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:    ftp.ccs.uky.edu (128.163.209.106)

World Wide Web:  http://www.mgnet.org or
                 http://www.cerfacs.fr/~douglas/mgnet.html or
                 http://phase.etl.go.jp/mgnet or
                 http://www.ccs.uky.edu/mgnet

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

Volume 8, Number 2 (approximately February 28, 1998)

Today's topics:

     Preprint from Y. Saad and J. Zhang
     Graduate Research Assistantship at Clarkson University
     Preliminary Program for 5th Copper Mountain Conference on Iterative Methods
     Some of the new entries in the bibliography

    Editor's Note:
    -------------

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

Date: Mon, 23 Feb 1998 17:34:24 -0600 (CST)
From: Jun Zhang 
Subject: Preprint from Y. Saad and J. Zhang
     
We wish to announce of availability of the following preprint.
     
      Diagonal Threshold Techniques in Robust Multi-Level ILU 
         Preconditioners for General Sparse Linear Systems

                      Yousef Saad and Jun Zhang

    E-mail: saad@cs.umn.edu,           jzhang@cs.umn.edu
    URL: http://www.cs.umn.edu/~saad   http://www.cs.umn.edu/~jzhang

                        ABSTRACT

This paper introduces techniques based on diagonal threshold tolerance when
developing multi-elimination and multi-level incomplete LU (ILUM)
factorization preconditioners for solving general sparse linear systems.
Existing heuristics solely based on the adjacency graph of the matrices have
been used to find independent sets and are not robust for matrices arising
from certain applications in which the matrices may have small or zero
diagonals.  New heuristic strategies based on the adjacency graph and the
diagonal values of the matrices for finding independent sets are introduced.
Analytical bounds for the factorization and preconditioned errors are obtained
for the case of a two-level analysis.  These bounds provide useful information
in designing robust ILUM preconditioners.  Extensive numerical experiments are
conducted in order to compare robustness and efficiency of various heuristic
strategies.

Key Words:  Incomplete LU factorization, reordering techniques, multi-level
preconditioner, Krylov subspace methods, multi-elimination ILU factorization.

PostScript file of the above preprint may be downloaded from either 
authors' home page as listed above.

For those who do not have access to web facility, send an e-mail to
jzhang@cs.umn.edu for a PostScript file or a hard copy.

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

Date: Fri, 27 Feb 98 17:11:56 EST
From: fulton@sun.mcs.clarkson.edu (Scott Fulton)
Subject: Graduate Research Assistantship at Clarkson University

Clarkson University anticipates an opening in Fall 1998 for a 
Graduate Research Assistantship in Mathematics at the M.S. or 
Ph.D. level.  This student will join an active group working
on multigrid methods and their application to modeling hurricane 
dynamics and motion.  Several Teaching Assistantships will also
be available.

For information see our web page (http://www.clarkson.edu/~mcs/)
or contact Scott Fulton (fulton@clarkson.edu).

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

Date: Sat, 28 Feb 1998 14:42:12 -0400
From: Craig Douglas 
Subject: Preliminary Program for 5th Copper Mountain Conference on Iterative Methods

The abstracts can be found through 

    http://amath-www.colorado.edu/appm/faculty/copper

The virtual proceedings will be on MGNet later this month.


                              Sunday, March 29

                           7:00-9:00 PM Reception

                              Monday, March 30

       Room                    A                           B
     Session I
       Topic            Preconditioning            Multilevel Methods
       Chair                                        Steve McCormick
 8:00               K. Vuik                  I.Yavneh
 8:25               M. Drexler               D. Melson
 8:50am             R. Bridson               C. Pflaum
 9:15am             W. Joubert               M. Holst
 9:40am                  Coffee Break
    Session II
       Topic            Preconditioning           Algebraic Multigrid
       Chair                                        Steve McCormick
 10:10am            S. Brenner               V. Henson
 10:35am            T. Dayar                 J. Ruge
 11:00am            J. Zhang                 A. Cleary
 11:25am            M. Lambert               R. Falgout
 11:50am            F. Wang                  M. Brezina
 12:15pm            Lunch
    Session III
       Topic            Preconditioning                Multigrid
       Chair                                          S. McCormick
 4:30pm             D. Szyld                 C. Greif
 4:55pm             S. Toledo                S. Sokal
 5:20pm             A. Pothen                J. Moulton
 5:45pm             V. Pan                   Y. Shapira
 6:10pm             Dinner

                             Tuesday, March 31

       Room                      A                           B
     Session I
       Topic             Eigenvalue Methods           Parallel Methods
       Chair             Henk van der Vorst
 8:00               R. Lehoucq                   J. Jones
 8:25               Open                         C. Tong
 8:50am             W. Gansterer                 S. Oliveira
 9:15am             K. Wu                        D. Quinlan
 9:40am                     Coffee Break
    Session II
       Topic             Eigenvalue Methods           Parallel Methods
       Chair             Henk van der Vorst
 10:10am            Z. Bai                       R. Clay
 10:35am            A. Edelman                   N. Jovanovic
 11:00am            Y. Saad                      A. Krommer
 11:25am            D. Sorrenson                 J. Malard
 11:50am            H. Van der Vorst             P. Rucho
 12:15pm            Lunch
    Session III
       Topic             Eigenvalue Methods             Applications
       Chair             Henk van der Vorst
 4:30pm             A. Knyazev                   V. Howle
 4:55pm             W. Demeo                     M. Huhtanen
 5:20pm             E. Gallopoulos               P. Saylor
 5:45pm             M. Tocci                     A. Slavova
 6:10pm             Dinner

                             Wednesday, April 1

    Room                       A                              B
  Session I
    Topic      First Order Systems Least-Squares      Nonlinear Solvers
    Chair               Tom Manteuffel                  Homer Walker
 8:00         S. McCormick                        C. Kelley
 8:25         M. Berndt                           D. Knoll
 8:50am       G. Starke                           R. Freund
 9:15am       D. Chan                             H. Walker
 9:40am                  Coffee Break
 Session II
    Topic      First-Order Systems Least-Squares      Nonlinear Solvers
    Chair               Tom Manteuffel                  Homer Walker
 10:10am      P. Bochev                           C. Woodward
 10:35am      T. Sun                              E. Bowman
 11:00am      Z. Cai                              F. Meier
 11:25am      J. Pasciak                          J. Meulman
 11:50am      B. Lee                              M. Seaid
 12:15pm      Lunch
 Session III
    Topic                    Misc.                 Krylov Subspace Methods
    Chair
 4:30pm       J. Hennart                          L. Bergamaschi
 4:55pm       A. Stathopoulos                     J. Cullum
 5:20pm       D. Daoud                            A. Wathen
 5:45pm       A. Williams                         M Yeung
 6:10pm       Dinner

                             Thursday, April 2

      Room                   A                            B
    Session I
      Topic             Applications              Multigrid Methods
      Chair
 8:00             M. Tretter                R. Bermejo
 8:25             S. Vandewalle             R. Menikoff
 8:50am           J. Marin                  J. Gopalakrishnan
 9:15am           W. Spotz                  V. Sarin
 9:40am                 Coffee Break
   Session II
      Topic          ASCI Applications          Discretization Methods
      Chair
 10:10am          C. Aro                    C. Romine
 10:35am          W. Rider                  V. Druskin
 11:00am          J. Shadid                 H. Bungartz
 11:25am          F. Graziani               D. Smolarski
 11:50am          A. Robertson              M. Shashkov
 12:15pm          Lunch
   Session III
      Topic             Applications                Student Papers
      Chair
 4:30pm           T. Tamarchenko            M. Adams
 4:55pm           H. Jang                   W. Ching
 5:20pm           G. Newman                 D. Loghlin
 5:45pm           J. Rahola                 C. Lin
 6:10pm           Break

Banquet 6:30 to 9:30 pm

                              Friday, April 3

       Room                       A                            B
    Session I
      Topic            Krylov Subspace Methods          Preconditioning
      Chair
 8:00             O. Ernst                           A. Ramage
 8:25             R. Morgan                          M. Trummer
 8:50am           E. Ng                              C. Oosterlee
 9:15am           E. de Sturler                      V. Delafosse
 9:40am                      Coffee Break
    Session II
      Topic            Domain Decomposition/MG          Preconditioning
      Chair
 10:10am          D. Day                             P. Farrell
 10:35am          B. Lally                           H. Elman
 11:00am          G. Mateescu                        Y. Shih
 11:25am          R. Renaut                          J. Simoens
 11:50am          M. Sosonkina                       G. Wade
 12:15pm          Lunch
   Session III
      Topic            Krylov Subspace Methods          Preconditioning
      Chair
 4:30pm           D. Kincaid                         A. Grama
 4:55pm           W. Luk                             Open
 5:20pm           S. Goossens                        N. Nguyen
 5:45pm           M. Buecker                         A. Nishida
 6:10pm           Close of Meeting

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

Date: Sat, 28 Feb 1998 14:42:12 -0400
From: Craig Douglas 
Subject: Some of the new entries in the bibliography

Here is a large set of publications.  They will be reformatted and the ones
that have appeared will be entered into the MGNet bibliography over the next
few weeks.

As usual, please send additions and corrections.

                             REFERENCES

  [1] I. Babu~ska, F. Ihlenburg, E.T. Paik, and S.A. Sauter, A
          generalized finite element method for solving the Helmholtz
          equation in two dimensions with minimal pollution, Comp.
          Meth. Appl. Mech. Eng., 128 (1995), pp. 325-359.
  [2] I.  Babu~ska,  F.  Ihlenburg,  and  S.A.  Sauter,  Reliabil-
          ity  of  finite  element  methods  for  the  numerical  computa-
          tion of waves, Advances in Engineering Software, 28 (1997),
          pp. 417-424.
  [3] I. Babu~ska and S.A. Sauter, Is the pollution effect of the
          FEM avoidable for the Helmholtz equation considering high
          wave numbers., SIAM, J. Numer. Anal., 34 (1997), pp. 2392
          - 2423.
  [4] Randy Bank and Sabine Gutsch, The generalized hierarchi-
          cal basis two-level method for the convection-diffusion equa-
          tion on a regular grid,  in Proceedings of the EMG 1996,
          Stuttgart, 1996. to appear.
  [5] ______,  Hierarchical basis for the convection-diffusion equation
          on unstructured meshes, in Ninth International Symposium
          on Domain Decomposition Methods for Partial Differential
          Equations, D.Keyes P.Bjorstadt, M.Espedal, ed., J. Wiley
          and Sons, New York, 1996.
  [6] ______, An algebraic approach to the hbmg method for unstruc-
          tured grids, in ZAMM, 1997. to appear.
  [7] Jens Burmeister and Wolfgang Hackbusch, On a time
          and space multi-grid method including remarks on filtering
          techniques, in Flow Simulation with High-Performance Com-
          puters, E. Hirschel, ed., no. 52-2 in NNFM, Vieweg, 1996,
          pp. 5-19.
  [8] Jens  Burmeister  and  Graham  Horton,  Time-parallel
          multigrid solution of the Navier-Stokes equations, in Multi-
          grid  Methods  III,  Wolfgang  Hackbusch  and  Ulrich  Trot-
          tenberg, eds., vol. 98 of International Series of Numerical
          Mathematics, Basel, 1991, Birkh"auser Verlag, pp. 155-166.
          Proceedings of the 3rd European Conference on Multigrid
          Methods, Bo nn, October 1-4, 1990.
  [9] Jens Burmeister and Rainer Paul, Time-adaptive solution
          of  discrete  parabolic  problems  with  time-parallel  multigrid
          methods, in Computational Fluid Dynamics on Parallel Sys-
          tems, Siegfried Wagner, ed., vol. 50 of NNFM, Vieweg, 1995,
          pp. 49-58.
[10]  W.  Busch,  R.  Esser,  and  W.  Hackbusch,  Extrapolation
          applied to the method of characteristics for a first order sys-
          tem of two partial differential equations, Numer. Math., 24
          (1975), pp. 331-353.
[11]  S. Dittrich and W. Hackbusch, A method of characteristics
          solving the initial-boundary value problem of a hyperbolic dif-
          ferential equation of second order, Numer. Math., 34 (1980),
          pp. 217-234.
[12]  M.  Dryja  and  W.  Hackbusch,  On  the  nonlinear  domain
          decomposition method, BIT, 37 (1997), pp. 296-311.
[13]  Birgit Faermann, Lokale a-posteriori Fehlersch"atzer bei der
          Diskretisierung  von  Randintegralgleichungen,  PhD  thesis,
          Universit"at Kiel, 1993.
[14]  ______,               Lokale           a-posteriori-Fehlersch"atzer
          bei der Diskretisierung von Randintegralgleichungen, ZAMM
          (Z. angw. Math. Mech), 75 (1995), pp. S 681-682.
[15]  ______, Local a-posteriori error estimators for the discretization
          of boundary integral equations, in Boundary Elements:  Im-
          plementation and Analysis of Advanced Algorithms,  Pro-
          ceedings of the 12th Kieler GAMM-Seminar, vol. 54 of Notes
          on Numerical Fluid Mechanics, Braunschweig, 1996, Vieweg,
          pp. 68-81.
[16]  ______, Adaptive Galerkin boundary element methods, in ZAMM
          (Z. angw. Math. Mech), 1997.
[17]  B.  Faermann,  Efficient  and  reliable  a-posteriori  error  esti-
          mates for boundary element methods, in Analysis, Numer-
          ics and Applications of Differential and Integral Equations,
          C. Constanda, M. Bach, A.M. Saendig, P. Werner, and G.C.
          Hsiao, eds., London, 1997, Addison Wesley Longman.  (to
          appear).
[18]  I.G. Graham, W. Hackbusch, and S. Sauter, The hybrid
          galerkin boundary element method, in Proceedings of the first
          UK  conference  on  Boundary  Integral  Methods,  L.  Elliot,
          D.B. Ingham, and D. Lesnic, eds., Leeds University Press,
          1997, pp. 98-107. submitted to Numer. Math.
[19]  W. Hackbusch, Extrapolation applied to certain discretization
          methods solving the initial value problem for hyperbolic dif-
          ferential equations, Numer. Math., 28 (1977), pp. 121-142.
[20]  ______,  Extrapolation  to  the  limit  for  numerical  solutions  of
          hyperbolic differential equations, Numer. Math, 28 (1977),
          pp. 455-474.
[21]  ______, A numerical method for solving parabolic equations with
          opposite orientations, Computing, 20 (1978), pp. 229-240.
[22]  ______, On a method of characteristics for solving a hyperbolic
          equation of second order, Computing, 20 (1978), pp. 47-60.
[23]  ______, A note on the penalty correction method, Zeitschrift f"ur
          Analysis und ihre Anwendungen, 2 (1982), pp. 59-69.
[24]  ______, Schnelle L"oser f"ur partielle Differentialgleichungen, PM
          Mathematik, 27 (1985), pp. 478-501.
[25]  ______, Theorie und Numerik elliptischer Differentialgleichungen,
          Teubner, 1986.
[26]  ______, Multi-grid methods and applications, Springer, 1988. Chi-
          nese translation.
[27]  ______,  Integralgleichungen.  Theorie  und  Numerik,  Teubner,
          1989.
[28]  ______, Iterative L"osung grosser schwachbesetzter Gleichungssys-
          teme, Teubner, 1991.
[29]  ______, Comparison of different multi-grid variants for nonlinear
          equations, ZAMM, 72 (1992), pp. 148-151.
[30]  ______, Elliptic Differential Equations, Springer, 1992.  English
          translation.
[31]  ______,  A  parallel  conjugate  gradient  method,  J. of Numerical
          Linear Algebra with Applications, 1 (1992), pp. 133-147.
[32]  ______, Iterative solution of large sparse systems, Springer, 1994.
          English translation.
[33]  ______,  Integral Equations. Theory and Aplication,  vol. 120 of
          ISNM, Birkh"auser, 1995. English translation.
[34]  ______,  A  note  on  Reusken's  lemma,  Computing,  55  (1995),
          pp. 181-189.
[35]  ______,   Numerische  Mathematik  und  ihre  Wechselwirkung
          mit  der  gegenw"artigen  Rechnerentwicklung,   in  Berlin-
          Brandenburgische  Akademie  der  Wissenschaften,  Bericht
          und Abhandlungen, vol. 4, Berlin, 1997, Akademie-Verlag,
          pp. 55-67.
[36]  Wolfgang Hackbusch, On the feedback vertex set problem
          for a planar graph, Computing, 58 (1997), pp. 129-155.
[37]  W. Hackbusch and G. Hofmann, Results of the eigenvalue
          problem for the plate equation, Z. Angew. Math. Phys., 31
          (1980), pp. 730-739.
[38]  W. Hackbusch, C. Lage, and S.A. Sauter, On the efficient
          realization of sparse matrix techniques for integral equations
          with focus on panel clustering, cubature and software design
          aspects, in Boundary Element Topics, W.L. Wendland, ed.,
          Springer, 1997, pp. 51-76.
[39]  Wolfgang  Hackbusch  and  Rainer  Paul,  Kopplung  von
          Finite-Element-  und  Randelementmethoden  f"ur  die  nu-
          merische  Simulation  von  piezokeramischen  Strukturen,  in
          Mathematik:   Schl"usseltechnologie  f"ur  die  Zukunft;  Ver-
          bundprojekte  zwischen  Universit"at  und  Industrie,  Karl-
          Heinz Hoffmann, Willi J"ager, Thomas Lohmann, and Her-
          mann  Schunk,  eds.,  Berlin  Heidelberg  New  York,  1997,
          Springer-Verlag, pp. 151-160.
[40]  Wolfgang  Hackbusch  and  Thomas  Probst,  Downwind
          gauss-seidel  smoothing  for  convection  dominated  problems,
          in ZAMM, 1997. to appear.
[41]  W.  Hackbusch  and  T.  Probst,  Downwind  Gauss-Seidel
          smoothing  for  convection  dominated  problems,  Numerical
          Linear Algebra with Applications, 4 (1997), pp. 85-102.
[42]  W.  Hackbusch  and  S.A.  Sauter,  On the efficient use of
          the Galerkin method to solve Fredholm integral equations,
          Applications of Mathematics, 38 (1993), pp. 301-322.
[43]  ______, On numerical cubatures of nearly singular surface inte-
          grals arising in BEM Collocation,  Computing,  52 (1994),
          pp. 139-159.
[44]  ______, A new finite element approach for problems containing
          small geometric details, in Proceedings of the ENUMATH
          '95-Konferenz, Paris, 1995.
[45]  ______,  Adaptive  Composite  Finite  Elements  for  the  solution
          of PDEs containing non-uniformly distributed micro-scales,
          Matematicheskoe modelirovanie, 8 (1996), pp. 31-43.
[46]  ______, Composite Finite Elements for problems containing small
          geometric  details.  Part  II:  Implementation  and  numerical
          results, Computing and Visualization in Science, 1 (1997),
          pp. 15-25.
[47]  ______,  Composite  Finite  Elements  for  the  approximation  of
          PDEs on domains with complicated micro-structures,  Nu-
          mer. Math., 75 (1997), pp. 447-472.
[48]  Wolfgang Hackbusch and Jens Uwe Wappler, Remarks
          on error estimation in the presence of iteration errors, sub-
          mitted to Computing, (1996).
[49]  K. Hayami and S.A. Sauter, A formulation of the panel clus-
          tering method for the three-dimensional elastostatic problem,
          in Proceedings of the JASCOME 13th symposium on BEM,
          Tokyo, 1996, pp. 125-130.
[50]  ______, A formulation of the Panel-Clustering Method for three-
          dimensional  elastostatics,  in  Proceedings  of  the  Annual
          Meeting of the Japanese Society for Industrial and Applied
          Mathematics (JSIAM), Tokyo, 1996, pp. 218-219.
[51]  ______, Application of the panel clustering method for the three-
          dimensional  elastostatic  problem,  in  Boundary  Elements
          XIX, Proceedings of the 19th International Conference on
          the Boundary Element Method, C.A. Brebbia M. Marchetti
          and M.H.Aliabadi, eds., Rome, 1997, Computational Me-
          chanics Publications, pp. 625-634.
[52]  ______, Cost estimation of the panel clustering method applied
          to 3-d elastostatcs,  in Proceedings of the EUROBEM `98
          conference, Paris, 1998.
[53]  Peter Kosmol and Ivor Nissen, A minimal residual class
          of  algorithms  for  linear  systems,  Computing,  51  (1993),
          pp. 335-343.
[54]  S. Lorenz, C. Solterbeck, W. Schattke, J. Burmeister,
          and W. Hackbusch, Electron scattering states at solid sur-
          faces calculated with realistic potentials, Phys. Rev. B, 55
          (1997), p. R13432.
[55]  J"org-Peter   Mayer,   Zur   L"osung   von   geod"atischen
          Randwertproblemen durch einen hypersingul"aren Potential-
          Ansatz, PhD thesis, Universit"at Kiel, 1997.
[56]  Rainer  Paul,  Eigenwertprobleme bei der Simulation piezok-
          eramischer Strukturen, PhD thesis, Universit"at Kiel, 1997.
[57]  S.A.   Sauter,   Ein   Mehrgitterverfahren   zur   Berechnung
          der Eigenschwingungen von abgeschlossenen Wasserbecken,
          Master's thesis, Universit"at Heidelberg, 1989.
[58]  ______,  The  ILU  method  for  finite  element  discretizations,  J.
          Comp. Appl. Math., 36 (1991), pp. 91-106.
[59]  ______,  "Uber die effiziente Verwendung des Galerkinverfahrens
          zur L"osung Fredholmscher Integralgleichungen, PhD thesis,
          Universit"at Kiel, 1992.
[60]  ______,  On  the  stability  of  the  ILU  method  for  singular  per-
          turbed  finite  element  problems,  in Incomplete Decomposi-
          tions (ILU), Theory, Technique and Applications, Proceed-
          ings of the 8th Kieler GAMM-Seminar, W. Hackbusch and
          G. Wittum, eds., Vieweg, Notes on Numerical Fluid Me-
          chanics, 1993, pp. 139-149.
[61]  ______,  On  the  efficient  implementation  of  Galerkin-BEM,
          ZAMM, 74 (1994), pp. T 516-518.
[62]  ______, On the stability of the incomplete Cholesky decomposition
          for a singular perturbed problem, where the coefficient matrix
          is not an M-matrix, J. Numer. Lin. Alg. Appl., 2 (1995),
          pp. 17-28.
[63]  ______, Cubature techniques for 3-d Galerkin BEM, in Boundary
          Elements: Implementation and Analysis of Advanced Algo-
          rithms, W. Hackbusch and G. Wittum, eds., Vieweg, Notes
          on Numerical Fluid Mechanics, 1996, pp. 29-44.
[64]  ______, Composite finite elements for problems with complicated
          boundary. part iii:  Essential boundary conditions, submit-
          ted to:  Computing and Visualization in Sciences, (1997).
          Institutsbericht, Nr. 97-16.
[65]  ______,  Vergr"oberung  von  Finite-Elemente-R"aumen,  Habilita-
          tionsschrift, Universit"at Kiel, 1997.
[66]  ______, The Panel Clustering Method in 3-d BEM, in Wave Prop-
          agation in Complex Media, G. Papanicolau, ed., no. 96 in
          IMA-Volumes in Mathematics and Applications, Springer,
          1998, pp. 199-224.
[67]  S.A. Sauter and A. Krapp, On the effect of numerical in-
          tegration in the Galerkin boundary element method, Numer.
          Math., 74 (1996), pp. 337-360.
[68]  S.A. Sauter and C. Lage, On the efficient computation of
          singular and nearly singular surface integrals arising in 3D-
          Galerkin BEM, ZAMM, 76 (1996), pp. 273-275.
[69]  ______, Transformation of hypersingular integrals and black-box
          cubature, Math. Comp, (1997). submitted.
[70]  S.A.  Sauter  and  C.  Schwab,  Realization  of  hp-Galerkin
          BEM  in  3-d,  in  Boundary  Elements:   Implementation
          and Analysis of Advanced Algorithms, W. Hackbusch and
          G. Wittum, eds., Vieweg, Notes on Numerical Fluid Me-
          chanics, 1996, pp. 194-206.
[71]  ______, Quadrature for hp-Galerkin BEM in 3-d, Numer. Math.,
          (to appear).
[72]  S.A.  Sauter  and  G.  Wittum,  On the computation of the
          eigenmodes  of  Lake  Constance  by  means  of  a  multi-grid
          method, in GMD-Studien of the 3rd European Conference
          of Multigrid Methods, W. Hackbusch and U. Trottenberg,
          eds., Bonn, 1991.
[73]  ______, A multigrid method for the computation of eigenmodes
          of closed water basins, Impact of Computing in Science and
          Engineering, 4 (1992), pp. 124-152.

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

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