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Volume 4, Number 11 (approximately November 30, 1994)

Today's topics:

     Student Paper Deadline for Copper Mountain Meeting
     Looking for someone using MG and FEM to solve the NS eqs.
     WWW and Copper
     German Scientific Computing Home Page
     Multigrid and Domain Decomposition Days at CERFACS in 1995
     Flame paper with detailed chemistry
     A new book


Date: Wed, 30 Nov 94 14:50:01 EST
From: Craig Douglas 
Subject: Student Paper Deadline for Copper Mountain Meeting

  ----> December 1, 1994 <----

Send last minute papers (PostScript) by e-mail to

A reminder of what this:

    Travel and lodging assistance will be awarded to students judged to
    have the best research papers.  Papers with original research due
    mainly to the student must be received before December 1, 1994.  They
    must be singly authored and no more than 10 pages in length.  Sending
    only an abstract is unacceptable.  A panel of judges will determine the
    best papers.  Authors of the three best papers will be given a travel
    stipend, free lodging, and registration, and will be expected to
    present their papers in a special session at the conference.  Several
    other students who participate in the competition may be awarded free
    lodging and registration, depending on availability of funds.


Date: Fri, 4 Nov 94 12:33:53 -0800
From: (guoping li)
Subject: Looking for someone using MG and FEM to solve the NS eqs.

   I want to find someone who have simple research codes to solve the 
Navier-Stokes equations, based on multigrid AND finite element methods,
AND will allow me to use their codes on the conditions they specify.
I want to use the codes solely for my research in heat transfer. I am 
not look for a commercial code.
   Any direction and suggestion on how to find them are welcome.


Date: Sat, 12 Nov 1994 11:13:32 -0700
From: (Steve McCormick)
Subject: WWW and Copper

We are now on WWW: is
the WWW address for Copper info. Craig, can you (and anyone else for that
matter) please put this link in whatever home page (MGNet, etc.) you would?
Also, any suggestions for new/revised info or format are welcome...

    Editor's Note: I have updated the MGNet WWW entries at Yale, CERFACS,
    -------------  and IBM so that the postcard button of Copper Mountain
                   goes over to Steve's URL.


Date: Mon, 21 Nov 1994 19:36:31 +0100
From: Ulrich Ruede 
Subject: German Scientific Computing Home Page

We have recently started to provide a collection of WWW
pages accessible via URL
These documents collect information about Scientific Computing in Germany.
We invite the active participation of the Scientifc Computing Community
both within Germany and internationally. All feedback to
is welcome.

Please help to make this service useful by sending us the information
you have!

Uli Ruede


Date: Wed, 30 Nov 94 15:35:42 EST
From: Craig Douglas 
Subject: Multigrid and Domain Decomposition Days at CERFACS in 1995

CERFACS is having a special year on linear algebra in 1995.  Part of this will
be 4 workshops on particular topics.  The first of these will be April 10-13
and will focus on iterative methods.  This workshop is being organized by Iain
Duff, Luc Giraud, and myself.  The tentative schedule is the following:

    April 10    an industrial tutorial,
    April 11    Krylov space methods,
    April 12    multigrid methods
    April 13    domain decomposition methods

A collection of experts will give talks on these days.  If you are interested
in attending, please send e-mail to Dr. Chiara Puglisi:


Date: Wed, 30 Nov 94 15:07:13 EST
From: Craig Douglas 
Subject: Flame paper with detailed chemistry

Detailed Chemistry Modeling of Laminar Diffusion Flames on Parallel Computers

Craig C. Douglas
IBM T. J. Watson Research Center and
Department of Computer Science, Yale University

Alexandre Ern
Department of Mechanical Engineering, Yale University, and

Mitchell D. Smooke
Department of Mechanical Engineering, Yale University

Abstract:  We present a numerical simulation of an axisymmetric, laminar
diffusion flame with finite rate chemistry on serial and distributed memory
parallel computers.  We use the total mass, momentum, energy, and species
conservation equations with the compressible Navier-Stokes equations written
in vorticity-velocity form.  The computational algorithm for solving the
resulting nonlinear coupled elliptic partial differential equations involves
damped Newton iterations, Krylov-type linear system solvers, and adaptive mesh
refinement.  The results presented here are the first in which a lifted
diffusion flame structure is obtained on a nonstaggered grid.  The numerical
solution is in very good agreement with previous numerical and experimental

Key words:  combustion, finite rate chemistry, vorticity-velocity, nonlinear
methods, iterative methods, parallel computers.

AMSMOS Classification:  80A32, 80-08, 65C20, 65N20, 65F10.

    Editor's Note: in mgnet/papers/Douglas-Ern-Smooke/ and
    -------------     mgnet/papers/Douglas-Ern-Smooke/detailed.abs.  There
                      are some color figures that have been left out of the
                      online version.  Contact one of the authors for these.


From: AOH Axelsson 
Date: Sat, 12 Nov 1994 18:09:43 GMT
Subject: A new book

                     New book available

           Cambridge University Press, 1994
                  Author: O. Axelsson

654 pages
ISBN 0-521-44524-8 hardback
List price (Europe) \pounds 50.

The first  seven  chapters and appendix  A  and  B can be used as a 
textbook for a master-class course in numerical linear algebra.  It 
presents  also some basic theory in linear  algebra.  There  is  an 
abundance of exercises, some of which presenting additional methods
in a self-programmed style.

The remaining six chapters  present  recent  results  in  iterative 
solution methods and can be used in a more advanced course. It  can
also be useful for research- or application-oriented  students  and

1.Direct solution methods
1.1  Introduction: Networks and structures
1.2  Gaussian Elimination and Matrix Factorization
1.3  Range and Nullspace
1.4  Practical Considerations
1.5  Solution of Tridiagonal Systems of Equations

2. Theory of Matrix Eigenvalues
2.1  The Minimal Polynomial
2.2  Selfadjoint and Unitary Matrices
2.3  Matrix Equivalence (Similarity Transformations)
2.4  Normal and H-normal Matrices

3. Positive Definite Matrices, Schur Complements and General Eigenvalue
3.1  Positive Definite Matrices
3.2  Schur Complements
3.3  Condition Numbers
3.4  Estimates of Eigenvalues of Generalized Eigenvalue Problems
3.5  Congruent Transformations
3.6  Quasisymmetric Matrices

4. Reducible and Irreducible Matrices and the Perron-Frobenius Theory for
   Nonnegative Matrices
4.1  Reducible and Irreducible Matrices
4.2  Gershgorin Type Eigenvalue Estimates
4.3  The Perron-Frobenius Theorem
4.4  Rayleigh Quotient and Numerical Range
4.5  Some Estimates of the Perron-Frobenius Root of Nonnegative Matrices
4.6  A Leontief Closed Input-Output Model

6. M-Matrices, Convergent Splittings and the SOR Method
6.1  M-Matrices
6.2  Convergent Splittings
6.3  Comparison Theorems
6.4  Diagonally Compensated Reduction of Positive Matrix Entries
6.5  The SOR Method

7. Incomplete Factorization Preconditioning Methods
7.1  Point Incomplete Factorization
7.2  Block Incomplete Factorization; Introduction
7.3  Block Incomplete Factorization of M-Matrices
7.4  Block Incomplete Factorization of Positive Definite Matrices
7.5  Incomplete Factorization Method for Block H-Matrices
7.6  Inverse Free Form for Block Tridiagonal Matrices
7.7  Symmetrization of Preconditioners and the SSOR and ADI Methods

8. Approximate Matrix Inverses and Corresponding Preconditioning Methods
8.1  Two Methods of Computing Approximate Inverses of Block Bandmatrices
8.2  A Class of Methods for Computing Approximate Inverses of Matrices
8.3  A Symmetric and Positive Definite Approximate Inverse
8.4  Combinations of Explicit and Implicit Methods
8.5  Methods of Matrix Action
8.6  Decay Rates of (Block-) Entries of Inverse of (Block-) Tridiagonal
     s.p.d. Matrices

9. Block Diagonal and Schur Complement Preconditionings
9.1  The C.B.S. Constant
9.2  Block-Diagonal Preconditioning
9.3  Schur Complement Preconditioning
9.4  Full Block-Matrix Factorization Methods
9.5  Indefinite Systems

10. Estimates of Eigenvalues and Condition Numbers for Preconditioning

10.1  Upper Eigenvalue Bounds
10.2  Perturbation Methods
10.3  Lower Eigenvalue Bounds for M-Matrices
10.4  Upper and Lower Bounds of Condition Numbers
10.5  Asymptotic Estimates of Condition Numbers for Second-Order Elliptic

11. Conjugate Gradient and Lanczos-Type Methods
11.1  The Three-Term Recurrence Form of the Conjugate Gradient Method
11.2  The Standard Conjugate Gradient Method
11.3  The Lanczos Method for Generating A-Orthogonal Vectors

12. Generalized Conjugate Gradient Methods
12.1  Generalized Conjugate Gradient, Least Squares Methods
12.2  Orthogonal Error Methods
12.3  Generalized Conjugate Gradient Methods and Variable (Nonlinear)

13. The Rate of Convergence of the Conjugate Gradient Method
13.1  Rate of Convergence Estimates based on Min Max Approximations
13.2  Estimates based on the Condition Number
13.3  An Estimate Based on a Ratio Involving the Trace and the Determinant
13.4  Estimates of the Rate of Convergence Using Different Norms
13.5  Conclusions

A  Matrix Norms, Inherent Errors and Computation of Eigenvalues
B  Chebyshev Polynomials
C  Some Inequalities for Functions of Matrices


End of MGNet Digest