Send mail to:             for the digests or bakeoff
            for comments or help
 Current editor:  Craig Douglas       
Anonymous ftp repository: (

Today's editor:  Craig Douglas (

Volume 2, Number 1 (January 16, 1992)

Today's topics:

     New book on fast solver for large sparse systems
     Book Announcement
     Multigrid 6 (2 messages)


Date: Tue, 17 Dec 91 17:59:47 +0100
From: (Gabriel Wittum)
Subject: New book on fast solver for large sparse systems

My book
         Filternde Zerlegungen
         Schnelle Loeser fuer grosse Gleichungssysteme
         Teubner Skripten zur Numerik, Bd. 1
         Teubner Verlag Stuttgart, 1992, DM 29.-
         (in German)
is avilable now. It presents Frequency Filtering Decompositions, a new class
of solvers for large systems of equations. These merely algebraic solvers are
based on a special kind of incomplete decompositions. The basic idea is very
similar to multigrid, but the method needs only one single grid. It is very
efficient and is suited for symmetric, unsymmetric, and nonlinear problems.
The decompositions may also be used as preconditioner or smoother within
usual accelerating methods.

Besides the description of the algorithms and some model problem analysis,
the book includes a convergence theory for these methods. A large section
further concentrates on the numerical application. Results of numerical tests
are given for several scalar pde such as linear and nonlinear diffusion type
equations with varying coeficients, linear and nonlinear convection-diffusion
equations with dominating convection, interface problems etc. The results are
compared to known methods, showing that frequency filtering is able to compete
with standard solvers.


Date: Fri, 10 Jan 92 15:54:37 MET
From: Piet Wesseling(NW) 
Subject: Book Announcement

     I am pleased to announce the publication of the following book:

     An Introduction to Multigrid Methods    by P.Wesseling
     John Wiley & Sons, Chichester, 1992. ISBN 0 471 93083 0
     284 pages. Price: $105

     Table of contents:
     1. Introduction
     2. The Essential Principle of Multigrid Methods for Partial Differential
        1. Introduction 2. The Essential Principle 3. The Two-Grid  Algorithm
        4. Two-Grid Analysis
     3. Finite Difference and Finite Volume Discretization
        1. Introduction 2. An Elliptic Equation 3. A One-Dimensional Example
        4. Vertex-Centered Discretization 5. Cell-Centered Discretization
        6. Upwind Discretization 7. A Hyperbolic System
     4. Basic Iterative Methods
        1. Introduction 2. Convergenc of Basic Iterative Methods
        3. Examples of Basic Iterative Methods: Jacobi and Gauss-Seidel
        4. Examples of Basic Iterative Methods: Incomplete Point LU
        Factorization 5. Examples of Basic Iterative Methods: Incomplete Block
        LU Factorization 6. Some Methods for Non-M-Matrices
     5. Prolongation and Restriction
        1. Introduction 2. Stencil Notation 3. Interpolating Transfer Operators
        4. Operator-Dependent Transfer Operators
     6. Coarse Grid Approximation and Two-Grid Convergence
        1. Introduction 2. Computation of the Coarse Grid Matrix with Galerkin
        Approximation 3. Some Examples of Coarse Grid Operators 4. Singular
        Equations 5. Two-Grid Analysis; Smoothing and Approximation Properties
        6. A Numerical Illustration
     7. Smoothing Analysis
        1. Introduction 2. The Smoothing Property 3. Elements of Fourier
        Analysis in Grid-Function Space 4. The Fourier Smoothing Factor
        5. Fourier Smoothing Analysis 6. Jacobi Smoothing 7. Gauss-Seidel
        Smoothing 8. Incomplete Point LU Smoothing 9. Incomplete Block
        Factorization Smoothing 10. Fourier Analysis of White-Black and Zebra
        Gauss-Seidel Smoothing 11. Multistage Smoothing Methods
        12. Concluding Remarks
     8. Multigrid Algorithms
        1. Introduction 2. The Basic Two-Grid Algorithm 3. The Basic Multigrid
        Algorithm 4. Nested Iteration 5. Rate of Convergence of the Multigrid
        Algorithm 6. Convergence of Nested Iteration 7. Non-Recursive
        Formulation of the Basic Multigrid Algorithm 8. Remarks on software
        9. Comparison with conjugate gradient methods
     9. Applications of Multigrid Methods in Computational Fluid Dynamics
        1. Introduction 2. The Governing Equations 3. Grid Generation
        4. The Full Potential Equation 5. The Euler Equations of Gasdynamics
        6. The Compressible Navier-Stokes Equations 7. The Incompressible
        Navier-Stokes and Boussinesq Equations 8. Final Remarks


Date: Tue, 17 Dec 91 16:50:52 -0700
From: smccormi@copper.Denver.Colorado.EDU (McCormick Steve)
Subject: Sixth Copper Mountain Conference on Multigrid Methods

This is in response to the request by Pat Collins about the next Copper
Mountain Conference on Multigrid Methods. Continuing the tradition of
having it every two years in the first full week of April, the Sixth
conference will be held April 4-10, 1993. The rationale for this timing
is that it's the beginning of off-peak season as defined by the Copper
Mountain Ski Association, so all prices are much lower, but it's almost
always great ski conditions. The conference format has always been with
intense morning and evening sessions. I think that this works best in
an environment that allows for afternoon recreation to clear the mind
and renew energy. Most of you seem to agree.

I was just getting ready to write the proposal for funding (Thanks, Craig!
Argh!!!) when I read Pat's request for information. This brings me to a
request for help: Does anyone out there have any suggestions of (almost)
any kind that the organizing committee (which I will soon activate) should
consider for the next meeting? We'd love to consider new ideas, or critique
of the old ones. You can send them directly to me at:

As most of you know, the multigrid conferences now alternate with the
Copper Mountain Conferences on Iterative Methods, the second of which
will be held April 9-14, 1992. It will have a multigrid component to it
as before. For more information on that conference, send a message by
e-mail (content is irrelevant) to:

Steve McCormick


Date: Fri, 20 Dec 91 19:52:22 -0500
From: bells (Craig Douglas)
Subject: Copper Mountain 6


I would like to organize a session on trying to define what components should
go into a differential equations' library.  By this, I do not mean including
routines to model underground contaminants or semiconductor devices at the
molecular level, but rather, what would these modeling software need in order
to construct high level solvers more easily.  If you are interested in this,
and want to include something in the grant proposal, let me know and I will
send you a few pages of LaTeX on this.  I spent a lot of time thinking about
this during the summer of 1990 and I think I know exactly what not to propose.

This could be thought of as a BDES (ala BLAS), but I do not think the field is
that well defined.  This cannot be a multigrid only library.  In fact, it
should not even be serial computer only.  I am not sure it should be in
Fortran, C, C++, or something entirely new.  I have an opinion on this, too.
(I know, someday I should learn to keep my mouth shut.)



From: Various_People
Subject: Movements

George ABE
Sony Corporation, Research Center
Yokohama, Japan.

Dongming Hwang

Hubert Ritzdorf
Institute I1.T
5205 St. Augustin


End of MGNet Digest