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 Current editor:  Craig Douglas       
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Volume 4, Number 3 (March 31, 1994)

Today's topics:

     MG Methods for acoustic wave propagation
     C++ MG codes
     Adaptive Grid MG
     Adaptive Finite Difference MG / Richardson Extrapolation Question
     GAMM Workshop on Multigrid Methods
     References / Bibliography


Date: Fri, 4 Mar 1994 18:49:55 -0500 (EST)
From: Sylvia Isler 
Subject: MG Methods for acoustic wave propagation

I am working on simulating ultrasound wave propagation through human tissue.
Given an incident field, the simulation computes the scattered field that
results from the incident wave encountering objects in a host medium that are
more dense and less compressible than the medium.

In the software that I've developed, the complex pressure amplitude is
expressed in terms of a Kirchoff integral equation with a 3-D Green's function
as the kernel.  My advisor suggested looking into multigrid methods for
improving the efficiency of the computation which is O(n^4) and takes hours.

I would like to know if there is some literature on multigrid methods for
solving this type of equation.

Thanks in advance,
Sylvia Isler


Date: Tue, 8 Mar 94 18:35:15 -0800
From: (Scott B. Baden)
Subject: C++ MG codes

We have written a portable parallel implementation of multigrid in C++, using
a software tool called LPAR-X, which has been developed in my research group.

We will be distributing LPAR-X along with the multigrid codes in a few weeks.
We are finishing a paper on LPAR-X; in the meatime, there is an extended
abstract via anonymous ftp at, in directory pub/baden/LPARX Get
the file

LPAR-X runs on the CM-5, Intel Paragon, KSR-1, Cray C-90 (single processor in
this release) and networks of workstations under PVM.  The multigrid code will
run on any of these machines and is is partially dimension-independent.

Since LPAR-X simulates parallelism on a single processor, software can be
developed on a workstation rather than on production hardware.  We will
announce the availablility of LPAR-X in a few weeks.

Scott Baden
CSE Department
U. C. San Diego

    Editor's Note: Coming soon to MGNet, but it is not there yet.


Date: Thu, 10 Mar 1994 17:01:51 -0500 (EST)
Subject: Adaptive Grid MG


I am looking for an adaptive grid multigrid algorithm for solving non-linear
partial differential equations using finite difference discretization.  Is
this available from someone or somewhere?

Thanks a lot,
Sara Perkovic

Chem. Dept.
Cornell University
Ithaca, N.Y. 14850
(607) 255-0577

    Editor's Note: Please cc


Date: Mon, 28 Mar 1994 08:49:07 -0600 (CST)
Subject: Adaptive Finite Difference MG / Richardson Extrapolation Question

I have seen your multi grid digest, and I was wondering if you are someone you
know can help me with a multigrid problem.

The problem in some sense seems trivial, it is to get an adaptive multigrid
code working, using finite differencing, to second order.  Then, if the
solution is precisely second order, it should be extrapolatable to fourth
order via Richardson extrapolation.

The example problem which I'm trying to solve is:

$$ \frac{\partial^2 u}{x^} = f ~~ i = 2,\cdots n-1 $$

with the Dirichlet boundary conditions: $ u_1 = u1 $ , $u_n = un$

where the interior equations are finite differenced to 

$$ \frac { u_{i+1} + u_{i-1} - 2u_i }{h^2} = f_i . $$

Now I know that there are better methods to solve these equations, but I feel
that whatever technique used in one dimension will work in multiple

My domain will look something like:

0  .                               .                               . 
1  .               .               .               .               .
2  .       .       .       .       .       .       .       .       .
3  .   .   .   .   .   .   .   .   .
4  . . . . . . . . . 

i.e. finer grids will in general cover less of the entire the domain then
     then coarser grids.

The algorithm must use finite differencing for arguements which need not be
explained.  I have searched literature for this and have not been able to come
up with anything.  And when I try to program this I get results that are not
second order, i.e.  when I run convergence tests where I keep on doubling the
points on the coarsest level, I do not get errors ( u-uexact)/ (uexact), which
are reduced by a factor of four, for each doubling.  I am in some sense trying
to use standard MLAT's.

I would appreciate any help

Thank you

Scott Klasky
(512)-471-4700 t,th
(512)-471-2479 m,w,f  


Date: Mon, 14 Mar 94 13:45:08 PST
From: reb@sdna1.UCSD.EDU (Randolph E. Bank)
To: douglas-craig
Subject: pltmg7

I am happy to announce that a new version of the PLTMG package is now
available.  PLTMG edition 7.0 is a package for solving linear and nonlinear
elliptic partial differential equations in general regions of the plane.  It
is based on continuous piecewise linear triangle finite element approximation,
and features a damped Newton iteration, adaptive local mesh refinement,
hierarchical basis multigrid iteration, and pseudo-arclength continuation for
parameter dependencies.  The package also includes an initial mesh generator,
a skeleton generator, and several graphics routines.  The source code is
available by anonymous ftp from Netlib and Mgnet.

Full documentation can be obtained in the PLTMG User's Guide, available from
SIAM publications, 1400 Architects Building, 117 South 17th Street,
Philadelphia PA 19103-5052.  They can also be reached by email at  The title is:  PLTMG:  A Software Package for Solving Elliptic
Partial Differential Equations (ISBN 0-89871-330-7).

Randy Bank

    Editor's Note: in mgnet/pltmg/pltmg7.tar


Date: Mon, 21 Mar 1994 16:02:41 +0200 (MESZ)
From: Friedhelm Schieweck 
Subject: GAMM Workshop on Multigrid Methods

Dear colleagues,

in the following I want to announce an international
workshop on multilevel methods organized by our institute
in September this year. If anybody is interested please
contact me.

Friedhelm Schieweck

                 1. Announcement

The Institute for Analysis and Numerical Mathematics of the
University Magdeburg in cooperation with the GAMM Committee
"Efficient numerical methods for pde" organizes the

              GAMM - Workshop
             Multilevel Methods

Chairmanship:   D.Braess (Bochum), U.Langer (Linz),
                L.Tobiska (Magdeburg)

Date:           September 26 to 28, 1994

Location:       Parkhotel "Schloss Meisdorf", Meisdorf (Harz)

Topics:         theory and applications of multilevel 
                methods, parallelization aspects, subspace
                correction methods, hierarchical basis
                techniques, adaptive refinement

Conference fee: about 80 DM

Invited Speakers (preliminary list):
                S.C.Brenner, W.Hackbusch, S.V.Nepomnyaschikh,
                A.Reusken, V.Shaidurov, J.Xu

Registration:   until April 15, 1994

Abstracts:      10-20 lines,  deadline: May 15, 1994

Accommodation:  you can be accommodated in the Parkhotel
                "Schloss Meisdorf". The price for single
                and double rooms ranges between 40 and 115 DM
                per night

Contact address:   F.Schieweck
                   Department of Mathematics
                   University Magdeburg
                   PSF 4120
                   D-39016 Magdeburg


Phone:  +49-391 5592-2236     Fax:  +49-391 5592-2758


Date: Thur, 31 Mar 1994 13:27:31 -0500
From: douglas-craig (Craig Douglas)
Subject: References / Bibliography

The bibliography has been extensively updated in the last month.  Special
thanks to Frederic Lebon, Jeff Scroggs, and Nigel Wright for contributions.
Jeff contributed numerous domain decomposition entries from his extensive

What was added this month was a large number of papers that appeared in
journals in 1993.  As this digest is already too long, I will put these out
later in future digests.


Date: Tue, 22 Mar 94 15:49:21 +0100
From: (Frederic LEBON LMGC)
Subject: References of Frederic Lebon

I would like to add publications to the mg-net.

1 Lebon F , Raous M
a Multigrid method for the Coulomb friction law. Application in reactor 
Proceedings Femcad-88 Vol2 pp 292-301 Pergamon Press 1988
b Multigrid method for contact with friction in structure assembling problems.
Proceedings Smirt 10 Vol B pp 197-202 AASMIRT 1989
c Fixed point and internal multigrid method for friction problems in structural
Proceedings Gamni 5 vol 1 pp 457-462 Springer-Verlag 1989
2 Lebon F Ledain MA Bellet M Chenot JL Raous M
Introduction aux mithodes multigrilles en micanique des structures lineaires et
non liniaires. (in french)
Calcul des Structures et intelligence artificielle T3 pp 215-230 Pruralis
3 Lebon F Raous M Latil JC Grego L
a Multigrid method in non linear structure mechanics
New advances in computational structural mechanics Elsevier 1991
b Multigrid method for non linear structure mechanics problems
Publications du LMA n0 124 ISSN 0750-7356 pp 127-138 1991
4 Lebon F
Remarks on multigrid methods for frictional elastostatics
Proceedings of 1st Internatioanl symposium on contact mechanics p 504 1992
5 Alart P Lebon F
Multigrid method applied to mixed formulation for frictional contact problem
Contact mechanics pp 227-234 Computational mechanics publications 1993

Not yet published in a journal or book
1 Lebon F
Two-grid method for regularized frictional elastostatics problem 
December 1993
2 Grego L Latil JC Lebon F Raous M
Multigrid method for unilateral problems with friction
February 1994
3 Alart P Lebon F
Solution of frictional contact problems using performing preconditioners
4 Lebon F Alart P Doudet P
Friction and preconditioners

Frederic Lebon
Universite Montpellier 2
Laboratoire de Micanique et Ginie Civil
Pl. E. Bataillon CC048
34095 Montpellier Cedex 5


Date: 3 Mar 94 09:35:37 GMT
Subject: bibliography

  author = {P.H. Gaskell and N.G. Wright},
  title = {A Multigrid Algorithm for the Investigation of Thermal,
          Recirculating Fluid Flow Problems},
  year = 1987,
  booktitle = {Numerical Methods in Thermal Problems, Proceedings of The
              Fifth International Conference},
  publisher = {Pineridge Press}
  author = {P.H. Gaskell and A.K.C. Lau and N.G. Wright},
  title = {Two Efficient Solution Strategies for Use with Higher Order
          Discretisation Schemes, in the Simulation of Fluid Flow Problems},
  year = 1987,
  booktitle = {Numerical Methods in Laminar and Turbulent Problems,
              Proceedings of The Fifth International Conference},
  publisher = {Pineridge Press}
  author = {P.H. Gaskell and A.K.C. Lau and N.G. Wright},
  title = {Comparison of Two Strategies for Use with Higher Order
          Discretisation Schemes in Fluid Flow Simulation},
  year = 1988,
  journal = {International Journal for Numerical Methods in Fluids},
  volume = 8,
  pages = {1203-1215}
  author = {P.H. Gaskell and N.G. Wright},
  editor = {A.J. Osiadacz},
  title = {Multigrids Applied to a Solution Technique for Recirculating
          Fluid Flow Problems},
  year = 1988,
  pages = {51-55},
  booktitle = {The Proceedings of the IMA Conference on Simulation and
              Optimisation of Large Systems},
  address = {Reading}
  author = {P.H. Gaskell and A.K.C. Lau and N.G. Wright},
  editor = {Morton {\&} Baines},
  title = {The accurate approximation and economic solution of steady-state
          convection dominated flows},
  year = 1988,
  pages = 425,
  booktitle = {Numerical Methods for Fluid Dynamics III},
  publisher = {Clarendon Press},
  address = {Oxford},
  series = {IMA Conference series}
  author = {P.H. Gaskell and N.G. Wright},
  title = {An Improved Multigrid Strategy for the Investigation of Highly
          Recirculating Fluid Flows},
  year = 1988,
  number = {AIAA 88-3651},
  institution = {AIAA}
  author = {P.H. Gaskell and P.A. Sleigh and N.G. Wright},
  title = {Multigrids and their Role in the Solution of Practical {CFD}
  year = 1990,
  booktitle = {Multigrid Methods: Special Topics and Applications II},
  publisher = {Gesellschaft f\"{u}r Mathematik und Datenverarbeitung},
  address = {Sankt Augustin}
  author = {P.H. Gaskell and P.A. Sleigh and N.G. Wright},
  title = {Buoyancy driven flow in a uniformly heated cavity: Multigrid
          benchmark solutions},
  year = 1993,
  pages = 144,
  booktitle = {Proceedings of the 8th International Conference on Numerical
              Methods for Thermal Problems},
  address = {Swansea}
  author = {P.A. Sleigh and P.H. Gaskell and N.G. Wright},
  title = {Non-linear coupled multigrid solutions to thermal problems,
          employing different nodal grid arrangements and convective
          transport approximations},
  year = 1991,
  booktitle = {Numerical Methods in Laminar and Turbulent Problems,
              Proceedings of The Seventh International Conference},
  publisher = {Pineridge Press}
  author = {N.G. Wright and P.A. Sleigh and P.H. Gaskell},
  title = {Application of numerical methods to convection in a
          differentially heated cavity at high aspect ratio},
  year = 1993,
  pages = 443,
  booktitle = {Proceedings of the 8th International Conference on Numerical
              Methods for Thermal Problems},
  address = {Swansea}


End of MGNet Digest