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 Current editor:  Craig Douglas       
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Volume 6, Number 8 (approximately August 31, 1996)

Today's topics:

     Dissertation - Adaptive Iterative & Multigrid on Non-structured Meshes
     Four Preprints (Jun Zhang)
     Preprint for MGNet (Gjesdal and Lossius)
     Multigrid for Refined Triangle Meshes Paper
     MGNet Bib Entries (Vandewalle et al)
     Strobl Virtual Proceedings Updated
     8th Copper Mountain Conference on Multigrid Methods


Date: Tue, 13 Aug 1996 11:03:42 -0300
From: Marco Lucio Bittencourt 
Subject: Dissertation - Adaptive Iterative & Multigrid on Non-structured Meshes

             Adaptive Iterative and Multigrid Methods Applied to 
                            Non-structured Meshes

                           Marco Lucio Bittencourt

                      Universidade Estadual de Campinas
                       Faculdade de Engenharia Mecanica
                      Dipartimento de Projecto Mecanico
                            Campinas, S.P. - Brasil


This work presents direct, iterative and multigrid methods for solving systems
of equations obtained by means of the finite element method applied to linear
elliptic problems, considering two and three dimensional elastic examples.
Adaptive analysis aspects are also discussed by taking an error estimator and
some stress recovery procedures.  All the algorithms are implemented using the
object-oriented model with the C++ language.

Comparisons between direct and iterative methods concerned to the number of
operations and memory space are presented.  The superiority of the iterative
techniques accelerated by multigrid strategies can be detected, mainly on
three dimensional applications.

The multigrid methods have been used at most with nested meshes.  In such
cases the treatment of engineering problems with complex boundaries becomes
difficult.  In this thesis, the meshes are non-structured and non-nested and
they are generated by frontal and Delaunay techniques.  By using adaptive
procedures, it is possible to get an optimal sequence of meshes for solving a
problem within a specified admissible error.

The numerical procedures were linked with some other developed programs, using
the object paradigm in C++.  Two environments with tools for defining
geometrical boundaries, automatic meshes generation, errors estimation, meshes
refinement and visualization of results are also presented, considering two
dimensional linear elastic problems.

    Editor's Note: now in mgnet/papers/Bittencourt/


Date: Sat, 17 Aug 1996 12:24:26 -0400
From: Jun Zhang 
Subject: Four Preprints (Jun Zhang)

I have uploaded four preprints to mgnet...

Jun Zhang
Department of Mathematics
The George Washington University
Washington, DC 20052, USA

                A Cost-Effective Multigrid Projection Operator

       (to appear in Journal of Computational and Applied Mathematics.)


A novel heuristic residual analysis is proposed to derive a computationally
cost-effective residual projection operator in multigrid with the five-point
Red-Black Gauss-Seidel relaxation for solving the two dimensional Poisson
equation.  This optimal residual injection operator is as cheap as the trivial
injection operator, but is more efficient than the costly full-weighting
operator and achieves near-optimal convergence rate.

1991 Mathematical Subject Classification:  65F10, 65N06, 65N22, 65N55.

Key words and phrases:  Multigrid method, residual projection, Poisson
equation, Red-Black Gauss-Seidel.

    Editor's Note: in mgnet/papers/Zhang/

             Accelerated Multigrid High Accuracy Solution of the
           Convection-Diffusion Equation with High Reynolds Number

                  (to appear in Numerical Methods for PDEs)


A fourth-order compact finite difference scheme is employed with the multigrid
algorithm to obtain highly accurate numerical solution of the
convection-diffusion equation with very high Reynolds number and variable
coefficients.  The multigrid solution process is accelerated by a minimal
residual smoothing (MRS) technique.  Numerical experiments are employed to
show that the proposed multigrid solver is stable and yields accurate solution
for high Reynolds number problems.  We also show that the MRS acceleration
procedure is efficient and the acceleration cost is negligible.

Key words:  Convection-diffusion equation, multigrid method, high-order
compact discretization, minimal residual smoothing.

    Editor's Note: in mgnet/papers/Zhang/

                   On Convergence of Iterative Methods for
                    a Fourth-Order Discretization Scheme 

                  (to appear in Applied Mathematics Letters)


We prove that, under certain conditions, some classical iterative methods
converge for the linear system resulting from a fourth-order compact
discretization of the convection-diffusion equation.

Key words:  Linear systems, iterative methods, fourth-order compact
discretization scheme, convection-diffusion equation.

    Editor's Note: in mgnet/papers/Zhang/

        Residual Scaling Techniques in Multigrid, I: Equivalence Proof

              (to appear in Applied Mathematics and Computation)


This paper addresses the residual scaling techniques (coarse-grid-correction
optimization techniques) in multigrid methods.  We survey recent developments
in this area and prove the equivalence of the over-weighted residual technique
and the over-correction technique.  This leads to the proof of mathematical
equivalence of the pre-scaling and post-scaling acceleration techniques.  Two
theorems have been proved to unify the concept of the residual scaling
techniques.  These theoretical results clear the way for developing efficient
pre-scaling acceleration techniques for practical applications.  Those
practical pre-scaling acceleration techniques are discussed in a companion
paper:  Residual scaling techniques, II:  practical applications.

Key words and phrases:  Multigrid method, residual scaling techniques,
heuristic residual analysis.

    Editor's Note: in mgnet/papers/Zhang/


Date: Thu, 22 Aug 1996 16:26:11 +0200
From: Thor Gjesdal 
Subject: Preprint for MGNet

               Comparison of Pressure Correction Smoothers for 
                  Multigrid Solution of Incompressible Flow

                Thor Gjesdal and Magni El\'{e}n Hope Lossius 
                       Christian Michelsen Research as
              Fantoftvegen 38, PO Box 3, N-5036 Fantoft, Norway
                Phone (+47) 55 57 40 40, fax (+47) 55 57 40 41


We compare the performance of different pressure correction algorithms used as
basic solvers in a multigrid method for the solution of the incompressible
Navier-Stokes equations on non-staggered grids.  Numerical tests were
performed on several cases of lid-driven cavity flow using four different
pressure correction schemes, including the traditional SIMPLE and SIMPLEC
methods as well as novel variants, and varying combinations of
under-relaxation parameters.  The results show that three of the four
algorithms tested are robust smoothers for the multigrid solver, and that one
of the new methods converges fastest in most of the tests.

Keywords: Incompressible laminar flow, Navier-Stokes equations,
          Multigrid methods, Pressure correction methods.
1991 Mathematics Subject Classification: 76D05, 76M20, 65N55, 35A40

    Editor's Note: in mgnet/papers/Gjesdal-Lossius/


Date: Thu, 29 Aug 1996 18:04:04 -0600 (MDT)
From: Yair Shapira 
Subject: Multigrid for Refined Triangle Meshes Paper

                    Multigrid for Refined Triangle Meshes

                                Yair Shapira *


A two-level preconditioning method for the solution of (locally) refined
finite element schemes using triangle meshes is introduced.  In the isotropic
SPD case, it is shown that the condition number of the preconditioned
stiffness matrix is bounded uniformly for all sufflciently regular
triangulations.  This is also verified numerically for an isotropic diffusion
problem with highly discontinuous coefflcients.

* Computer Science Department, Technion, Haifa 32000, Israel.  Now at Los
Alamos National Laboratory, MS B-256, Los Alamos, NM 87545, e-mail:

    Editor's Note: in mgnet/papers/Shapira/


Date: Thu, 8 Aug 1996 10:17:41 +0200
From: Stefan Vandewalle 
Subject: MGNet Bib Entries

      AUTHOR = {Vandewalle, S. and Van de Velde, E.},
      TITLE  = {Space-time Concurrent Multigrid Waveform Relaxation},
      YEAR   = 1994,
      JOURNAL= {Annals of Num. Math.},
      MONTH  = apr,
      VOLUME = 1,
      NUMBER = {1-4},
      PAGES  = {347--363}           }

@ARTICLE {jans:vdw:96a,
     AUTHOR = "Janssen, J. and Vandewalle, S.",
     TITLE  = "Multigrid waveform relaxation on spatial finite element meshes:
               the discrete-time case",
     MONTH  = jan,
     JOURNAL= sisc,
     VOLUME = 17,
     NUMBER = 1,
     YEAR   = 1996,
     Pages  = {133--155}  }

@ARTICLE {jans:vdw:96b,
      AUTHOR = "Janssen, J. and Vandewalle, S.",
      TITLE  = "Multigrid waveform relaxation on spatial finite element
                meshes: the continuous-time case",
      MONTH  = apr,
      JOURNAL= sinum,
      VOLUME = 33,
      NUMBER = 2,
      YEAR   = 1996,
      PAGES  = {456--474} }

    Editor's Note: added to mgnet/bib/mgnet.bib in the MGNet format.


Date: Tue, 3 Sep 96 10:29:11 +0200
From: (Dr. Gundolf Haase)
Subject: Strobl Virtual Proceedings Updated

Now, there are 
                28 contributions
available in the
                V i r t u a l   P r o c e e d i n g s 
of the
           N i n t h   I n t .   G A M M - W o r k s h o p
          P a r a l l e l   M u l t i g r i d   M e t h o d s

    Editor's Note: These can be accessed through the MGNet virtual conference
    -------------  web page (or ftp) and through the web page at Linz,

                   The additions since last month's digest are the following:

Carsten Carstensen:  Domain Decomposition For A Non-smooth Convex Minimization
Problem And Its Application To Plasticity.

Michael Griebel, Thomas Grauschopf, and Hans Regler :  Additive Multilievel
Preconditioners based on Bilinear Interpolation, Matrix Dependent Geometric
Coarsening and Algebraic Multigrid Coarsening for Second Order Elliptic PDEs.

Bodo Heise and Michael Jung :  Robust Parallel Newton-Multilevel Methods.

Ferdinand Kickinger :  Algebraic Multigrid Solver for Discrete Elliptic Second
Order Problems.
Michael Kuhn, M. Goppold, Bodo Heise, and Gundolf Haase :  Preprocessing in
FE/BE Domain Decomposition Methods.

Joachim Schoeberl :  Solving the Signorini Problem on the Basis of Domain
Decomposition Techniques.
Joachim Schoeberl :  An Automatic Mesh Generator using Geometric Rules for Two
and Three Space Dimensions.


Date: Wed, 28 Aug 1996 08:04:35 -0600
From: (steve mccormick)
Subject: 8th Copper Mountain Conference on Multigrid Methods

The 8th Copper Mountain Conference on Multigrid Methods is to be held at
Copper Mountain, Colorado, April 9-13, 1997.

We are seeking funds to support perhaps 10 or more students to attend the
Conference and present their papers. The deadline for submission of student
papers is December 15, 1996.

The deadline for regular submission of author abstracts is January 15, 1997.

Information is available on the web at:

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

    Editor's Note: Here is what I found at this address.  There are many
    -------------  hyperlinks, so please look at the document directly.

APRIL 6-11, 1997


   * Conference Chairs
   * Program Committee
   * Circus Chair
   * Workshop Chair

   * Special Features
   * Format
   * Conference Deadlines
   * Submission of Abstracts
   * Where to Submit
   * Virtual Pre-Proceedings
   * NASA Proceedings
   * Special Issue of ETNA
   * Student Papers
   * Workshops and Circus Sessions
   * Location
   * Conference Registration
   * Accommodations at Copper Mountain
   * Transportation
   * Tentative Schedule (subject to change)
   * Registration Form


Tom Manteuffel, University of Colorado
Steve McCormick, University of Colorado


Joel Dendy , Los Alamos
Van Henson , Naval Postgraduate School
Jim Jones , ICASE
Kirk Jordan, IBM
Jan Mandel, CU-Denver
Duane Melson, NASA Langley
Seymour Parter, Univ. Wisconsin
Joseph Pasciak, Brookhaven
John Ruge, CU-Denver
Klaus Stueben, GMD, Germany
Ulrich Trottenberg, GMD, Germany
Pieter Wesseling , Univ. of Delft
Olof Widlund , Courant Institute
Irad Yavneh , Technion


Craig Douglas , Yale/IBM


Paul Frederickson, MathCube


* Circus--Forum for Late-Breaking Results
* Workshops--Informal Topical Discussions
* Student Papers and Travel Support
* MGNet Virtual Proceedings
* NASA Publication of Proceedings
* Special Issue of ETNA


Morning and afternoon sessions will consist of individual talks of
approximately 25 minutes each. Workshop and Circus sessions will be held in
the evenings.


Student Papers                        December 15, 1996
Author Abstracts                      January 15, 1997
Papers for NASA Proceedings           March 15, 1997
Guaranteed Availibility of Lodging    February 6, 1997
Early Registration                    February 6, 1997


In order to guarantee a spot in the program, each speaker will be asked to
submit an abstract by January 15, 1997. Abstracts will only be accepted from
the intended speaker. In the list of papers that we will eventually post, we
will include the name of the person who submitted the abstract as the
speaker along with a link to the email address used in the submission. This
year we are asking authors to submit html versions of their abstracts, so
symbols should not be used, or at least they should be kept to a minimum.
You will find the form for html abstract submission below. Also, anyone who
wants to expand on their abstract is encouraged to submit a ps file to the
Virtual Proceedings described below.


Potential contributors should submit an abstract by email to .

Click here to display the html form for submitting your abstract. Then
please download or copy it, fill in the information, and submit it to us by

Please do not send a ps, TeX, or LaTeX file. It will be returned if you do.
Your abstract submission must be in html format, but you are also welcome to
submit a ps file of an extended abstract or paper to the Virtual Proceedings
described below. Student papers should be submitted in ps format, but
students whose papers are accepted will be asked to submit abstracts in html
format in due time.

Deadline for submission of abstracts is January 15, 1997.


A tradition of these conferences is a pre-proceedings, available before the
conference. As with the 1993 and 1995 conferences, this will only be
available electronically on MGNet. There will be no multiple volume set of
papers to take home from Copper Mountain.

Instead of having to cram your paper into a few pages, you have as many
pages as you wish, preferably in an easy to read font. Please submit a
PostScript file using the directions for a MGNet preprint submission. Then
send e-mail with a message that you submitted a pre-proceedings paper.


Each speaker will be invited to submit a paper to NASA for publication in
the final proceedings, which will be published in NASA's Conference
Proceedings series.


We are planning to have a special issue of ENTA (Electronic Transactions on
Numerical Analysis) dedicated to this conference. The tentative time-table
for submission to ETNA is May 15, 1997. Final versions of all papers
(including changes determined in the refereeing process) must be in the
hands of ENTA by Dec. 15, 1997. Expected publication (posting) as an ETNA
volume: February 15, 1998. Click here to access the ETNA journal and author


Travel and lodging assistance will be awarded to student authors judged to
have the best research papers. Papers containing original research due
mainly to the student must be received before Dec. 15, 1995. They must be
singly authored and may be 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 best papers will be given a travel stipend, free lodging, and
registration, and each will be expected to present their paper in one of the
regular conference sessions. We are hoping to support 10 or more students
who submit acceptable papers, but this is contingent on funding we are
currently seeking. Student papers should be submitted as ps files by e-mail.
If this is not possible, a hard copy of the paper may be submitted by
regular post to:

BOULDER CO 80309-0526

Postdocs are not considered "students" for this competition--nor are they
eligible for student registration fees.


The program will include special time set aside for Workshops and Circuses.
The Workshop Chairman will encourage and support informal workshops on
special topics of interest. The Circus Chairman, for each of the three
planned circus sessions, will encourage participation and contributions and
will organize, set the schedule, and oversee its progress.


The conference will be held at Copper Mountain, Colorado, located 75 miles
west of Denver. They have a current weather picture that you might want to
view as the conference approaches!

Condominium accommodations and adjacent meeting rooms are located in the
Mountain Plaza Conference Center located at the base of the Copper Mountain
ski lifts.


Conference registration is available on line.

If you use the on-line registration, your payment must still be received by
Feb. 6th, 1997 in order to receive the discounted rates. Sending your name
by using the on-line registration will get you on the registeration list,
but your fee depends on whether or not you make the early registration
deadline of Feb. 6th, 1997. At the bottom of this message are instructions
for accessing and sending your registration form. If you are paying by
credit card, your form must include the card number and expiration date. If
you are paying by check, please mail it with your form. You will receive a
discounted rate if your payment is postmarked before February 6, 1997. The
only types of payments accepted will be VISA, MASTER CARD, or CHECK (money
order). We DO NOT accept American Express.

Registration fees include a registration packet, a reception on Sunday
evening, coffee breaks each day, and a banquet on Wednesday evening. The fee
schedule is stated on the form. Please check the appropriate rate. If paying
with a Eurocheque, please add $6.00 for processing.


BOULDER CO 80309-0526

or fax it to CMCMM97 Attn: Steve McCormick at 303-492-4066.

No refunds will be given for cancellations after March 6. Full refunds less
a $50 service charge will be given if notified before March 6, 1997.


A lodge room has one or two queen beds, and a two-bedroom condominium has
one or two queen beds in each bedroom, two baths, a kitchen, a dining area,
and fireplace. Please be sure to verify the number of beds with your

Per night rates are as follows:

Lodge Room              $92/night
Deluxe Studio           $107/night
One Bedroom Condo       $120/night
Two Bedroom Condo       $183/night

Make your room reservation directly with Copper Mountain before February 6,
1997. Availability of rooms cannot be guaranteed after February 6--Copper
Mountain reserves the right to release part of our room block if 50% of our
block is not reserved at this time. After March 6, all remaining unreserved
rooms will be released from our group.

Please reserve your lodging as soon as possible:

State and local taxes (5.5%) will be added to the cost of the room. Rates
prior to April 6 are higher. If available, group rates will be given 2 days
before and after the conference. Identify yourself with the CU Math Dept.
Conference to get group rates. At time of reservation, a credit card number
can hold the room, or you will be asked to send in 1 night's deposit within
14 days.

Copper Mountain Resort Reservations

North America Toll Free Phone Number: 1-800-458-8386
Direct Phone #: 970-968-2882 & Fax Number: 970-968-6227

Room sharing bulletin board

If you are interested in sharing a room (the two bedroom condos are
especially nice for that because they sleep up to two per room and they have
kitchens and livingrooms), you may scan current contents and/or post your
own message.


Copper Mountain is located 75 miles west of Denver via Interstate 70, at
exit 195. Please make your airline reservation destination Denver
International Airport. All major car rental agencies have counters at the
airport. We will be arranging for group discounted rates with Resort Express
shuttle service. You must identify yourself as attending the "CU Multigrid
Methods" conference to receive whatever group rates are arranged.
Reservations should be made by calling: 1-800-334-7433 or direct
970-468-7600, or fax: 970-468-0364. Resort Express is located on level 5,
the baggage claim level, in the center of the main terminal. In order to
receive a full refund for a cancellation, cancellations must be received
more than 24 hours in advance of scheduled trip.

TENTATIVE SCHEDULE (subject to change)

Sunday,  April 6   Registration
7:00 - 9:00 p.m.   Reception

Monday, April 7
8:00 - 12:00       Session 1
4:30 - 6:30 p.m.   Session 2
7:30 - 9:30 p.m.   Workshops & Circus

Tuesday, April 8
8:00 - 12:00       Session 3
4:30 - 6:30 p.m.   Session 4
7:30 - 9:30 p.m.   Workshops & Circus

Wednesday, April 9
8:00 - 12:00       Session 5
4:30 - 6:30 p.m.   Session 6
7:30 - 9:30 p.m.   Banquet

Thursday, April 10
8:00 - 12:00       Session 7
4:30 - 6:30 p.m.   Session 8
7:30 - 9:30 p.m.   Workshops & Circus

Friday, April 11
8:00 - 12:00       Session 9
4:30 - 6:30 p.m.   Session 10

The preliminary program will be available by mid to late February by e-mail
or on the net.

For further information

e-mail to
Steve McCormick
(303) 492-0662
Cat Rachwalski
(303) 980-8522 phone & fax number
Duplication of messages is not necessary!


   * On line registration.
   * Registration form LaTeX file

Register by mail by downloading the file. Make hard copy and mail with your
fee to:

BOULDER CO  80309-0526

or Fax to: (303) 492 - 4066.

Sample Form

Copper Mountain Conference on Iterative Methods
Copper Mountain, Colorado, April 6th - April 11, 1997

please use the address you want on the attendee list.

Name _________________________________________________

Affiliation _________________________________________

Street Address ______________________________________



Country        ______________________________________

e-mail address ______________________________________

phone #        ______________________________________

Advanced Registration Fee
postmarked before February 6, 1997
(   ) SIAM Member $225.00
(   ) Non-SIAM Member $255.00
(   ) Student $50.00

Registration Fee
postmarked 2/6/97 and after or paid at conference
(   ) SIAM Member $265.00
(   ) Non-SIAM Member $295.00
(   ) Student $50.00

Method of Payment
(   )  Check or money order enclosed

Checks written to: Copper Mountain Conference
Must be in U.S. funds drawn on a U.S. bank.  If paying with
a EuroCheque please add $6 to your fee for bank processing.

(   ) VISA or MASTERCARD only (No Am.Ex)
Card # _______________________________________
Exp. Date _____________________
(if sending by e-mail no signature necessary)


End of MGNet Digest