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)
ftp.cerfacs.fr     (138.63.200.33)

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 5 (approximately May 31, 1995)

Today's topics:

Best V-cycle Algorithm for 2D Poisson Equation
New paper on MGNet (Ruede)
Announcement of WWW multigrid tutorial
Paper on cache based multigrid
Oberwolfach
An MPI based multigrid solver for 1 or more processors
Some of the new entries in the bibliography

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

Date: Sun, 28 May 1995 03:38:05 -0400
From: Jun Zhang
Subject: Best V-cycle Algorithm for 2D Poisson Equation

Best V-cycle algorithm to Solve 2D Poisson Equation

I'm interested in knowing the best V-cycle algorithm to solve 2D
Poisson equation
- (Uxx + Uyy) = f(x,y)       (x,y) in OMEGA
u(x,y)     = g(x,y)       (x,y) on OMEGA
For simplicity, OMGEA is a unit square. I have 3 test problems (courtesy
of Dr. S. Fulton)

Test 1.   f(x,y) = -x^2(1-x^2)(2-12y^2) - y^2(1-y^2)(2-12x^2),
g(x,y) =  x^2*y^2(1-x^2)(1-y^2).
Test 2.   f(x,y) = -(x^2 + y^2)*exp(xy),
g(x,y) =  exp(xy).
Test 3.   f(x,y) =  52*cos(2x + 6y),
g(x,y) =  cos(4x + 6y).

Conditions and Cost: 5-point finite difference discretization. V(1,1)-cycle
algorithm with point Red-Black Gauss-Seidel, injection and bi-linear
interpolation.  Fortran 77, double precision, stop when L2-error < 10^(-9).
Meshsize h= 1/N. Initial guess U(x,y)=0. Computer is a SUN  SPARCstation.
Below are the best results I got:

N     Test 1      Test 2       Test 3
16       9           11           10
32       9           11           11            These are V(1,1) cycle
64       9           12           12            numbers, i.e. the iteration
128      9           13           12            numbers.
256      9           13           13
512      9           14           13

If you know better results with comparable cost, would you please send
me an email? I'm also interested in knowing the limit of improving these
results,  so if you know better results with slightly higher cost, I
will appreciate your sending me a message. (I can modify the code to give
slightly better data to some entry, but the above is the best on average.)

Jun Zhang                 zhang@math.gwu.edu
Department of Mathematics
George Washington University
Washington, DC 20052

Editor's Note: I would have used a nested iteration V cycle myself, but
-------------  there is an algorithm using nonstandard grids which is a
direct method effectively (1 iteration, 0 contraction
factor) by (I think) Ruge and Stuben (correction?).  Also,
some of the multiple coarse space methods are similar to
this (e.g., see a paper by Brezzi, me, and Marini in the
MGNet bibliography for an 8 coarse grid decomposition of
this problem).

requestor.

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

Date: Wed, 31 May 1995 17:33:57 +0200 (MESZ)
From: Ulrich Ruede
Subject: New paper on MGNet

My paper

Stability of implicit extrapolation methods

has been downloaded to the mgnet ftp repository.  This paper has been
submitted to the proceedings of the 8th International Conference on Domain
Decomposition, May 16-20, Beijing, China.

Keywords: Implicit extrapolation, multigrid, multilevel subspace splitting
AMS Classification:     65N22, 65N50, 65N55}

Abstract

Multilevel methods are generally based on a splitting of the solution
space associated with a nested sequence of coarser grids.  Besides the
straightforward application of extrapolation on the grid system, we
propose to use extrapolation implicitly, similar to multigrid
tau-extrapolation.  This implicit extrapolation, when applied to linear
finite elements is related to the p-version of the finite element
method.  The method depends on a stability condition which must be
enforced by a suitable modification of the problem.

This (and others of may papers) are available from mgnet and in the WWW
through URL

http://www5.informatik.tu-muenchen.de/persons/ruede/info/refs.html

Ulrich Ruede
Institut fuer Informatik, Technische Universitaet,
D-80290 Muenchen, Germany, e-mail: ruede@informatik.tu-muenchen.de
Tel: +49 89 21058238, Fax: +49 89 21052022
URL: http://www5.informatik.tu-muenchen.de/persons/ruede.html

Editor's Note: in mgnet/papers/Ruede/stable_extra.ps.gz and
-------------     mgnet/papers/Ruede/stable_extra.abstract.

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

Date:   Wed, 31 May 1995 17:59:39 +0200 (MESZ)
Subject: Announcement of WWW multigrid tutorial
From: Ulrich Ruede

On the WWW an

Online Multigrid Tutorial,

the

Multigrid Workbench

is available. The start page is accessible through URL

http://www5.informatik.tu-muenchen.de/sci-comp/xwb/xwb.html

The workbench features an active image showing a standard multigrid
V-cycle algorithm. By clicking on parts of this algorithm, the
corresponding status of the iteration is displayed graphically. In
contrast to conventional text, there is no natural sequence, how the
different pages should be read.  All information is accessible by

I'd appreciate any feedback and comments that would help me to improve
this resource. I'd also be interested in hearing about technical
problems, e.g. whether the current network speed (in Germany) is still
acceptable for using the workbench in its present form.

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

Date: Wed, 31 May 1995 13:48:39 -0400
From: douglas@watson.ibm.com (Craig Douglas)
Subject: Paper on cache based multigrid

Caching in with Multigrid Algorithms: Problems in Two Dimensions

Craig C. Douglas

IBM T. J. Watson Research Center,
Yorktown Heights, NY, USA
and
Computer Science Department,
Yale University,
New Haven, CT, USA

Abstract

Multigrid methods combine a number of standard sparse matrix techniques.
Usual implementations separate the individual components (e.g., an iterative
methods, residual computation, and interpolation between grids) into nicely
structured routines.  However, many computers today employ quite sophisticated
and potentially large caches whose correct use are instrumental in gaining
much of the peak performance of the processors.

We investigate when it makes sense to combine several of the multigrid
components into one, using block oriented algorithms.  We determine how large
(or small) the blocks must be in order for the data in the block to just fit
into the processor's primary cache.  By re-using the data in cache several
times, a potential savings in run time can be predicted.  This is analyzed for
a set of examples.

Key words:  multigrid, cache, sparse matrix, iterative methods, domain
decomposition.

Note:  This paper will be in the proceedings of the International Conference
on Parallel Algorithms, October 15-19, Wuhan, China.

Editor's Note: in mgnet/papers/Douglas/cache1.dvi.gz and
-------------     mgnet/papers/Douglas/cache1.abs.

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

Date: Wed, 31 May 1995 12:24:30 +0200
From: P.W.Hemker@cwi.nl
Subject: Oberwolfach

Dear Craig,

Please find below the titles of the talks, as announced in Oberwolfach.  Sue

I also add a list of participants.

Pieter.

Monday
AM

P. Wesseling "Multigrid solution of the incompressible Navier-Stokes equations
in general coordinates"
("Krylov subspace and multigrid methods applied to the
incompressible Navier-Stokes equations" (with C. Vuik, S. Zeng))
K. Oosterlee "Multigrid and defect correction for the 3D incompressible
Navier-Stokes equations in general coordinates"
("A GMRES-based plane smoother in multigrid for solving
3D anisotropic fluid flow problems")
E. Dick      "Multigrid methods of Navier-Stokes equations coupled to
k-$\epsilon$- turbulence equations"
("Modelling transitional fronts")
D. Haenel    "Application of multi-sequence Runge-Kutta methods to
adaptive solutions of the Navier-Stokes equations"
("Computation of compressible strongly unsteady flows on algebraic
unstructured grids")

PM
U. Ruede     "Implicit multilevel extrapolation methods"
J. Dendy     "Variants of the frequency decomposition MG-method"
("Grandchild of the frequency decomposition method")
R. Stevenson "Frequency decomposition multilevel methods"
("Multilevel methods based on space decompositions orthogonal
w.r.t. discrete scalar products")

Tuesday
AM
S. Vandewalle "Acceleration of multilevel domain decomposition and multigrid
by Krylov subspace methods"
("Schwarz methods: to symmetrize or not to symmetrize")
A. Meyer      "Preconditioning the pseudo-Laplacian for CFD-simulation"
M. Jung       "On the parallelization of multigrid methods using a
nonoverlapping DD data structure"
G. Haase      "Dirichlet DD vs. global multigrid methods" (with U. Langer)

PM
S. Brenner    "Convergence of nonconforming or nonnested multigrid methods
without full elliptic regularity"
S. Turek      "On robust and efficient multilevel Schur-complement solvers
for incompressible and compressible Stokes and Navier-Stokes
equations"
D. Braess     "Efficient smoothing of the Navier-Stokes equations by
u-dominant iterations" (with R. Sarazin)

Wednesday
AM
M. Feistauer  "Numerical solution of nonlinear convection-diffusion problems
and applications to compressible fluid flow"
A. Reusken    "Analysis of multigrid methods for convection-diffusion problems"
J. Fuhrmann   "On algebraic multigrid methods for PDEs"
N. Neuss      "Homogenization and multigrid"

PM
hike

Thursday
AM
P. Oswald    "Multilevel preconditioners for nonconforming elements"
J. Junkherr  "Multigrid methods for weakly singular integral equations of the
first kind"
R. Kornhuber "A posteriori error estimates for linear and nonlinear elliptic
problems"

PM
R. Bank   "An algorithm for coarsening unstructured meshes" (with J. Xu)
S. Sauter "Composite finite element spaces, coarsening and MG methods"
("A new finite element space for the approx. of PDEs on domains
with complicated microstructures") (with W. Hackbusch)
R. Hoppe  "Adaptive multilevel methods for mixed FEM for 2nd order
elliptic BVPs"  (with B. Wohlmuth)

Friday
AM
F. Bornemann "Cascadic multigrid methods"  (with P. Deuflhard)
C. Wagner    "Filtering decompositions for asymmetric and heterogeneous
problems"
("Frequency filtering decomposition")
P. Vanek     "Algebraic multigrid for thin elastic problems"
("Algebraic multigrid by smoothed aggregation for 2nd and
4th order elliptiv BVPs" (with J. Mandel and M. Brezina)
W. Mulder    "Application of multigrid to porous media flow"

========================================================================

Participants:

rbank@ucsd.edu                          (Randy Bank),
peter@ica3.uni-stuttgart.de             (Peter Bastian),
juergen@na.mathematik.uni-tuebingen.de  (Juergen Bey),
bornemann@zib-berlin.de                 (Folkmar Bornemann),
braess@num.ruhr-uni-bochum.de           (Dietrich Braess),
brenner@math.scarolina.edu              (Susanne Brenner),
dahmen@igpm.rwth-aachen.de              (Wolfgang Dahmen),
jed@lanl.gov                            (J.E. Dendy),
deuflhard@zib-berlin.de                 (Peter Deuflhard),
Erik.Dick@rug.ac.be                     (Erik Dick),
FEIST@MS.MFF.CUNI.CZ                    (Miloslav Feistauer),
fuhrmann@iaas-berlin.d400.de            (Juergen Fuhrmann),
griebel@informatik.tu-muenchen.de       (Michael Griebel),
ghaase@numa.uni-linz.ac.at              (Gundolf Haase),
wh@informatik.uni-kiel.de               (Wolfgang Hackbusch),
hj454ha@vug.uni-duisburg.de             (Dieter Haenel),
pieth@cwi.nl                            (Piet Hemker),
rohop@mathematik.tu-muenchen.de         (Ronald Hoppe),
dr.michael.jung@mathematik.tu-chemnitz.de  (Michael Jung),
jj@informatik.uni-kiel.de               (Joerg Junkherr),
kornhuber@iaas-berlin.d400.de           (Ralf Kornhuber),
ulanger@miraculix.numa.uni-linz.ac.at   (Ulrich Langer),
maitre@cc.ec-lyon.fr                    (Jean-Francois Maitre),
a.meyer@mathematik.tu-chemnitz.de       (Arndt Meyer),
mittelmann@math.la.asu.edu              (Hans D. Mittelmann),
mulderw@ksepl.nl                        (W. A. Mulder),
neuss@iwr.uni-heidelberg.de             (Nikolas Neuss),
KEES.OOSTERLEE@GMD.DE                   (K. Oosterlee),
Peter.Oswald@math.tamu.edu              (Peter Oswald),
WSANAR@WIN.TUE.NL                       (Arnold Reusken),
ruede@informatik.tu-muenchen.de         (Ulrich Ruede),
sas@informatik.uni-kiel.de              (Stefan Sauter),
stevenso@win.tue.nl                     (Rob Stevenson),
ture@gaia.iwr.uni-heidelberg.de         (Stefan Turek),
STEFAN@AMA.CALTECH.EDU                  (Stefan Vandewalle),
rv@silly.num1.ruhr-uni-bochum.de        (Ruediger Verfuerth),
chris@ica3.uni-stuttgart.de             (Christian Wagner),
p.wesseling@math.tudelft.nl             (Pieter Wesseling),
wieners@ica3.uni-stuttgart.de           (Wieners),
wittum@icasun.ica.uni-stuttgart.de      (Gabriel Wittum),
harry@na.uni-tuebingen.de               (Harry Yserentant)

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

Date: Wed, 31 May 1995 14:20:32 -0400
From: douglas-craig@CS.YALE.EDU (Craig Douglas)
Subject: An MPI based multigrid solver for 1 or more processors

At the Copper Mountain meeting, I talked very briefly one evening at a
workshop about what I thought was new and interesting for parallel multigrid.
I pointed out that MPI is a standard, developed by academics and computer
companies, that is actually appearing to make headway as a very nice
parallel computer message passing system.  I even ran a demonstration on an
IBM ThinkPad (running Linux, not DOS/Windows) of how it works on a single
processor, but fakes the system into simulating (quasi-randomly) a
multiprocessor.  I volunteered to put a demonstration code on MGNet, which I
have done, in Codes/douglas.  There are several examples in 2D (Poisson's
equation and variable coefficients) with a variety of matrix storage formats
(including matrix-free).  They can be modified quite easily.

I will put some 3D codes out when they are cleaned up sufficiently.

These codes are not meant for high speed, just to demonstrate how MPI can be
used in interesting ways (such as transferring non-stride 1 data without
having to pack and unpack data yourself).

One word of warning.  I used the experimental version (1.0.9) of mpich that is
in pub/mpi/misc on info.mcs.anl.gov and also IBM's MPI product for the SP2 in
developing this.  With mpich, I found that one of the routines (the
simulataneous send and receive routine) did not quite work correctly on a mesh
of processors (it worked with the IBM product).  Bill Gropp fixed this within
2 hours of hearing about it and pointed me to a newer version (many thanks,
Bill).

Editor's Note: in mgnet/Codes/douglas/2d.tgz.
-------------

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

Date: Wed, 31 May 1995 14:19:28 -0400
From: douglas-craig@CS.YALE.EDU (Craig Douglas)
Subject: Some of the new entries in the bibliography

This is somewhat repetitive (my apologies).  The next batch is in next month's
digest.

\begin{thebibliography}{100}

\bibitem{VIAgoshkov_1994a}
{\sc V.~I. Agoshkov}, {\em Domain decomposition methods using modified basis
functions}, in Domain Decomposition Methods in Science and Engineering: The
Sixth International Conference on Domain Decomposition, vol.~157 of
Contemporary Mathematics, Providence, Rhode Island, 1994, American
Mathematical Society, pp.~3--15.

\bibitem{GAguilar_FLisbona_1994a}
{\sc G.~Aguilar and F.~Lisbona}, {\em Interface conditions for a kinf of non
linear elliptic--hyperbolic problems}, in Domain Decomposition Methods in
Science and Engineering: The Sixth International Conference on Domain
Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode
Island, 1994, American Mathematical Society, pp.~89--95.

\bibitem{RArina_CCanuto_1994a}
{\sc R.~Arina and C.~Canuto}, {\em A {X}--formulation of the viscous--inviscid
domain decomposition for the {E}uler/{N}avier--{S}tokes equations}, in Domain
Decomposition Methods in Scientific and Engineering Computing: Proceedings of
the Seventh International Conference on Domain Decomposition, vol.~180 of
Contemporary Mathematics, Providence, Rhode Island, 1994, American
Mathematical Society, pp.~453--458.

\bibitem{SFAshby_CTKelley_PESaylor_JSScroggs_1994a}
{\sc S.~F. Ashby, C.~T. Kelley, P.~E. Saylor, and J.~S. Scroggs}, {\em
Preconditioning via asymptotically--defined decomposition}, in Domain
Decomposition Methods in Scientific and Engineering Computing: Proceedings of
the Seventh International Conference on Domain Decomposition, vol.~180 of
Contemporary Mathematics, Providence, Rhode Island, 1994, American
Mathematical Society, pp.~139--150.

\bibitem{MAzaiez_AQuarteroni_1994a}
{\sc M.~Azaiez and A.~Quarteroni}, {\em A spectral {S}tokes solver in domain
decomposition methods}, in Domain Decomposition Methods in Scientific and
Engineering Computing: Proceedings of the Seventh International Conference on
Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode
Island, 1994, American Mathematical Society, pp.~151--156.

\bibitem{NSBakhvalov_AVKnyazev_1994a}
{\sc N.~S. Bakhvalov and A.~V. Knyanzev}, {\em Preconditioned iterative methods
in a subspace for linear algebraic equations with large jumps in the
coefficients}, in Domain Decomposition Methods in Scientific and Engineering
Computing: Proceedings of the Seventh International Conference on Domain
Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode
Island, 1994, American Mathematical Society, pp.~157--162.

\bibitem{REBank_JXu_1994a}
{\sc R.~E. Bank and J.~Xu}, {\em The hierarchical basis multigrid method and
incomplete {LU} decompostion}, in Domain Decomposition Methods in Scientific
and Engineering Computing: Proceedings of the Seventh International
Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics,
Providence, Rhode Island, 1994, American Mathematical Society, pp.~163--173.

\bibitem{JDBenamou_YBrenier_1994a}
{\sc J.-D. Benamou and Y.~Brenier}, {\em A domain decomposition method for the
polar factorization of vector fields}, in Domain Decomposition Methods in
Science and Engineering: The Sixth International Conference on Domain
Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode
Island, 1994, American Mathematical Society, pp.~231--236.

\bibitem{BBialecki_XCCai_MDryja_GFairweather_1994a}
{\sc B.~Bialecki, X.-C. Cai, M.~Dryja, and G.~Fairweather}, {\em An additive
{S}charz algorithm for piecewise {H}ermite bicubic orthogonal spline
collocation}, in Domain Decomposition Methods in Science and Engineering: The
Sixth International Conference on Domain Decomposition, vol.~157 of
Contemporary Mathematics, Providence, Rhode Island, 1994, American
Mathematical Society, pp.~237--244.

{\sc P.~E. Bj{\o}rstad, W.~M. Coughran, and E.~Gross}, {\em Parallel domain
decomposition applied to coupled transport equations}, in Domain
Decomposition Methods in Scientific and Engineering Computing: Proceedings of
the Seventh International Conference on Domain Decomposition, vol.~180 of
Contemporary Mathematics, Providence, Rhode Island, 1994, American
Mathematical Society, pp.~369--380.

\bibitem{FABornemann_1994a}
{\sc F.~A. Bornemann}, {\em Interpolation spaces and optimal multilevel
preconditioners}, in Domain Decomposition Methods in Scientific and
Engineering Computing: Proceedings of the Seventh International Conference on
Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode
Island, 1994, American Mathematical Society, pp.~3--8.

\bibitem{JFBourgat_PLeTallec_BPerthame_YQiu_1994a}
{\sc J.~F. Bourgat, P.~LeTallec, B.~Perthame, and Y.~Qiu}, {\em Coupling
{B}oltzmann and {E}uler equations without overlapping}, in Domain
Decomposition Methods in Science and Engineering: The Sixth International
Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics,
Providence, Rhode Island, 1994, American Mathematical Society, pp.~377--398.

\bibitem{ABrambilla_CCarlenzoli_GGazzaniga_PGervasio_GSacchi_1994a}
{\sc A.~Brambilla, C.~Carlenzoli, G.~Gazzaniga, P.~Gervasio, and G.~Sacchi},
{\em Implementation of domain decomposition techniques on n{CUBE}2 parallel
machine}, in Domain Decomposition Methods in Science and Engineering: The
Sixth International Conference on Domain Decomposition, vol.~157 of
Contemporary Mathematics, Providence, Rhode Island, 1994, American
Mathematical Society, pp.~345--351.

\bibitem{JHBramble_JEPasciak_1994a}
{\sc J.~H. Bramble and J.~E. Pasciak}, {\em Uniform convergence estimates for
multigrid {V}--cycle algorithms with less than full elliptic regularity}, in
Domain Decomposition Methods in Science and Engineering: The Sixth
International Conference on Domain Decomposition, vol.~157 of Contemporary
Mathematics, Providence, Rhode Island, 1994, American Mathematical Society,
pp.~17--26.

\bibitem{ABrandt_BDiskin_1994a}
{\sc A.~Brandt and B.~Diskin}, {\em Multigrid solvers on decomposed domains},
in Domain Decomposition Methods in Science and Engineering: The Sixth
International Conference on Domain Decomposition, vol.~157 of Contemporary
Mathematics, Providence, Rhode Island, 1994, American Mathematical Society,
pp.~135--155.

\bibitem{SCBrenner_1994b}
{\sc S.~C. Brenner}, {\em Two--level additive {S}chwarz preconditioners for
nonconforming finite elements}, in Domain Decomposition Methods in Scientific
and Engineering Computing: Proceedings of the Seventh International
Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics,
Providence, Rhode Island, 1994, American Mathematical Society, pp.~9--14.

\bibitem{FBrezzi_LDMarini_1994a}
{\sc F.~Brezzi and L.~D. Marini}, {\em A three--fold domain decomposition
method}, in Domain Decomposition Methods in Science and Engineering: The
Sixth International Conference on Domain Decomposition, vol.~157 of
Contemporary Mathematics, Providence, Rhode Island, 1994, American
Mathematical Society, pp.~27--34.

\bibitem{MOBristeau_RGlowinski_JPeriaux_1994a}
{\sc M.~O. Bristeau, R.~Glowinski, and J.~P{\'e}riaux}, {\em On the numerical
solution of the {H}elmholtz equations at large wave numbers using exact
controllability methods. {A}pplication to scattering}, in Domain
Decomposition Methods in Science and Engineering: The Sixth International
Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics,
Providence, Rhode Island, 1994, American Mathematical Society, pp.~399--419.

\bibitem{HJBungartz_MGriebel_DRoschke_CZenger_1994a}
{\sc H.-J. Bungartz, M.~Griebel, D.~R{/"}oschke, and C.~Zenger}, {\em Two
proofs of convergence for the combination technique for the efficient
solution of sparse grid problems}, in Domain Decomposition Methods in
Scientific and Engineering Computing: Proceedings of the Seventh
International Conference on Domain Decomposition, vol.~180 of Contemporary
Mathematics, Providence, Rhode Island, 1994, American Mathematical Society,
pp.~15--20.

\bibitem{WCai_1994a}
{\sc W.~Cai}, {\em Domain decomposition and computation of two dimensional
detonation waves}, in Domain Decomposition Methods in Scientific and
Engineering Computing: Proceedings of the Seventh International Conference on
Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode
Island, 1994, American Mathematical Society, pp.~459--464.

\bibitem{XCCai_MDryja_1994a}
{\sc X.-C. Cai and M.~Dryja}, {\em Domain decomposition methods for monotone
nonlinear eliptic problems}, in Domain Decomposition Methods in Scientific
and Engineering Computing: Proceedings of the Seventh International
Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics,
Providence, Rhode Island, 1994, American Mathematical Society, pp.~21--27.

\bibitem{XCCai_WDGropp_DEKeyes_MDTidriri_1994a}
{\sc X.-C. Cai, W.~D. Gropp, D.~E. Keyes, and M.~D. Tidriri}, {\em Parallel
implicit methods for aerodynamics}, in Domain Decomposition Methods in
Scientific and Engineering Computing: Proceedings of the Seventh
International Conference on Domain Decomposition, vol.~180 of Contemporary
Mathematics, Providence, Rhode Island, 1994, American Mathematical Society,
pp.~465--470.

\bibitem{YCai_IMNavon_1994a}
{\sc Y.~Cai and I.~M. Navon}, {\em Parallel domain--decomposed preconditioners
in finite element shallow water flow modeling}, in Domain Decomposition
Methods in Scientific and Engineering Computing: Proceedings of the Seventh
International Conference on Domain Decomposition, vol.~180 of Contemporary
Mathematics, Providence, Rhode Island, 1994, American Mathematical Society,
pp.~471--476.

\bibitem{FCamilli_MFalcone_PLanucara_ASeghini_1994a}
{\sc F.~Camilli, M.~Falcone, P.~Lanucara, and A.~Seghini}, {\em A domain
decomposition method for {B}ellman equations}, in Domain Decomposition
Methods in Scientific and Engineering Computing: Proceedings of the Seventh
International Conference on Domain Decomposition, vol.~180 of Contemporary
Mathematics, Providence, Rhode Island, 1994, American Mathematical Society,
pp.~477--483.

\bibitem{CCanuto_ARusso_1994a}
{\sc C.~Canuto and A.~Russo}, {\em Self--adaptive coupling of mathematical
models and/or numerical methods}, in Domain Decomposition Methods in Science
and Engineering: The Sixth International Conference on Domain Decomposition,
vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994,
American Mathematical Society, pp.~35--44.

\bibitem{TFChan_TPMathew_1994b}
{\sc T.~F. Chan and T.~P. Mathew}, {\em Doamin decomposition preconditioners
for convection diffusion problems}, in Domain Decomposition Methods in
Science and Engineering: The Sixth International Conference on Domain
Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode
Island, 1994, American Mathematical Society, pp.~157--175.

\bibitem{TFChan_BFSmith_1994a}
{\sc T.~F. Chan and B.~F. Smith}, {\em Domain decomposition and multigrid
algorithms for elliptic problems on unstructured meshes}, in Domain
Decomposition Methods in Scientific and Engineering Computing: Proceedings of
the Seventh International Conference on Domain Decomposition, vol.~180 of
Contemporary Mathematics, Providence, Rhode Island, 1994, American
Mathematical Society, pp.~175--189.

\bibitem{JGChefter_CKChu_DEKeyes_1994a}
{\sc J.~G. Chefter, C.~K. Chu, and D.~E. Keyes}, {\em Domain decomposition for
the shallow water equations}, in Domain Decomposition Methods in Scientific
and Engineering Computing: Proceedings of the Seventh International
Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics,
Providence, Rhode Island, 1994, American Mathematical Society, pp.~485--490.

\bibitem{NChrisochoides_GFox_JThompson_1994a}
{\sc N.~Chrisochoides, G.~Fox, and J.~Thompson}, {\em {MENUS--PGG}: {A} mapping
environment for unstructured numerical parallel grid generation}, in Domain
Decomposition Methods in Scientific and Engineering Computing: Proceedings of
the Seventh International Conference on Domain Decomposition, vol.~180 of
Contemporary Mathematics, Providence, Rhode Island, 1994, American
Mathematical Society, pp.~381--386.

\bibitem{PGCiarletJr_1994b}
{\sc P.~G. Ciarle{t,~Jr.}}, {\em A comparison of three iterative algorithms
based on domain decomposition methods}, in Domain Decomposition Methods in
Scientific and Engineering Computing: Proceedings of the Seventh
International Conference on Domain Decomposition, vol.~180 of Contemporary
Mathematics, Providence, Rhode Island, 1994, American Mathematical Society,
pp.~387--393.

\bibitem{PGCiarletJr_GMeurant_1994a}
{\sc P.~G. Ciarle{t,~Jr.} and G.~Meurant}, {\em A class of domian decomposition
preconditioners for massively parallel computers}, in Domain Decomposition
Methods in Science and Engineering: The Sixth International Conference on
Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode
Island, 1994, American Mathematical Society, pp.~353--359.

{\sc M.~C. Ciccoli, J.~A. Desideri, and J.~P{\'e}riaux}, {\em Introduction of
domain decomposition techniques in time-- dependent flow problems}, in Domain
Decomposition Methods in Science and Engineering: The Sixth International
Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics,
Providence, Rhode Island, 1994, American Mathematical Society, pp.~433--439.

\bibitem{RKCoomer_IGGraham_1994a}
{\sc R.~K. Coomer and I.~G. Graham}, {\em Domain decomposition methods for
device modelling}, in Domain Decomposition Methods in Scientific and
Engineering Computing: Proceedings of the Seventh International Conference on
Domain Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode
Island, 1994, American Mathematical Society, pp.~491--496.

\bibitem{MCCurran_1994a}
{\sc M.~C. Curran}, {\em An iterative finite--element collocation method for
parabolic problems using domain decomposition}, in Domain Decomposition
Methods in Science and Engineering: The Sixth International Conference on
Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode
Island, 1994, American Mathematical Society, pp.~245--253.

\bibitem{CNDawson_TFDupont_1994b}
{\sc C.~N. Dawson and T.~F. Dupont}, {\em Noniterative domain decomposition for
second order hyperbolic problems}, in Domain Decomposition Methods in Science
and Engineering: The Sixth International Conference on Domain Decomposition,
vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994,
American Mathematical Society, pp.~45--52.

\bibitem{CNDawson_MFWheeler_1994a}
{\sc C.~N. Dawson and M.~F. Wheeler}, {\em Two--grid methods for mixed finite
element approximations of nonlinear parabolic equations}, in Domain
Decomposition Methods in Scientific and Engineering Computing: Proceedings of
the Seventh International Conference on Domain Decomposition, vol.~180 of
Contemporary Mathematics, Providence, Rhode Island, 1994, American
Mathematical Society, pp.~191--203.

\bibitem{FDellagiacoma_SPaoletti_FPoggi_MVitaletti_1994a}
{\sc F.~Dellagiacoma, S.~Paoletti, F.~Poggi, and M.~Vitaletti}, {\em A domain
decomposition environment for local time dependent problems}, in Domain
Decomposition Methods in Science and Engineering: The Sixth International
Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics,
Providence, Rhode Island, 1994, American Mathematical Society, pp.~361--366.

\bibitem{PDeuflhard_1994a}
partial differential equations: algorithm and numerical results}, in Domain
Decomposition Methods in Scientific and Engineering Computing: Proceedings of
the Seventh International Conference on Domain Decomposition, vol.~180 of
Contemporary Mathematics, Providence, Rhode Island, 1994, American
Mathematical Society, pp.~29--42.

\bibitem{ZDostal_1994a}
{\sc Z.~Dost{\'a}l}, {\em The {S}chur complement algorithm for the solution of
contact problems}, in Domain Decomposition Methods in Science and
Engineering: The Sixth International Conference on Domain Decomposition,
vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994,
American Mathematical Society, pp.~441--446.

\bibitem{CCDouglas_1995a}
{\sc C.~C. Douglas}, {\em Madpack: A family of abstract multigrid or multilevel
solvers}, Comput. Appl. Math., 14 (1995), pp.~3--20.

\bibitem{MDryja_1994a}
{\sc M.~Dryja}, {\em Multilevel methods for elliptic problems with
discontinuous coeffiecients in three dimensions}, in Domain Decomposition
Methods in Scientific and Engineering Computing: Proceedings of the Seventh
International Conference on Domain Decomposition, vol.~180 of Contemporary
Mathematics, Providence, Rhode Island, 1994, American Mathematical Society,
pp.~43--47.

\bibitem{MDryja_OBWidlund_1994b}
{\sc M.~Dryja and O.~B. Widlund}, {\em Some recent results on {S}chwarz type
domain decomposition algorithms}, in Domain Decomposition Methods in Science
and Engineering: The Sixth International Conference on Domain Decomposition,
vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994,
American Mathematical Society, pp.~53--61.

\bibitem{OErnst_GHGolub_1994a}
{\sc O.~Ernst and G.~H. Golub}, {\em A domain decomposition approach to solving
the {H}elmholtz equation with a radiation boundary condition}, in Domain
Decomposition Methods in Science and Engineering: The Sixth International
Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics,
Providence, Rhode Island, 1994, American Mathematical Society, pp.~177--192.

\bibitem{EFaccioli_AQuarteroni_ATagliani_1994a}
{\sc E.~Faccioli, A.~Quarteroni, and A.~Tagliani}, {\em Spectral multidomain
methods for the simulation of wave propagation in heterogeneous media}, in
Domain Decomposition Methods in Science and Engineering: The Sixth
International Conference on Domain Decomposition, vol.~157 of Contemporary
Mathematics, Providence, Rhode Island, 1994, American Mathematical Society,
pp.~447--455.

\bibitem{CFarhat_PSChen_1994a}
{\sc C.~Farhat and P.-S. Chen}, {\em Tailoring domain decomposition methods for
efficient parallel coarse grid solution and for systems with many right hand
sides}, in Domain Decomposition Methods in Scientific and Engineering
Computing: Proceedings of the Seventh International Conference on Domain
Decomposition, vol.~180 of Contemporary Mathematics, Providence, Rhode
Island, 1994, American Mathematical Society, pp.~401--406.

\bibitem{CFarhat_FXRoux_1994a}
{\sc C.~Farhat and F.-X. Roux}, {\em The dual {S}chur complement method with
well--posed local {N}eumann problems}, in Domain Decomposition Methods in
Science and Engineering: The Sixth International Conference on Domain
Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode
Island, 1994, American Mathematical Society, pp.~193--201.

\bibitem{PFFischer_1994a}
{\sc P.~F. Fischer}, {\em Parallel domain decomposition for incompressible
fluid dynamics}, in Domain Decomposition Methods in Science and Engineering:
The Sixth International Conference on Domain Decomposition, vol.~157 of
Contemporary Mathematics, Providence, Rhode Island, 1994, American
Mathematical Society, pp.~313--322.

element--by--element method for large--scale computations with h -- p--
finite elements}, in Domain Decomposition Methods in Science and Engineering:
The Sixth International Conference on Domain Decomposition, vol.~157 of
Contemporary Mathematics, Providence, Rhode Island, 1994, American
Mathematical Society, pp.~367--373.

\bibitem{LGastaldi_1994a}
{\sc L.~Gastaldi}, {\em A domain decomposition for the transport equation}, in
Domain Decomposition Methods in Science and Engineering: The Sixth
International Conference on Domain Decomposition, vol.~157 of Contemporary
Mathematics, Providence, Rhode Island, 1994, American Mathematical Society,
pp.~97--102.

\bibitem{AGersztenkorn_JCDiaz_1994a}
{\sc A.~Gersztenkorn and J.~C. Diaz}, {\em Domain decomposed preconditioning
for faulted geological blocks}, in Domain Decomposition Methods in Science
and Engineering: The Sixth International Conference on Domain Decomposition,
vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994,
American Mathematical Society, pp.~457--462.

\bibitem{LGiraud_RSTuminaro_1994a}
{\sc L.~Giraud and R.~S. Tuminaro}, {\em Domain decomposition algorithms for
{PDE} problems with large scale variation}, in Domain Decomposition Methods
in Scientific and Engineering Computing: Proceedings of the Seventh
International Conference on Domain Decomposition, vol.~180 of Contemporary
Mathematics, Providence, Rhode Island, 1994, American Mathematical Society,
pp.~205--210.

\bibitem{RGlowinski_TWPan_JPeriaux_1994a}
{\sc R.~Glowinski, T.-W. Pan, and J.~P{\'e}riaux}, {\em A fictitious domain
method for unsteady incompressible viscous flow modelled by
{N}avier--{S}tokes equations}, in Domain Decomposition Methods in Science and
Engineering: The Sixth International Conference on Domain Decomposition,
vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994,
American Mathematical Society, pp.~421--431.

\bibitem{RGlowinski_TWPan_JPeriaux_1994b}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em A one shot domain
decomposition/fictitious domain method for {N}avier--{S}tokes equations}, in
Domain Decomposition Methods in Scientific and Engineering Computing:
Proceedings of the Seventh International Conference on Domain Decomposition,
vol.~180 of Contemporary Mathematics, Providence, Rhode Island, 1994,
American Mathematical Society, pp.~211--222.

\bibitem{MGriebel_1994b}
{\sc M.~Griebel}, {\em Domain--oriented multilevel methods}, in Domain
Decomposition Methods in Scientific and Engineering Computing: Proceedings of
the Seventh International Conference on Domain Decomposition, vol.~180 of
Contemporary Mathematics, Providence, Rhode Island, 1994, American
Mathematical Society, pp.~223--229.

\bibitem{MGriebel_1994a}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em A domain
decomposition method using sparse grids}, in Domain Decomposition Methods in
Science and Engineering: The Sixth International Conference on Domain
Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode
Island, 1994, American Mathematical Society, pp.~255--261.

\bibitem{WDGropp_DEKeyes_JSMounts_1994a}
{\sc W.~D. Gropp, D.~E. Keyes, and J.~S. Mounts}, {\em Implicit domain
decomposition algorithms for steady, compressible aerodynamics}, in Domain
Decomposition Methods in Science and Engineering: The Sixth International
Conference on Domain Decomposition, vol.~157 of Contemporary Mathematics,
Providence, Rhode Island, 1994, American Mathematical Society, pp.~203--213.

\bibitem{WDGropp_BFSmith_1994a}
{\sc W.~D. Gropp and B.~F. Smith}, {\em Experiences with domain decomposition
in three dimensions: overlapping {S}chwarz methods}, in Domain Decomposition
Methods in Science and Engineering: The Sixth International Conference on
Domain Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode
Island, 1994, American Mathematical Society, pp.~323--333.

\bibitem{JLGuermond_WZShen_1994a}
{\sc J.-L. Guermond and W.-Z. Shen}, {\em A domain decomposition method for
simulating 2{D} external viscous flows}, in Domain Decomposition Methods in
Science and Engineering: The Sixth International Conference on Domain
Decomposition, vol.~157 of Contemporary Mathematics, Providence, Rhode
Island, 1994, American Mathematical Society, pp.~463--467.

\bibitem{WHeinrichs_1994b}
{\sc W.~Heinrichs}, {\em Domain decomposition for the {S}tokes equations in
streamfunction formulation}, in Domain Decomposition Methods in Science and
Engineering: The Sixth International Conference on Domain Decomposition,
vol.~157 of Contemporary Mathematics, Providence, Rhode Island, 1994,
American Mathematical Society, pp.~263--269.

\bibitem{MHolst_FSaied_1994a}
{\sc M.~Holst and F.~Saied}, {\em Multigrid and domain decomposition methods
for electrostatics problems}, in Domain Decomposition Methods in Scientific
and Engineering Computing: Proceedings of the Seventh International
Conference on Domain Decomposition, vol.~180 of Contemporary Mathematics,
Providence, Rhode Island, 1994, American Mathematical Society, pp.~231--238.

\bibitem{GCHsiao_MDMarcozzi_SZhang_1994a}
{\sc G.~C. Hsiao, M.~D. Marcozzi, and S.~Zhang}, {\em An efficient
computational method for the flow past an airfoil}, in Domain Decomposition
Methods in Scientific and Engineering Computing: Proceedings of the Seventh
International Conference on Domain Decomposition, vol.~180 of Contemporary
Mathematics, Providence, Rhode Island, 1994, American Mathematical Society,
pp.~497--502.

\end{thebibliography}

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

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