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)
                             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 6 (approximately June 30, 1995)

Today's topics:

     Best V-cycle Algorithm for 2D Poisson Equation
     Multigrid tutorial, with applications to molecular dynamics
     MGLab on MGNet
     Overhaul of 1993 Copper Mountain electronic proceedings
     Some of the new entries in the bibliography

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

Date: Fri, 30 June 1995 17:00:01 -0400
From: douglas-craig@CS.YALE.EDU (Craig Douglas)
Subject: Best V-cycle Algorithm for 2D Poisson Equation

The message in the last issue from

    Jun Zhang 

in the last issue sparked several interesting responses (one of which is still
open).  Due to a couple of unexpected trips that I took this month, I have not
yet had a chance to edit these and see if the last open question can be
answered.  Stay tuned until next month.

Craig

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

Date: Wed, 14 Jun 95 15:05:34 +0300
From: MABRANDT@WEIZMANN.weizmann.ac.il
Subject: Multigrid tutorial, with applications to molecular dynamics

                   MULTIGRID TUTORIAL, WITH APPLICATIONS TO
                              MOLECULAR DYNAMICS


                                October 10-12

                        Weizmann Institute of Science
                               Rehovot, Israel



Current molecular mechanics algorithms severely restrict the modelling efforts
to relatively small molecular systems and/or tiny evolution intervals, since
their computing cost rises very steeply with problem size.  Model studies have
shown that this steep rise can be substantially reduced by combining several
types of multiscale methods.  These are multigrid-like methods, based on
designing a hierarchy of molecular motions on increasingly larger scales, with
several kinds of inter-scale interactions.  For large molecular structures,
such methods might yield the following benefits:

(1) fast energy minimization;

(2) fast solution of the implicit systems of equations needed to
    perform large time steps in dynamics simulations;

(3) fast calculation and compact description of a multitude of
    normal modes;

(4) elimination of the slowing down and fast convergence of
    statistics in equilibrium Monte-Carlo calculations;

(5) efficient combination of small-scale statistics with
    large-scale dynamics; and

(6) direct computation of bulk material properties.

The course will teach the elements of the multigrid methods for PDEs;
algebraic multigrid (AMG), especially for non-PDE problems; multi-scale
Monte-Carlo techniques; fast multi-scale summation of long-range forces; and
global optimization by multi-level annealing.  First steps in introducing such
methods to molecular systems will be reported.  Also, poster sessions on
molecular mechanics and dynamics will be given by some of the course
participants, exposing the audience to a large number of other topics and
ideas.

The course will assume an audience with a good working knowledge of numerical
methods and a strong interest in molecular mechanics and dynamics simulations.

Registration fee is $50.00.  The number of participants will be limited.  Some
background reading material will be suggested and/or sent upon request.

People interested in participating should contact the course secretary:

             Ms. Carol Weintraub
             Dept. of Applied Math. & Computer Science
             The Weizmann Institute of Science
             Rehovot 76100, Israel
             email: carol@wisdom.weizmann.ac.il
             tel: 972-8-343545

Organizers:     Achi Brandt
----------      email: mabrandt@weizmann.weizmann.ac.il

                Tamar Schlick
                email: schlick@nyu.edu

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

Date: Tue, 20 Jun 1995 15:31:06 -0500 (CDT)
From: bordner@ta18.cs.uiuc.edu
Subject: MGLab on MGNet

Craig,

I have uploaded the files MGLab1.0.tar and MGLab.README to casper.cs.yale.edu
in /mgnet/incoming.  Note that MGLab.README is identical to the file README in 
the tar file.

There are no constraints for using MGLab, it is public domain software.

James

    Editor's Note: in mgnet/Codes/mglab/MGLab1.0.tgz.
    -------------  Here is the MGLab.README file:

What is MGLab?

    MGLab is a set of public domain Matlab functions that defines an 
    interactive environment for experimenting with multigrid algorithms.  The 
    package solves two-dimensional elliptic partial differential equations 
    using finite differences and includes several built-in problems (Poisson
    Helmholtz, discontinuous coefficient problems and non-self adjoint
    problems).  A number of parameters controlling the V-cycle can be set
    using a point and click mechanism.  The menu-based user interface also
    allows a choice of several Krylov subspace accelerators (PCG, GMRES(k),
    BiCG/STAB).  The package exploits Matlabs visualization and
    sparse matrix features and has been structured to be extensible.

MGLab Files

    The Graphical User Interface
 
        MGLab.m
        show_params.m
        set_defaults.m
        run.m
        multigrid_setup.m
        menu_header.m
        menu_item.m
        version_info.m
        Contents.m
    
    Global Variables
    
        include_globals.m
        extract_globals.m
        include_flags.m
        include_figs.m
    
    Linear Systems
    
        get_matrix.m
        sp_laplace.m
        sp_cutsq2d.m
        sp_convdiff.m
        get_rhs.m
    
    Solvers
    
        solve.m
        converged.m
        vmg.m
        fmg.m
        pcg.m
        pcgs.m
        pbicgstab.m
        pgmres.m
        sor.m
        get_SOR_omega.m
    
    Preconditioners
    
        precondition.m
        precond_mg.m
    
    Results
    
        update_results.m
    
    Multigrid Routines: High Level
    
        mg_cycle.m
        vmg_cycle.m
        fmg_cycle.m
        wmg_cycle.m
        halfvmg_cycle.m
    
    Multigrid Routines: Middle Level
    
        smooth.m
        residual.m
        restrict.m
        coarse_grid_solve.m
        interpolate.m
        sp_prolong.m
    
    Multigrid Routines: Low Level
    
        coarsest.m
        max_level.m
    
    Demos
    
        demo_globals.m
        demo1.m
        demo1_run.m
        demo2.m
        demo2_run.m
        demo2_Vcycle.m 
        demo3.m
        demo3_run.m
        demo3_vmg.m
        sint.m
        sint2.m
   
Documentation
 
    Thanks to Craig Douglas, a PostScript version of a short paper describing
    MGLab is available from mgnet.  The paper can be retrieved by anonymous
    ftp to
                ftp.cerfacs.fr
    or          casper.cs.yale.edu
    in the directory
                pub/mgnet/Conferences/CopperMtn95
    The name of the file is
                bordner_saied.ps.gz
 
    To run MGLab, simply start up Matlab (Version 4.0 or later) and type
    `MGLab'.  You may wish to include this directory in your Matlab path by
    typing `path (path,pwd)' while in your MGLab directory.

Future Releases
 
    Comments about and suggestions for improvements of the code are welcome:
    we plan to have future versions of MGLab that incorporate enhancements and
    bug fixes.  To be put on a mailing list to be informed of new versions,
    send email to James Bordner (bordner@cs.uiuc.edu).

Revision History
   
       10 June 1995 V1.00beta: Initial release
       20 June 1995 V1.0:      SOR solver added

James Bordner (bordner@cs.uiuc.edu)
Faisal Saied (saied@cs.uiuc.edu)
University of Illinois at Urbana-Champaign
Department of Computer Science
20 June 1995

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

Date: Fri, 30 June 1995 16:47:18 -0400
From: douglas@mlat.watson.ibm.com (Craig Douglas)
Subject: Overhaul of 1993 Copper Mountain electronic proceedings

Those of you who access MGNet through the World Wide Web can now view the
electronic version of the 1993 Copper Mountain proceedings in what I think is
a much nicer manner.  You can see the papers or abstracts conveniently
(particularly if your web browser understands HTML 3.0 tags like ).
You can point and click on just what you want.

What was done here will also be done to the 1995 proceedings over the next
month or so.  Hence, any feedback would be appreciated.

Thanks,
Craig

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

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 a bit repetitious, but next month's entries will be from all over the
place.

Sorry about this...
Craig

\begin{thebibliography}{100}

\bibitem{MIsraeli_LVozovoi_AAverbuch_1994a}
{\sc M.~Israeli, L.~Vozovoi, and A.~Averbuch}, {\em Domain decomposition
  methods with local {F}ourer basis for parabolic 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.~223--230.

\bibitem{PGJacobs_VAMousseau_PRMcHugh_DAKnoll_1994a}
{\sc P.~G. Jacobs, V.~A. Mousseau, P.~R. McHugh, and D.~A. Knoll}, {\em
  Newton--{K}rylov--{S}chwarz techniques applied to the two--dimensional
  imcompressible {N}avier--{S}tokes and energy 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.~503--507.

\bibitem{EKatzer_1994a}
{\sc E.~Katzer}, {\em A parallel subspace decomposition method for hyperbolic
  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.~239--244.

\bibitem{DEKeyes_JXu_1994a}
{\sc D.~E. Keyes and J.~Xu}, {\em Domain Decomposition Methods in Scientific
  and Engineering Computing: Proceedings of the Seventh International
  Conference on Domain Decomposition}, vol.~180 of Contemporary Mathematics,
  American Mathematical Society, Providence, Rhode Island, 1994.

\bibitem{SKim_1994a}
{\sc S.~Kim}, {\em Numerical treatments for the {H}elmholtz problem by domain
  decomposition techniques}, 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.~245--250.

\bibitem{RKornhuber_HYserentant_1994a}
{\sc R.~Kornhuber and H.~Yserentant}, {\em Multilevel methods for elliptic
  problems on domains not resolved by the coarse grid}, 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.~49--60.

\bibitem{HCKu_HEGilreath_RRaul_JCSommerer_1994a}
{\sc H.~C. Ku, H.~E. Gilreath, R.~Raul, and J.~C. Sommerer}, {\em Direct
  numerical simulation of jet flow via a multi--block technique}, 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.~509--514.

\bibitem{YAKuznetsov_1994a}
{\sc Yu.~A. Kuznetsov}, {\em Overlapping domain decomposition methods for
  parabolic 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.~63--69.

\bibitem{YAKuznetsov_PNeittaanmaki_PTarvainen_1994a}
{\sc Yu.~A. Kuznetsov, P.~Neittaanm{\"a}ki, and P.~Tarvainen}, {\em Overlapping
  domain decomposition methods for the obstacle problem}, 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.~271--277.

\bibitem{YAKuznetsov_PNeittaanmaki_PTarvainen_1994b}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em Schwarz methods for
  obstacle problems with convection-- diffusion operators}, 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.~251--256.

\bibitem{CHLai_1994a}
{\sc C.~H. Lai}, {\em An iterative scheme for non--symmetric interface
  operator}, 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.~279--285.

\bibitem{CHLai_1994b}
{\sc C.-H. Lai}, {\em On domain decomposition and shooting methods for
  two--point boundary value 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.~257--263.

\bibitem{ULanger_1994a}
{\sc U.~Langer}, {\em Parallel iterative solution of symmetric coupled
  {FE}/{BE}--equations via 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.~335--344.

\bibitem{WLayton_JMaubach_PRabier_1994a}
{\sc W.~Layton, J.~Maubach, and P.~Rabier}, {\em Robust methods for highly
  nonsymmetric 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.~265--270.

\bibitem{PLeTallec_JMandel_MVidrascu_1994a}
{\sc P.~LeTallec, J.~Mandel, and M.~Vidrascu}, {\em Balancing domain
  decomposition for plates}, 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.~515--524.

\bibitem{PLeTallec_TSassi_MVidrascu_1994a}
{\sc P.~LeTallec, T.~Sassi, and M.~Vidrascu}, {\em Three--dimensional domain
  decomposition methods with nonmatching grids and unstructured coarse
  solvers}, 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.~61--74.

\bibitem{ILie_1994a}
{\sc I.~Lie}, {\em Interface conditions for heterogeneous domain decomposition:
  {C}oupling of different hyperbolic systems}, 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.~469--476.

\bibitem{HXLin_1994a}
{\sc H.~X. Lin}, {\em Analysis and implementation of {DD} methods for parallel
  {FE} computations}, 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.~407--412.

\bibitem{NJLybeck_KLBowers_1994a}
{\sc N.~J. Lybeck and K.~L. Bowers}, {\em Domain decomposition via the
  {S}inc--{G}alerkin method for second order differential 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.~271--276.

\bibitem{JMandel_1994a}
{\sc J.~Mandel}, {\em Hybrid domain decomposition with unstructured
  subdomains}, 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.~103--112.

\bibitem{DMansutti_FPitolli_1994a}
{\sc D.~Mansutti and F.~Pitolli}, {\em Simultation of 3{D} {N}avier--{S}tokes
  flows via domain decomposition by the modified discrete vector potential
  model}, 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.~477--482.

\bibitem{MRMehrabi_RABrown_1994a}
{\sc M.~R. Mehrabi and R.~A. Brown}, {\em Finite--element/{N}ewton method for
  solution of nonlinear problems in transport processes using domain
  decomposition and nested dissection on {MIMD} parallel computers}, 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.~413--425.

\bibitem{PMejzlik_1994a}
{\sc P.~Mejzl{\'i}k}, {\em A bisection method to find all solutions of a system
  of nonlinear 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.~277--282.

\bibitem{SMicheletti_AQuarteroni_RSacco_1994a}
{\sc S.~Micheletti, A.~Quarteroni, and R.~Sacco}, {\em Nonlinear block
  iterative solution of semiconductor device equations by a domain
  decomposition method}, 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.~525--531.

\bibitem{IDMishev_1994a}
{\sc I.~D. Mishev}, {\em Preconditioning cell--centered finite difference
  equations on grids with local refinement}, 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.~283--288.

\bibitem{MMu_JRRice_1994a}
{\sc M.~Mu and J.~R. Rice}, {\em Modeling with collaborating {PDE} solvers:
  Theory and practice}, 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.~427--438.

\bibitem{FNataf_FRogier_1994a}
{\sc F.~Nataf and F.~Rogier}, {\em Factorization of the convection--diffusion
  operator and a (possibly) non overlapping {S}chwarz 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.~287--292.

\bibitem{FNataf_FRogier_1994b}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em Outflow boundary
  conditions and domain decomposition method}, 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.~289--293.

\bibitem{SVNepomnyaschikh_1994a}
{\sc S.~V. Nepomnyaschikh}, {\em Domain decomposition for elliptic problems
  with large condition numbers}, 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.~75--85.

\bibitem{JTOden_APatra_YFeng_1994a}
{\sc J.~T. Oden, A.~Patra, and Y.~Feng}, {\em Domain decomposition for adaptive
  hp finite element 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.~295--301.

\bibitem{POswald_1994a}
{\sc P.~Oswald}, {\em Stable subspace splittings for {S}obolev spaces and
  domain decomposition algorithms}, 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.~87--98.

\bibitem{SVParter_1988a}
{\sc S.~V. Parter}, {\em Estimates for multigrid methods based on red--black
  {G}auss--{S}eidel smoothings}, Numer. Math., 52 (1988), pp.~701--723.

\bibitem{LFPavarino_1994c}
{\sc L.~F. Pavarino}, {\em Some {S}chwarz algorithms for the {P}--version
  finite element 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.~113--119.

\bibitem{LFPavarino_1994d}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em A wire basket based
  method for spectral elements 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.~99--104.

\bibitem{MPernice_1994a}
{\sc M.~Pernice}, {\em Domain decomposed preconditioners with {K}rylov methods
  as subdomain solvers}, 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.~303--309.

\bibitem{APothen_1994a}
{\sc A.~Pothen}, {\em An analysis of spectral graph partitioning via quadratic
  assignment 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.~105--110.

\bibitem{AQuarteroni_JPeriaux_YAKuznetsov_OBWidund_1994a}
{\sc A.~Quarteroni, J.~P{\'e}riaux, Yu.~A. Kuznetsov, and O.~B. Widund}, {\em
  Domain Decomposition Methods in Science and Engineering: The Sixth
  International Conference on Domain Decomposition}, vol.~157 of Contemporary
  Mathematics, American Mathematical Society, Providence, Rhode Island, 1994.

\bibitem{AQuarteroni_AValli_1994a}
{\sc A.~Quarteroni and A.~Valli}, {\em Numerical Approximation of Partial
  Differential Equations}, Springer--Verlag, Berlin, 1994.

\bibitem{IRaspo_JOuazzani_RPeyret_1994a}
{\sc I.~Raspo, J.~Ouazzani, and R.~Peyret}, {\em A direct {C}hebyshev
  multidomain method for flow computation with application to rotating
  systems}, 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.~533--538.

\bibitem{FXRoux_DTromeurDervout_1994a}
{\sc F.-X. Roux and D.~Tromeur-Dervout}, {\em Parallelization of a multigrid
  solver via a domain decomposition method}, 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.~439--444.

\bibitem{URude_1994b}
{\sc U.~R{\"u}de}, {\em Error estimators based on stable splittings}, 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.~111--118.

\bibitem{URude_1994a}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em On the robustness
  and efficiency of the fully adaptive multigrid 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.~121--126.

\bibitem{MSarkis_1994a}
{\sc M.~Sarkis}, {\em Multilevel methods for p1 nonconforming finite elements
  and discontinuous coefficients 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.~119--124.

\bibitem{CRSchneidesch_MODeville_EHMund_1994a}
{\sc C.~R. Schneidesch, M.~O. Deville, and E.~H. Mund}, {\em Domain
  decomposition method coupling finite elements and preconditioned {C}hebyshev
  collocation to solve elliptic 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.~293--298.

\bibitem{LRScott_1994a}
{\sc L.~R. Scott}, {\em Elliptic preconditioners using fast summation
  techniques}, 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.~311--323.

\bibitem{JPShao_1994a}
{\sc J.~P. Shao}, {\em The modified vertex space domain decomposition method
  for {N}eumann boundary value 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.~325--336.

\bibitem{JRShewchuk_OGhattas_1994a}
{\sc J.~R. Shewchuk and O.~Ghattas}, {\em A compiler for parallel finite
  element methods with domain--decomposed 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.~445--450.

\bibitem{TMShih_CBLiem_TLu_1994a}
{\sc T.-M. Shih, C.-B. Liem, and T.~Lu}, {\em Additive {S}chwarz methods and
  acceleration with variable weights}, 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.~299--309.

\bibitem{TMShih_CBLiem_TLu_AZhou_1994a}
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\end{thebibliography}

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