Send mail to:    mgnet@cs.yale.edu             for the digests or bakeoff
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

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

Volume 5, Number 1 (approximately January 31, 1995)

Today's topics:

MGNet WWW Access Change at Yale
GMD - Multigrid Course 1995
Copper Mountain Abstracts and Schedule Available Soon
Preprints from Z. Chen and D. Y. Kwak or T. Arbogast
Paper on Compressible Euler Equations (Sidilkover)
Interpolation/Projection/Restriction in Multigrid

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

Date: Thu, 2 Feb 1995 13:47:22 -0500
From: douglas-craig@cs.yale.edu (Craig Douglas)
Subject: MGNet WWW Access Change at Yale

We now have a http daemon running on the NA server at Yale.  The new URL is

http://na.cs.yale.edu/mgnet/www/mgnet.html

For those of you with the old URL in HTML files, please update your files to
either this one or, in Europe,

http://www.cerfacs.fr/~douglas/mgnet.html

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

Date: Thu, 12 Jan 1995 12:36:52 +0100
From: mgkurs@gmd.de (Barbara Steckel)
Subject: GMD - Multigrid Course 1995

****************************************
*                                      *
*     GMD - Multigrid Course 1995      *
*                                      *
*         April 24 - 28, 1995          *
*                                      *
*    Bad Honnef near Bonn, Germany     *
*                                      *
****************************************

The GMD (The German National Research Center for Computer Science) will give a
multigrid course on April 24 - 28, 1995 at Bad Honnef near Bonn, Germany.

The principal lecturer is Professor Achi Brandt from the Weizmann Institute,
Rehovot, Israel, one of the pioneers of multigrid.  The other lecturers are
members of the GMD multigrid research group.  The topics of this course will
cover the basic principles of multigrid, recent developments and applications.

The main scope of the course is to provide with an understanding of multigrid.
The visitor will, at the end of the course, be able to write a multigrid
program for model problems.  Additionally, the course will supply with an
overview of multigrid application and recent research activities.  The course
is especially designed for all those which have to solve partial differential
equations in practice.

For scalar linear elliptic model problems the efficiency of multigrid
algorithms was established at the very beginning of multigrid research.  These
methods turned out to be the most efficient techniques for solving elliptic
partial differential equations.  The theory states that a multigrid solution
is generally obtained in a time directly proportional to the number of
unknowns on serial computers.  The inherent locality of the multigrid
components allows a very efficient parallelization with nearly optimal speed
up.

Multigrid, or more general multilevel computational methods have evolved into
an independent discipline by itself, interacting with numerous engineering
application areas and impacting fundamental developments in several sciences.
The recent past shows an increased development of multilevel solvers for
various areas, including:  aerodynamics, atmospheric and oceanic research,
structural mechanics, quantum mechanics and VLSI-Design.

Barbara Steckel, Wolfgang Joppich
Gesellschaft fuer Mathematik und Datenverarbeitung (GMD)
Institute for Algorithms and Scientific Computing
Schloss Birlinghoven
53754 Sankt Augustin, Germany

Phone: (0)2241 14 2768 or - 2748
Fax:   (0)2241 14 2460
E-mail: mgkurs@gmd.de

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

Date: Thu, 2 Feb 1995 13:35:12 -0500
From: douglas-craig@cs.yale.edu (Craig Douglas)
Subject: Copper Mountain Abstracts and Schedule Available Soon

All of the abstracts that were received electronically will be available in
the next few days in the directory

mgnet/Conferences/CopperMtn95

These will be accessible through WWW or anonymous ftp.  The schedule will
appear sometime in February (hopefully in the middle of the month).  It will
be in the same directory under the name Schedule.

Papers contributed to the pre-proceedings will also appear in that directory.
A few are there already (contributed so far by Maliassov, Pflaum, Xie, and
Xu).  Hopefully, all will be there by the time of the conference or shortly
thereafter.

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

Date: Thu, 19 Jan 1995 20:12:14 -0600
From: zhangxin Chen
Subject: Preprints from Z. Chen and D. Y. Kwak or T. Arbogast

THE ANALYSIS OF MULTIGRID ALGORITHMS
FOR NONCONFORMING AND MIXED METHODS
FOR SECOND ORDER ELLIPTIC PROBLEMS

Zhangxin Chen

Department of Mathematics and Institute
for Scientific Computation, Texas A&M University
College Station, TX 77843--3404

Do Y. Kwak

Department of Mathematics, Korea Advanced Institute
cience and Technology, Taejon, Korea 305--701

Abstract.  In this paper we consider multigrid algorithms for nonconforming
and mixed finite element methods for second order elliptic problems on
triangular and rectangular finite elements.  We prove optimal convergence
properties of the W-cycle multigrid algorithm and uniform condition number
estimates for the variable V-cycle preconditioner.  Lower order terms are
treated, so our results also apply to parabolic equations.

Editor's Note: in mgnet/papers/ChenZ-et-al/MGnon.{abs,ps}.
-------------

ON THE IMPLEMENTATION OF MIXED
METHODS AS NONCONFORMING METHODS
FOR SECOND ORDER ELLIPTIC PROBLEMS

Todd Arbogast

Department of Computational and Applied
Mathematics, Rice University, Houston, Texas 77251

Zhangxin Chen

Department of Mathematics and the Institute
for Scientific Computation, Texas A&M University,
College Station, Texas 77843

Abstract.  In this paper we show that mixed finite element methods for a
fairly general second order elliptic problem with variable coefficients can be
given a nonmixed formulation.  (Lower order terms are treated, so our results
apply also to parabolic equations.) We define an approximation method by
incorporating some projection operators within a standard Galerkin method,
which we call a projection finite element method.  It is shown that for a
given mixed method, if the projection method's finite element space $M_h$
satisfies three conditions, then the two approximation methods are equivalent.
These three conditions can be simplified for a single element in the case of
mixed spaces possessing the usual vector projection operator.  We then
construct appropriate nonconforming spaces $M_h$ for the known triangular and
rectangular elements.  The lowest-order Raviart-Thomas mixed solution on
rectangular finite elements in $\Re^2$ and $\Re^3$, on simplices, or on
prisms, is then implemented as a nonconforming method modified in a simple and
computationally trivial manner.  This new nonconforming solution is actually
equivalent to a postprocessed version of the mixed solution.  A rearrangement
of the computation of the mixed method solution through this equivalence
allows us to design simple and optimal order multigrid methods for the
solution of the linear system.

Editor's Note: in mgnet/papers/ChenZ-et-al/mix.{abs,ps}.
-------------

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

Date: Wed, 1 Feb 1995 11:57:55 -0500
From: Sidilkover David
Subject: Paper on Compressible Euler Equations

A GENUINELY MULTIDIMENSIONAL UPWIND SCHEME
AND EFFICIENT MULTIGRID SOLVER
FOR THE COMPRESSIBLE EULER EQUATIONS

David Sidilkover
ICASE, Mail Stop 132C
NASA Langley Research Center
Hampton, VA 23681

ABSTRACT

We present a new approach towards the construction of a genuinely
multidimensional high-resolution scheme for computing steady-state solutions
of the Euler equations of gas dynamics.  The unique advantage of this approach
is that the Gauss-Seidel relaxation is stable when applied directly to the
high-resolution discrete equations, thus allowing us to construct a very
efficient and simple multigrid steady-state solver.  This is the only
high-resolution scheme known to us that has this property.  The
two-dimensional scheme is presented in detail.  It is formulated on triangular
(structured and unstructured) meshes and can be interpreted as a genuinely
two-dimensional extension of the Roe scheme.  The quality of the solutions
obtained using this scheme and the performance of the multigrid algorithm are
illustrated by the numerical experiments.  Construction of the
three-dimensional scheme is outlined briefly as well.  The quality of the
solutions obtained using this scheme and the performance of the multigrid
algorithm are illustrated by the numerical experiments.  Construction of the
three-dimensional scheme is outlined briefly as well.

Editor's Note: in mgnet/papers/Sidilkover/euler.{abs,ps}.
-------------

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

Date: Thu, 2 Feb 95 13:56:23 GMT
From: George Cardew
Subject: Interpolation/Projection/Restriction in Multigrid

Dear Sirs

I have just got started with a multigrid style application in Finite elements
on imbedded subgrids.  So far I've been unable to find an explanantion of how
I might perform an accurate interpolation (Projection) to a higher level
grid.  Currently , A simple interpolation is performed at element level
(using the Shape functions of that element) in either direction (Projecting
or Restricting/Injecting) .  I beleive it is important to enhance the
accuracy when projecting Up.  I therefore need to perform interpolation over a
patch of elements - therein lies the difficulty .  Interpolation over a patch
within a curvilinear grid implies that a transformation of coordinates X-Y-Z
to R-S-T (0 < R,S,T < 1) will be needed with an inversion of X,Y,Z of the
node involed in the interpolation/ projection .  I generate my grids using
either Transfinite interpolation or Elliptic equations (Thompson et al) - Do
I need to invert (say) the Transfinite equation at the node in question (by
iteration , naturally) ??

If you have any info on MGNET which could cast light on this problem I would
welcome it .

Many thanks ,   George Cardew  Univ of Sheffield , UK

Editor's Note: Please Cc mgnet@cs.yale.edu if you can help him.
-------------

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

Date: Thu, 12 Jan 95 18:35:40 EST
From: Susanne Brenner

@article{SCBrenner_1994a,
author =      "S. C. Brenner",
title =       "A nonconforming mixed multigrid method for the pure
traction problem in planar linear elasticity",
journal =     "Math. Comp.",
volume =      "63",
year =        "1994",
pages =       "435--460 and S1--S5",
}
@book{SCBrenner_LRScott_1994a,
author =      "S. C. Brenner and L. R. Scott",
title =       "The Mathematical Theory of Finite Element Methods",
series =      "Texts in Applied Mathematics",
vol =         "15",
publisher =   "Springer--Verlag",
year =        "1994",
}

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

Date: Sat, 29 Jan 1995 17:42:56 -0500
From: douglas@watson.ibm.com (Craig Douglas)
Subject: Some bibliography additions in mgnet/bib/mgnet.bib

@article{HNishida_NSatofuka_1994a,
author =      "H. Nishida and N. Satofuka",
title =       "Numerical solution of unsteady incompressible {N}avier
{S}tokes equations using high order method of lines",
journal =     "Finite Elem. Anal. Des.",
volume =      "16",
year =        "1994",
pages =       "P285--297",
}
@article{SWOtto_1993a,
author =      "SWOtto",
title =       "Parallel array classes and lightweight sharing mechanisms",
journal =     "Sci. Prog.",
volume =      "2",
year =        "1993",
pages =       "203--216",
}
author =      "J. Padovan and S. M. Sansgiri and L. Krishna",
title =       "Multiply gauged solution initialization with steepest
descent smoothing",
journal =     "Int. J. Comput. Math.",
volume =      "50",
year =        "1994",
pages =       "165--182",
}
@article{OPatzold_ASchuller_HSchwichtenberg_1994a,
author =      "O. Patzold and A. Schuller and H. Schwichtenberg",
title =       "Parallel applications and performance measurements on
{SUPRENUM}",
journal =     "Parallel Comput.",
volume =      "20",
year =        "1994",
pages =       "1571--1582",
}
@article{MRannacher_GZhou_1994a,
author =      "M. Rannacher and G. Zhou",
title =       "Analysis of a domain-splitting method for nonstationary
convection-diffusion problems",
journal =     "E. W. J. Numer. Math.",
volume =      "2",
year =        "1994",
pages =       "151--172",
}
@article{ARMRao_KLoganathan_NVRaman_1994a,
author =      "A. R. M. Rao and K. Loganathan and N. V. Raman",
title =       "Multi frontal based approach for concurrent finite element
analysis",
journal =     "Comput. Struct.",
volume =      "52",
year =        "1994",
pages =       "841--846",
}
@article{ARieder_ROWellsJr_XZhou_1994a,
author =      "A. Rieder and R. O. Wel{ls,~Jr.} and X. Zhou",
title =       "A wavelet approach to robust multilevel solvers for
anisotropic elliptic problems",
journal =     "Appl. Comput. Harmon. Anal.",
volume =      "1",
year =        "1994",
pages =       "355--367",
}
@article{ARieder_XZhou_1994a,
author =      "A. Rieder and X. Zhou",
title =       "On the robustness of the damped {V} cycle of the wavelet
frequency decomposition multigrid method",
journal =     "Comput.",
volume =      "53",
year =        "1994",
pages =       "155--171",
}
@article{HRitzdorf_ASchuller_ABSteckel_KStuben_1994a,
author =      "H. Ritzdorf and A. Sch{\"u}ller and A. B. Steckel and
K. St{\"u}ben",
title =       "$L_iSS$ -- {A}n environment for the parallel multigrid
solution of partial differential equations on general {2D}
domains",
journal =     "Parallel Comput.",
volume =      "20",
year =        "1994",
pages =       "1559--1570",
}
@inproceedings{JSingh_CHolt_JHennessy_AGupta_1993a,
author =      "J. Singh and C. Holt and J. Hennessy and A. Gupta",
title =       "Parallel adaptive fast multipole method",
booktitle =   "Proceedings of the Supercomputing Conference 1993",
editors =     "",
series =      "",
volume =      "",
publisher =   "IEEE, Computer Society Press",
year =        "1993",
pages =       "54--65",
}
@article{LCStone_SBShukla_BNeta_1994a,
author =      "L. C. Stone and S. B. Shukla and B. Neta",
title =       "Parallel satellite orbit prediction using a workstation
cluster",
journal =     "Comput. Math. Appl.",
volume =      "28",
year =        "1994",
pages =       "1--8",
}
@article{TStreit_1994a,
author =      "T. Streit",
title =       "Euler and {N}avier-{S}tokes solutions for supersonic flow
around a complex missile",
journal =     "J. Spacecraft Rockets",
volume =      "31",
year =        "1994",
pages =       "600--608",
}
@article{ASydow_1994a,
author =      "A. Sydow",
title =       "Parallel simulation of air pollution",
journal =     "IFIP Trans. A, Comput. Sci. Technol.",
volume =      "52",
year =        "1994",
pages =       "605--612",
}
@inproceedings{RFVanderWinjngaaart_1993a,
author =      "R. F. Van{~der~W}injngaaart",
title =       "Efficient implementation of a 3-dimensional {ADI} method on
the {iPSC}/860",
booktitle =   "Proceedings of the Supercomputing Conference 1993",
editors =     "",
series =      "",
volume =      "",
publisher =   "IEEE, Computer Society Press",
year =        "1993",
pages =       "102--111",
}
@article{AWiedermann_JIwamoto_1994a,
author =      "A. Wiedermann and J. Iwamoto",
title =       "Multigrid {TVD}-type scheme for computing inviscid and
viscous flows",
journal =     "Comput. Fluids",
volume =      "23",
year =        "1994",
pages =       "711--735",
}
@article{YZang_RLStreet_JRKoseff_1994a,
author =      "Y. Zang and R. L. Street and J. R. Koseff",
title =       "A non staggered grid, fractional step method for time
dependent incompressible {N}avier {S}tokes equations in
curvilinear coordinates",
journal =     "J. Comput. Phys.",
volume =      "114",
year =        "1994",
pages =       "18--33",
}
@article{LBZhang_1994a,
author =      "L. B. Zhang",
title =       "A multigrid solver for the steady incompressible {N}avier
{S}tokes equations on curvilinear coordinate systems",
journal =     "J. Comput. Phys.",
volume =      "113",
year =        "1994",
pages =       "26--34",
}
@article{SZhao_MJYedlin_1994a,
author =      "S. Zhao and M. J. Yedlin",
title =       "A new iterative {C}hebyshev spectral method for solving
the elliptic equation
$\bigtriangledown(\sigma\bigtriangledown u)=f$",
journal =     "J. Comput. Phys.",
volume =      "113",
year =        "1994",
pages =       "215--223",
}

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

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