200
From: Weintraub Carol 
Subject: Multiscale Phenomena, Modelling and Computation Workshop 

          Research Workshop of the Israel Science Foundation      
           MULTISCALE PHENOMENA, MODELLING AND COMPUTATION          
            March 2-7, 1997.  Neptune Hotel, Eilat, Israel          
                                                                    
Workshop Organizers:                     Secretary:                
--------------------                     ----------                  
Achi Brandt, Weizmann Institute          Carol Weintraub               
Gerhard Mack, Hamburg University         Office: 972-8-9343545           
Sorin Solomon, Hebrew University         Fax: 972-8-9344122            
        
         WWW: http://shum.cc.huji.ac.il/~sol/eilat/eilatcon.html          
                                                                        
  The nature of the interactions between different scales of phenomena
in a complex system is the focus of interest in an increasingly wider
range of scientific fields. This interest originated independently
in theoretical physics and in computational mathematics.

  Like the first Eilat workshop (February, 1995) the purpose of this
second one is to bring together different communities of researchers
having the common interest of studying the different ways in which 
inter-scale interactions occur in nature and can be devised and 
exploited in calculations. This time, computational chemistry will 
be added as one of the main themes.                     
                                                                          
  The participants include computational physicists, chemists and
mathematicians. The physicists are mainly from the field theory and
statistical mechanics communities, especially in the theoretical and/or
simulation aspects of renormalization group, criticality and universality,
with interest in the more general theory of dynamical and complex phenomena
and/or in their computational aspects. The chemists bring special interest
in ab initio quantum calculation and in large scale molecular dynamics.
The participating mathematicians will represent several research
communities which have adopted different versions of multiscale scientific
computation: multigrid, multipole, hierarchical bases, wavelets, and
other relatives.

  More information about the workshop, its scientific background, mode of
organization and location, including details on travel, climate, prices,  
accommodations, services, social program, etc. is available at the above  
Web site, together with registration, accommodation and travel forms.     
This information can also be received via email, fax or regular mail by   
request from the conference secretary: Carol Weintraub, Department of     
Applied Mathematics and Computer Science, Weizmann Institute of Science, 
Rehovot 76100, Email: carol@wisdom.weizmann.ac.il, Tel: +972-8-9343545,    
Fax: +972-8-9344122.                                                       
          
  Because time is short, hearing soon from anybody who intends to 
participate would be appreciated. The number of rooms in the hotels at 
the conference rate is, unfortunately, limited, so it is advisable to 
complete the accommodation forms as soon as possible.

-------------------------------------------------------

Date: Sat, 28 Dec 1996 11:53:16 -0500
From: Craig Douglas 
Subject: Various Conferences

I have received long announcements of a number of conferences for MGNet.  I
will put a link in the MGNet conferences' web page to each of the followinge
with the entire text sent to me.

Here is a very short summary:

1.  From: Jiangping Zhu 

    Third Mississippi State Conference on
    DIFFERENTIAL EQUATIONS & COMPUTATIONAL SIMULATIONS

    Preliminary Announcement and Call for Papers

    May 16-17, 1997
    Mississippi State University

    URL:    http://www.msstate.edu/Dept/Math/conf.html
    MGNet:  mgnet/conferences/msu-difeq.0597

2.  From: Guido Kanschat 

    Charles University Prague, Czech Technical University Prague, and
    Ruprecht-Karls-Universitaet Heidelberg

    First Announcement
    NUMERICAL MODELLING IN CONTINUUM MECHANICS

    Theory, Algorithms, Applications

    The Third Summer Conference
    Prague (Czech Republic), September 8 - 11, 1997

    Prof. Dr. Miloslav Feistauer, DrSc.
    Charles University Prague
    Faculty of Mathematics and Physics
    Institute of Numerical Mathematics
    Malostranske nam. 25
    118 00 Praha 1
    Czech Republic

    E-mail:  nmicm97@ms.mff.cuni.cz
    Phone:  +42 2 21914223, +42 2 535229
    Fax: +42 2 535229

    URL:    none listed
    MGNet:  mgnet/conferences/prague-nummodel.0997

3.  From: ENUMATH 
          Guido Kanschat

    2nd Announcement - Call for Papers

    ENUMATH 97
    Second European Conference on Numerical Mathematics and Advanced
    Applications

    September 29 - October 3, 1997
    New University
    Heidelberg, Germany

    URL:    http:gaia.iwr.uni-heidelberg.de/ENUMATH.html
    MGNet:  mgnet/conferences/enumath.0997

-------------------------------------------------------

Date: Mon, 30 Dec 1996 19:30:58 -0500
From: Jun Zhang 
Subject: New bib entry (Jun Zhang)

@ARTICLE{JZHANG_1997a,
      AUTHOR = {J. Zhang},
      TITLE  = {Accelerated multigrid high accuracy solution of the 
                convection-diffusion equation with high Reynolds number},
      YEAR   = 1997,
      JOURNAL= {Numerical Methods for Partial Differential Equations},
      MONTH  = January,
      VOLUME = 13,
      NUMBER = {1},
      PAGES  = {77-92}           }

    Editor's Note: will be in the bibliography shortly
    -------------

-------------------------------------------------------

Date: Sat, 28 Dec 1996 11:53:16 -0500
From: Craig Douglas 
Subject: Some of the new entries in the bibliography (> 3,000 entries warning)

The bibliography passed 3,000 entries and 69,000 fields this month.  Both are
fixed limits inside of the version of the bibtex program that I use.  I had to
get the web-6.1 and web2c-6.1 distributions, build bibtex.c, and modify all
instances of 3000 and 69000L (I changed them to 6000 and 140000L
respectively).  After recompiling bibtex, I could produce a new mgbib.bbl
file again.

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

                             REFERENCES

  [1] L.  M.  Adams, A multigrid algorithm for immersed interface
          problems, in Seventh Copper Mountain Conference on Multi-
          grid Methods, N. D. Melson, T. A. Manteuffel, S. F. Mc-
          Cormick, and C. C. Douglas, eds., vol. CP 3339, Hampton,
          VA, 1996, NASA, pp. 1-14.
  [2] E. Arian and S. Ta'asan, Smoothers for optimization prob-
          lems, in Seventh Copper Mountain Conference on Multigrid
          Methods, N. D. Melson, T. A. Manteuffel, S. F. McCormick,
          and C. C. Douglas, eds., vol. CP 3339, Hampton, VA, 1996,
          NASA, pp. 15-30.
  [3] M.  Berndt  and  K.  Witsch,  Multigrid  with  overlapping
          patches, in Seventh Copper Mountain Conference on Multi-
          grid Methods, N. D. Melson, T. A. Manteuffel, S. F. Mc-
          Cormick, and C. C. Douglas, eds., vol. CP 3339, Hampton,
          VA, 1996, NASA, pp. 31-40.
  [4] P. Bochev,  Z. Cai,  T. A. Manteuffel,  and S. F. Mc-
          Cormick, First-order system least squares for the Navier-
          Stokes equations, in Seventh Copper Mountain Conference
          on Multigrid Methods, N. D. Melson, T. A. Manteuffel, S. F.
          McCormick, and C. C. Douglas, eds., vol. CP 3339, Hamp-
          ton, VA, 1996, NASA, pp. 41-55.
  [5] J. Bordner and F. Saied, MGLab: An interactive multigrid
          environment,  in Seventh Copper Mountain Conference on
          Multigrid Methods, N. D. Melson, T. A. Manteuffel, S. F.
          McCormick, and C. C. Douglas, eds., vol. CP 3339, Hamp-
          ton, VA, 1996, NASA, pp. 57-71.
  [6] A.  Borz`i,  K.  W.  Morton,  E.  S"uli,  and  M.  Vanmaele,
          A full multi-grid method for the solution of the cell vertex
          finite volume Cauchy-Riemann equations, in Seventh Copper
          Mountain Conference on Multigrid Methods, N. D. Melson,
          T. A. Manteuffel, S. F. McCormick, and C. C. Douglas, eds.,
          vol. CP 3339, Hampton, VA, 1996, NASA, pp. 73-86.
  [7] A. Brandt and J. Dym, Effective boundary treatment for the
          biharmonic Dirichlet problem, in Seventh Copper Mountain
          Conference on Multigrid Methods, N. D. Melson, T. A. Man-
          teuffel, S. F. McCormick, and C. C. Douglas, eds., vol. CP
          3339, Hampton, VA, 1996, NASA, pp. 97-107.
  [8] A. Brandt and L. Yu. Zaslavsky, Multilevel algorithm for
          atmospheric assimilation, in Seventh Copper Mountain Con-
          ference on Multigrid Methods, N. D. Melson, T. A. Manteuf-
          fel, S. F. McCormick, and C. C. Douglas, eds., vol. CP 3339,
          Hampton, VA, 1996, NASA, pp. 87-96.
  [9] J.  Broeze,  B.  Geurts,  H.  Kuerten,  and  M.  Streng,
          Multigrid acceleration of time-accurate DNS of compressible
          turbulent flow, in Seventh Copper Mountain Conference on
          Multigrid Methods, N. D. Melson, T. A. Manteuffel, S. F.
          McCormick, and C. C. Douglas, eds., vol. CP 3339, Hamp-
          ton, VA, 1996, NASA, pp. 109-121.
[10]  Z. Cai, T. A. Manteuffel, and S. F. McCormick, First-
          order system least squares for the Stokes equations, with ap-
          plications to linear elasticity, in Seventh Copper Mountain
          Conference on Multigrid Methods, N. D. Melson, T. A. Man-
          teuffel, S. F. McCormick, and C. C. Douglas, eds., vol. CP
          3339, Hampton, VA, 1996, NASA, pp. 133-145.
[11]  ______,  First-order  system  least  squares  for  velocity-vorticity-
          pressure form of the Stokes equations, with applications to
          linear elasticity, in Seventh Copper Mountain Conference on
          Multigrid Methods, N. D. Melson, T. A. Manteuffel, S. F.
          McCormick, and C. C. Douglas, eds., vol. CP 3339, Hamp-
          ton, VA, 1996, NASA, pp. 123-132.
[12]  D.  Canright  and  V.  E.  Henson,  Towards  an  FVE-FAC
          method for determining thermocapillary effects on weld pool
          shape, in Seventh Copper Mountain Conference on Multigrid
          Methods, N. D. Melson, T. A. Manteuffel, S. F. McCormick,
          and C. C. Douglas, eds., vol. CP 3339, Hampton, VA, 1996,
          NASA, pp. 147-166.
[13]  M. Casarin, Quasi-optimal Schwarz methods for the conform-
          ing spectral element discretization, in Seventh Copper Moun-
          tain Conference on Multigrid Methods, N. D. Melson, T. A.
          Manteuffel,  S.  F.  McCormick,  and  C.  C.  Douglas,  eds.,
          vol. CP 3339, Hampton, VA, 1996, NASA, pp. 167-182.
[14]  Z. Chen and R. E. Ewing, Recent development of multigrid
          algorithms for mixed and nonconforming methods for second
          order elliptic problems, in Seventh Copper Mountain Confer-
          ence on Multigrid Methods, N. D. Melson, T. A. Manteuffel,
          S. F. McCormick, and C. C. Douglas, eds., vol. CP 3339,
          Hampton, VA, 1996, NASA, pp. 183-197.
[15]  M. B. Davis and G. F. Carey, A parallel multilevel spectral
          element scheme, in Seventh Copper Mountain Conference on
          Multigrid Methods, N. D. Melson, T. A. Manteuffel, S. F.
          McCormick, and C. C. Douglas, eds., vol. CP 3339, Hamp-
          ton, VA, 1996, NASA, pp. 213-225.
[16]  J.  E.  Dendy,  Revenge  of  the  semicoarsening  frequency  de-
          composition multigrid method, in Seventh Copper Mountain
          Conference on Multigrid Methods, N. D. Melson, T. A. Man-
          teuffel, S. F. McCormick, and C. C. Douglas, eds., vol. CP
          3339, Hampton, VA, 1996, NASA, pp. 227-239.
[17]  Q. Deng, An optimal order nonnested mixed multigrid method
          for generalized Stokes problems, in Seventh Copper Mountain
          Conference on Multigrid Methods, N. D. Melson, T. A. Man-
          teuffel, S. F. McCormick, and C. C. Douglas, eds., vol. CP
          3339, Hampton, VA, 1996, NASA, pp. 241-253.
[18]  C. C. Douglas, J. Douglas, and D. E. Fyfe, A note on
          multigrid theory for non-nested grids and/or quadrature, in
          Seventh Copper Mountain Conference on Multigrid Methods,
          N. D. Melson, T. A. Manteuffel, S. F. McCormick, and C. C.
          Douglas, eds., vol. CP 3339, Hampton, VA, 1996, NASA,
          pp. 255-264.
[19]  E. G. D'yakonov, Effective numerical methods for solving el-
          liptic problems in strengthened Sobolev spaces,  in Seventh
          Copper Mountain Conference on Multigrid Methods, N. D.
          Melson,  T.  A.  Manteuffel,  S.  F.  McCormick,  and  C.  C.
          Douglas, eds., vol. CP 3339, Hampton, VA, 1996, NASA,
          pp. 199-212.
[20]  P. Eliasson and B. Engquist, The effects of dissipation and
          coarse grid resolution for multigrid in flow problems, in Sev-
          enth Copper Mountain Conference on Multigrid Methods,
          N. D. Melson, T. A. Manteuffel, S. F. McCormick, and C. C.
          Douglas, eds., vol. CP 3339, Hampton, VA, 1996, NASA,
          pp. 265-281.
[21]  H. C. Elman, Multigrid and Krylov subspace methods for the
          discrete Stokes equations, in Seventh Copper Mountain Con-
          ference on Multigrid Methods, N. D. Melson, T. A. Manteuf-
          fel, S. F. McCormick, and C. C. Douglas, eds., vol. CP 3339,
          Hampton, VA, 1996, NASA, pp. 283-299.
[22]  C. Farhat and D. Rixen, A new coarsening operator for the
          optimal preconditioning of the dual and primal domain de-
          composition methods:  Application to problems with severe
          coefficient jumps, in Seventh Copper Mountain Conference
          on Multigrid Methods, N. D. Melson, T. A. Manteuffel, S. F.
          McCormick, and C. C. Douglas, eds., vol. CP 3339, Hamp-
          ton, VA, 1996, NASA, pp. 301-316.
[23]  P. O. Frederickson, High performance parallel multigrid al-
          gorithms for unstructured grids, in Seventh Copper Moun-
          tain Conference on Multigrid Methods, N. D. Melson, T. A.
          Manteuffel,  S.  F.  McCormick,  and  C.  C.  Douglas,  eds.,
          vol. CP 3339, Hampton, VA, 1996, NASA, pp. 317-326.
[24]  T. Gjesdal, A cell-centered multigrid for all grid sizes, in Sev-
          enth Copper Mountain Conference on Multigrid Methods,
          N. D. Melson, T. A. Manteuffel, S. F. McCormick, and C. C.
          Douglas, eds., vol. CP 3339, Hampton, VA, 1996, NASA,
          pp. 327-338.
[25]  W. L. Golik, Numerical study of multigrid methods with var-
          ious smoothers for the elliptic grid generation equations, in
          Seventh Copper Mountain Conference on Multigrid Methods,
          N. D. Melson, T. A. Manteuffel, S. F. McCormick, and C. C.
          Douglas, eds., vol. CP 3339, Hampton, VA, 1996, NASA,
          pp. 339-346.
[26]  H. Guillard and N. Marco, Some aspects of multigrid meth-
          ods on non-structured meshes, in Seventh Copper Mountain
          Conference on Multigrid Methods, N. D. Melson, T. A. Man-
          teuffel, S. F. McCormick, and C. C. Douglas, eds., vol. CP
          3339, Hampton, VA, 1996, NASA, pp. 347-362.
[27]  M.  J.  Holst  and  S.  Vanderwalle, Schwarz methods:  To
          symmetrize or not to symmetrize, in Seventh Copper Moun-
          tain Conference on Multigrid Methods, N. D. Melson, T. A.
          Manteuffel,  S.  F.  McCormick,  and  C.  C.  Douglas,  eds.,
          vol. CP 3339, Hampton, VA, 1996, NASA, pp. 363-378.
[28]  J. E. Jones, A mixed finite volume element method for flow
          calculations in porous media, in Seventh Copper Mountain
          Conference on Multigrid Methods, N. D. Melson, T. A. Man-
          teuffel, S. F. McCormick, and C. C. Douglas, eds., vol. CP
          3339, Hampton, VA, 1996, NASA, pp. 379-391.
[29]  M.  Jung  and  U.  R"ude,  Implicit  extrapolation  methods  for
          various coefficient problems,  in Seventh Copper Mountain
          Conference on Multigrid Methods, N. D. Melson, T. A. Man-
          teuffel, S. F. McCormick, and C. C. Douglas, eds., vol. CP
          3339, Hampton, VA, 1996, NASA, pp. 393-408.
[30]  R.  Jyotsna  and  S.  P.  Vanka,  A pressure based multigrid
          procedure for the Navier-Stokes equations on unstructured
          grids, in Seventh Copper Mountain Conference on Multigrid
          Methods, N. D. Melson, T. A. Manteuffel, S. F. McCormick,
          and C. C. Douglas, eds., vol. CP 3339, Hampton, VA, 1996,
          NASA, pp. 409-424.
[31]  H.-C. Ku and A. S. Popel, The multigrid-mask numerical
          method for solution of incompressible Navier-Stokes eqau-
          tions, in Seventh Copper Mountain Conference on Multigrid
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          and C. C. Douglas, eds., vol. CP 3339, Hampton, VA, 1996,
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