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 or
                 http://www.ccs.uky.edu/mgnet

Today's editor:  Craig Douglas (douglas-craig@cs.yale.edu)

Volume 7, Number 6 (approximately June 30, 1997)

Today's topics:

     MGNet finally synchronized
     Benchmark mailing lists
     Mesh Coarsening
     Three Papers by Z. Chen
     New Paper on MGNet
     Multigrid Course

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

Date: Thu, 19 Jun 97 20:20:01 -0400
From: Craig Douglas 
Subject: MGNet finally synchronized

After 6 years, I finally got all of the copies of MGNet synchronized today.
By that, I mean that all 1818 files (roughly 85 Mb total) have identical file
dates, sizes, and check sums.

There are 5 copies of MGNet, including one behind a firewall.  Hopefully, I
did not break or lose anything in the process.  All copies now look like the
main site at Yale.

For those of you interested in how the Internet is bearing up to the web, it
took about 4 hours to ftp all of MGnet from Yale to Europe.  It took about 8
hours to ftp it from Yale to Kentucky.

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

Date: Mon, 20 Jun 97 09:45:13 -0400
From: Craig Douglas 
Subject: Benchmark mailing lists

The two mailing lists,

    mgnetb@ccs.uky.edu      for discussions about multigrid benchmarks
                            and model problems

    mgnetbc@ccs.uky.edu     for people wanting to contribute multigrid
                            applications for major benchmarks (like
                            SPEC)

are set up and ready for use.  All they need now is some traffic.  They will
be moderated for the next few weeks.  Those who indicated they wanted to be
on one of these lists earlier (at Copper Mountain or by e-mail to me) need
do nothing more.  If you want on one of these lists, please send e-mail to
mgnet@ccs.uky.edu.

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

Date: Sun, 22 Jun 97 23:48:35 -0400
From: 
Subject: Mesh Coarsening

Short version:  I am seeking help from multigrid practitioners, in evaluating
our automatic mesh coarsening algorithm for 2D unstructured triangular meshes.

Long version:  I have worked, together with Gary Miller and Shang-Hua Teng, on
the geometrical problem of automatic mesh coarsening of two dimensional,
unstructured triangular meshes.  Our algorithm comes with theoretical
guarantees for the aspect-ratio and size of the meshes in the hierarchy, and
is very simple and efficient in practice.  I'd like to find a person willing
to collaborate on testing our algorithm within a multigrid framework:  using
the unstructured coarsening hierarchy our algorithm produces with a multigrid
solver, and seeing if the geometrically good sequence we produce results in
improved convergence.  I'd also appreciate pointers to other mesh coarsening
programs or papers.

We tried to address the mesh coarsening problem from a computational geometry
point of view.  We have developed an algorithm that is guaranteed to generate
a coarsening sequence such that all the meshes in the sequence are of good
aspect ratio, neighboring meshes approximate each other well, and the size of
the meshes is as small as possible (up to a constant factor) under the above
restrictions.  This work is described in SODA 97.  (look also in
http://www.cs.cmu.edu/~tdafna/soda97.html)

We also worked on a practical variant of the algorithm, and implemented it.
This work is not yet published, and is currently described only in my thesis.
The algorithm is very simple and efficient.  As part of my thesis work, I
tested it on a test suite of graded, unstructured meshes, and the algorithm
produces high-quality coarsening sequences.

The difficulty is, however, that our quality measures are only geometrical and
combinatorial in nature:  aspect ratio of the mesh elements, and number of
elements.  Ultimately, I'd like to verify that the coarsening sequences we
produce improve convergence behavior of the multigrid method.  For that, I'd
like to find someone to work with, who has tried to solve a particular
differential equation over a graded mesh, and would like to experiment with
the coarsening sequences our program generates.  I think the better quality of
the coarsening sequences we produce is particularly noticeable over very
graded, unstructured meshes.  Quasi-uniform unstructured meshes are simpler to
coarsen, for example by the MIS method.  Therefore, I'd like to find someone
trying to use the multigrid over very graded unstructured meshes.

Please contact me at tdafna@cs.cmu.edu.  I would greatly appreciate hearing
from people willing to experiment with our coarsening sequences, and I hope
that in turn, the coarsening sequences we produce will be helpful to the
multigrid community.

Thank you,
Dafna Talmor
tdafna@cs.cmu.edu

http://www.cs.cmu.edu/~tdafna

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

Date: Sat, 21 Jun 1997 12:04:36 -0500
From: Zhang-xin CHEN 
Subject: Three Papers by Z. Chen

I have put three papers chen I, II, and III (abstracts and PS-files) under
mgnet/incoming/ chen.  You may announce them in the mgnet news letter.

                  Expanded Mixed Finite Element Methods for
                   Linear Second-Order Elliptic Problems, I

                                Zhangxin Chen

                      Department of Mathematics, Box 156
                        Southern Methodist University
                       Dallas, Texas 75275--0156, USA.

                                   Abstract

We develop a new mixed formulation for the numerical solution of second-order
elliptic problems.  This new formulation expands the standard mixed
formulation in the sense that three variables are explicitly treated:  the
scalar unknown, its gradient, and its flux (the coefficient times the
gradient).  Based on this formulation, mixed finite element approximations of
the second-order elliptic problems are considered.  Optimal order error
estimates in the Lp- and H-s-norms are
obtained for the mixed approximations.  Various implementation techniques for
solving the systems of algebraic equations are discussed.  A postprocessing
method for improving the scalar variable is analyzed, and superconvergent
estimates in the Lp-norm are derived.  The mixed formulation
is suitable for the case where the coefficient of differential equations is a
small tensor and does not need to be inverted.

This paper will appear in RAIRO Mod\`el. Math. Anal. Num\'er.

    Editor's Note: in mgnet/papers/ChenZ/chenI.ps.gz
    -------------

                  Expanded Mixed Finite Element Methods for
                Quasilinear Second-Order Elliptic Problems, II

                                Zhangxin Chen

                      Department of Mathematics, Box 156
                        Southern Methodist University
                       Dallas, Texas 75275--0156, USA.

                                   Abstract

A new mixed formulation recently proposed for linear problems is extended to
quasilinear second-order elliptic problems.  This new formulation expands the
standard mixed formulation in the sense that three variables are explicitly
treated; i.e., the scalar unknown, its gradient, and its flux (the coefficient
times the gradient).  Based on this formulation, mixed finite element
approximations of the quasilinear problems are established.  Existence and
uniqueness of the solution of the mixed formulation and its discretization are
demonstrated.  Optimal order error estimates in Lp and
H-s are obtained for the mixed approximations.  A
postprocessing method for improving the scalar variable is analyzed, and
superconvergent estimates are derived.  Implementation techniques for solving
the systems of algebraic equations are discussed.  Comparisons between the
standard and expanded mixed formulations are given both theoretically and
experimentally.  The mixed formulation proposed here is suitable for the case
where the coefficient of differential equations is a small tensor and does not
need to be inverted.

This paper will appear in RAIRO Mod\`el. Math. Anal. Num\'er.

    Editor's Note: in mgnet/papers/ChenZ/chenII.ps.gz
    -------------

                      Analysis of Expanded Mixed Methods
                   for Fourth-Order Elliptic Problems, III

                                Zhangxin Chen

                      Department of Mathematics, Box 156
                        Southern Methodist University
                       Dallas, Texas 75275--0156, USA.

                                   Abstract

The recently proposed expanded mixed formulation for numerical solution of
second order elliptic problems is here extended to fourth order elliptic
problems.  This expanded formulation for the differential problems under
consideration differs from the classical formulation in that three variables
are treated, i.e., the displacement and the stress and moment tensors.  It
works for the case where the coefficient of the differential equations is
small and does not need to be inverted, or for the case in which the stress
tensor of the equations does not need to be symmetric.  Based on this new
formulation, various mixed finite elements for fourth order problems are
considered; error estimates of quasi-optimal or optimal order depending upon
the mixed elements are derived.  Implementation techniques for solving the
linear system arising from these expanded mixed methods are discussed, and
numerical results are presented.

This paper will appear in Numerical Methods for PDE.

    Editor's Note: in mgnet/papers/ChenZ/chenIII.ps.gz
    -------------

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

Date: Sun, 29 Jun 97 10:28:55 -0400
From: Craig Douglas 
Subject: New Paper on MGNet

This was added to mgnet/Conferences/CopperMtn97 and can be found through the
conference web page.

    Craig C. Douglas
    Minimizing memory cache usage for multigrid algorithms in two dimensions
    
For those of you at the conference dinner, I hope you see the humor in this
being the last paper added (so far).

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

Date: Mon, 30 Jun 1997 12:45:26 +0200
From: Wolfgang.Joppich@gmd.de (Wolfgang Joppich)
Subject: Multigrid Course

Dear Ladies and Gentlemen, dear colleagues and friends!

I am sorry to disturb you.  But this broadcast message is the easiest and
cheapest way to attract your attention to a MULTIGRID COURSE at the GMD from
Friday 10.10.97 to Sunday 12.10.1997.  For more information contact
joppich@gmd.de or look at the GMD web-pages

           http://www.gmd.de and go to News, upcoming events.

You may also view directly

           http://www.gmd.de/SCAI/scicomp/multigrid-course.html

If you know about persons which might be interested in such a course, please
inform them.  Thank you for your help.

With kind regards
Wolfgang Joppich, GMD-SCAI

    Editor's Note: This is the information available on the web...
    -------------

Multigrid Course - Introduction to Standard Methods

10 - 12 October 1997

The Course: This course results from several lecture series Algorithms I/II
at the Fachhochschule of Cologne. At the end of the course even beginners
without numerical experience will be able to write standard MG programs for
model problems. This is possible by an appropriate mixture of heuristics and
exactness combined with theory and practice. This concept proved to be
successful by the previous course in 1996.

Target Group: Everybody who is interested in numerical methods may use this
course to start with multilevel algorithms. Students with mathematical or
technical interest from universities and Fachhochschulen are encouraged to
visit the course.

Mathematical Prerequisite: A basic knowledge of numerical analysis is
helpful, including standard discretization techniques for partial
differential equations (finite differences and similar approaches on
cartesian grids), and a general familiarity with iterative solvers for large
systems of equations.

W. Joppich, GMD-SCAI

Program:

Friday 10.10.97
14:00 - 14:45 Registration
14:45 - 15:00 Welcome, History and Development of Multigrid Methods
15:00 - 16:30 Basic Principles
              - Analysis of Relaxation Methods, Course Grid Correction,
                Correction Scheme
16:30 - 17:00 Coffee Break
17:00 - 18:30 Components of the Multigrid Method
              - Discretization and Grids, Relaxation (Smoothing),
                Coarsening Strategies, Coarse Grid Operators,
                Cycles, Grid Transfer
18:30 - open  Programming

Saturday 11.10.97
 9:00 - 10:30 Full Approximation Scheme (FAS), Full Multigrid (FMG)
10:30 - 11:00 Coffee Break
11:00 - 12:30 Local Refinements (MLAT)
              - Adaptive Grids, Refinement Criteria, Estimation of
                the Discretization Error
12:30 - 14:00 Lunch Break
14:00 - 15:30 Parabolic Problems
              - Implicit Time Discretization, Direct and Indirekt MG
15:30 - 16:00 Coffee Break
16:00 - 17:30 Local Analysis
              - Smoothing Analysis, Two Grid Analysis
17:30 - 19:00 Programming

Sunday 12.10.97
 9:00 - 10:30 Presentation of selected Multigrid Programs
10:30 - 11:00 Coffee Break
11:00 - 12:30 Programming, Discussion
12:30         End of the Course

Secretariat: Conference and Software Consulting, Ms Karin Joppich,
Weilbergstrassee 16, D-53639 oenigswinter, Phone +49 (0) 2244 80098

Location: GMD, Sankt Augustin; C3-T26.

Accomodation: Rooms have been reserved for participants in Hotels close to
the GMD. The reservation in these hotels will be organized if the
subscription has been received before end of August 1997. The price per
night, including breakfast, is approximately 90 - 105 DM for a single room.
Further information after course subscription.

Number of Participants: The maximum number of participants is about 15. The
sequence of subscription decides on participation.

Course Fee: 350 DM, includes course material (copies of transparencies,
preprints, recent publications, if asked for Grundlagen der
Mehrgittermethode - eine Einfahrung in die Standardverfahren), refreshments
during coffee breaks, lunch on Saturday and sandwiches at Saturday evening.
On receiving your subscription form you will get a confirmation, additional
information and an invoice. The amount due is to reach us two weeks before
the first day of the course.

Subscription: Use the attached form and give the requested additional
information, if possible. For further information please contact the
secretariat or joppich@gmd.de.

Cancellation: Cancellations received earlier than two weeks before the first
day of the course will be reimbursed less 50 DM administration charge. No
reimbursement of the subscription fee will be made for cancellations
received later, unless the participant provides a replacement. If for any
reason the course will not take place, the subscription fee will be returned
in full. Further claims for compensation are excluded.

Subscription form - Multigrid Course, 10. - 12. Oktober 1997, please return
to

Conference and Software Consulting
Ms Karin Joppich
Weilbergstrasse 16
D-53639 Koenigswinter
Germany

Ms. / Mr.  :
Last name  :                        First name :
Affiliation:
Department :
Adress     :
Postal code:                        City       :
Country    :                        Phone/Fax  :
E-mail     :
Arrange accomodation ( ) no  ( ) yes
                                 Arrival  :
                                 Departure:
                             ( ) special requirement:

Place             Date           Signature

Registration implies acceptance of the above conditions of participation.
----------------------------------------------------------------------------
Wolfgang Joppich
Tue May 27 13:30:53 MDT 1997

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

End of MGNet Digest
**************************