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Anonymous ftp repository:  www.mgnet.org (128.163.209.19)
 
Current editor:  Craig Douglas douglas-craig@cs.yale.edu
 

World Wide Web:  http://www.mgnet.org or
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                 http://www.nchc.gov.tw/RESEARCH/Math/mgnet/www/mgnet.html

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

Volume 10, Number 5 (approximately May 31, 2000)

Today's topics:

     Schedule of AMG-WS in St.Wolfgang
     ParaSails and a Paper
     Contents of Int. J. of Nonlinear Sciences and Numerical Simulation
     Some papers of Xiao-Chuan Cai's
     References (Shapira)
     List of Publications for Panayot S. Vassilevski

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

Date: Fri, 02 Jun 2000 13:25:28 +0200
From: Gundolf Haase 
Subject: Schedule of AMG-WS in St.Wolfgang

You find the schedule of the workshop under

    http://www.numa.uni-linz.ac.at/Staff/haase/AMG-WS/workshop.html

    Editor's Note: A report will be in the next issue.
    -------------

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

From: Edmond Chow 
Date: Fri, 26 May 2000 15:07:51 -0700 (PDT)
Subject: ParaSails and a Paper

ParaSails, Parallel Sparse Approximate Inverse Preconditioner is available at

    http://www.llnl.gov/casc/parasails

along with links to papers.  ParaSails is a parallel sparse approximate
inverse preconditioner for the iterative solution of large, sparse systems of
linear equations.

ParaSails has been used to solve finite element elasticity problems inside a
Lawrence Livermore simulation code with more than 4 million equations on 1000
processors of ASCI Blue-Pacific (IBM SP).  It has also been demonstrated on
anisotropic diffusion problems with 216 million equations.

ParaSails uses least-squares (Frobenius norm) minimization to compute a sparse
approximate inverse.  The sparsity pattern of the approximate inverse is the
pattern of a power of a sparsified matrix.  ParaSails also uses a post-
filtering technique to reduce the cost of applying the preconditioner.  The
pattern of the preconditioner can be reused to generate preconditioners for
different matrices in a sequence of linear solves.

ParaSails solves symmetric positive definite problems using a factorized
preconditioner.  ParaSails can also solve general (nonsymmetric and/or
indefinite) problems with a nonfactorized preconditioner.  The software
available to be downloaded includes parallel CG and GMRES solvers, a parallel
matrix data structure and a test driver.  It is implemented with MPI message
passing.

The software is freely available for research and development purposes.
Commercial use is possible with a licensing agreement.

Here is the abstract of a new paper on that site, which you can run in MGNet.

Parallel implementation and performance characteristics of least squares
sparse approximate inverse preconditioners

Edmond Chow
Lawrence Livermore National Laboratory

ABSTRACT

This paper describes and tests a parallel, message passing code for
constructing sparse approximate inverse preconditioners using Frobenius norm
minimization.  The sparsity patterns of the preconditioners are chosen as
patterns of powers of sparsified matrices.  Sparsification is necessary when
powers of a matrix have a large number of nonzeros, making the approximate
inverse computation expensive.  For our test problems, the minimum solution
time is achieved with approximate inverses with fewer than twice the number of
nonzeros of the original matrix.  Additional accuracy is not compensated by
the increased cost per iteration.  The results lead to further understanding
of how to use these methods and how well these methods work in practice.  In
addition, this paper describes programming techniques required for high
performance, including one-sided communication, local coordinate numbering,
and load repartitioning.

This work was performed under the auspices of the U.S. Department of Energy
by University of California Lawrence Livermore National Laboratory under
contract No. W-7405-Eng-48.

Edmond Chow
Center for Applied Scientific Computing, LLNL

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

Date: Sun, 7 May 2000 11:42:34 -0400 (EDT)
From: Jun Zhang 
Subject: Contents of Int. J. of Nonlinear Sciences and Numerical Simulation

     International Journal of Nonlinear Sciences and Numerical Simulation

      Journal's home page is at http://www.cs.uky.edu/~jzhang/nsns.html

                    Contents of Volume 1, Number 1, 2000.

Personage in Science: Academician Yury Mitropolsky,
by O. Limarchenho, J.-H. He, p. 3-6;

Relationship theorem between nonlinear polynomial equation
and the corresponding Jacobian matrix, 
by W. Chen, p. 7-16;

The modified Adomian decomposition method for solving linear 
and nonlinear boundary value problems of tenth-order and 
twelfth-order,
by A. M. Wazwaz, p. 17-24;

A new finite element with self-adapting built-in discontinuity 
for shock-capturing in transonic flow, 
by Gao-Lian Liu, p. 25-30;

Inverse problem for the diffusional transport of water upon
single pellet moisture sorption, 
by S. I. KabanikhinI.V. Koptyug, K.T. Iskakov and R.Z. Sagdeev, 
p. 31-42;

A frame for development of approximate theories of 
geometrically-nonlinear plates, 
by Albert C.J. Luo, p. 43-50;

Review on some recently developed nonlinear analytical methods, 
by Ji-Huan He, p. 51-70;

DIFFEQ 2000 and Call for Paper, p. 71.

                    Contents of Volume 1, Number 2, 2000.

Review Article:

Review of Virtual Distortion Method and Its Applications to Fast
Redesign and Sensitivity Analysis
Jan Holnicki-Szulc, Tomasz Bielecki, p. 71-98;

Technical Papers:

Optic Discrete Breathers in Euclidean Invariant Systems
R.S.MacKay, p. 99-104;

Nonlinear Properties for Dynamic Behavior of Liquid with a Free
Surface in a Rigid Moving Tank
Oleg S. Imarchenko, p. 105-118;

Dynamics of Stochastic Layers in Nonlinear Hamiltonian Systems
Albert C.J. Luo and Ray P.S. Han, p. 119-132;

A Classical Variational Model for Micropolar Elastodynamics
Ji-Huan He, p. 133-138.

Letter:
A Variational Model for Micropolar Fluids in Lubrication Journal Bearing
Ji-Huan He, p. 139-142

Book Review:
Preprinciples of Mechanics (Veljko A. Vujicic)
Katica (Stevanovic) Hedrih, p. 143.

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

Date: Fri, 26 May 2000 17:43:11 -0600 (MDT)
From: "Xiao-Chuan Cai" 
Subject: Some papers of Xiao-Chuan Cai's

    Editor's Note: Access the abstracts and/or full papers using the URL
    -------------  http://www.cs.colorado.edu/~cai/mypapers.html

M. Paraschivoiu and X.-C. Cai, A unigrid multi-model full potential and
Euler formulation for transonic flows , Proceedings of the Copper
Mountain Conference on Multigrid Methods, 1999.

R. Aitbayev, X.-C. Cai, and M. Paraschivoiu, Parallel two-level methods
for three-dimensional transonic compressible flow simulations on
unstructured meshes, Proceedings of Parallel CFD'99, 1999.

M. Paraschivoiu, X.-C. Cai, M. Sarkis, D. P. Young, and D. Keyes,
Multi-domain multi-model formulation for compressible flows:
Conservative interface coupling and parallel implicit solvers for 3D
unstructured meshes, AIAA Paper 99-0784, 1999.

X.-C. Cai, M. Paraschivoiu, and M. Sarkis, An explicit multi-model
compressible flow formulation based on the full potential equation and
the Euler equations on 3D unstructured meshes, 11th International
Conference on Domain Decomposition Methods, C-H. Lai, P. Bjorstad, M.
Cross, O. Widlund, eds., 1999.

S. Goossens and X.-C. Cai, Lower dimensional interpolation in
overlapping composite mesh difference methods, 11th International
Conference on Domain Decomposition Methods, C-H. Lai, P. Bjorstad, M.
Cross, O. Widlund, eds., 1999.

X.-C. Cai, T. Mathew, and M. Sarkis, Maximum norm analysis of
overlapping nonmatching grid discretizations of elliptic equations,
SIAM J. Numer. Anal., 37 (2000), pp. 1709-1728.

X.-C. Cai and J. Zou, Some observations on the $L^2$ convergence of the
additive Schwarz preconditioned GMRES method, Tech Report CU-CS-865-98,
Dept. of Comp. Sci., Univ. of Colorado at Boulder, 1998.

X.-C. Cai, M. A. Casarin, Jr., F. W. Elliott, Jr., and, O. B. Widlund,
Overlapping Schwarz algorithms for solving Helmholtz's equation,
Proceedings of the 10th Intl. Conf. on Domain Decomposition Methods, J.
Mandel, C. Farhat and X.-C. Cai, eds., AMS, pp. 437-445, 1998.

Y. Wu, X.-C. Cai, and D. E. Keyes, Additive Schwarz methods for
hyperbolic equations, Proceedings of the 10th Intl. Conf. on Domain
Decomposition Methods, J. Mandel, C. Farhat and X.-C. Cai, eds., AMS,
pp. 513--521, 1998.

X.-C. Cai, C. Farhat, and M. Sarkis, A minimum overlap restricted
additive Schwarz preconditioner and applications in 3D flow
simulations, The Tenth International Conference on Domain Decomposition
Methods for Partial Differential Equations, J. Mandel, C. Farhat and
X.-C. Cai, eds, AMS, 1998.

X.-C. Cai and M. Sarkis, A restricted additive Schwarz preconditioner
for general sparse linear systems, SIAM J. Sci. Comput., 21 (1999), pp.
792-797

X.-C. Cai, M. Dryja, and M. Sarkis, Overlapping non-matching grid
mortar element methods for elliptic problems, SIAM J. Numer. Anal., 36
(1999), pp. 581-606.

X.-C. Cai, C. Farhat, and M. Sarkis, Variable degree Schwarz methods
for the implicit solution of unsteady compressible Navier-Stokes
equations on two-dimensional unstructured meshes, ICASE Report No.
96-48, NASA Langley Research Center, 1996.

X.-C. Cai, W. D. Gropp, D. E. Keyes, R. G. Melvin, and D. P. Young,
Parallel Newton-Krylov-Schwarz algorithms for the transonic full
potential equation, SIAM J. Sci. Comput., 19 (1998), pp. 246-265.

X.-C. Cai, C. Farhat, and M. Sarkis, Schwarz methods for the unsteady
compressible Navier-Stokes equations on unstructured meshes, Domain
Decomposition Methods in Sciences and Engineering, R. Glowinski, J.
Periaux, Z. Shi and O. Widlund, eds., John Wiley & Sons, Ltd., 1997.

X.-C. Cai, D. E. Keyes, and V. Venkatakrishnan, Newton-Krylov-Schwarz:
An implicit solver for CFD, Domain Decomposition Methods in Sciences
and Engineering, R. Glowinski, J. Periaux, Z. Shi and O. Widlund, eds.,
John Wiley & Sons, Ltd., 1996.

X.-C. Cai and M. Sarkis, Local multiplicative Schwarz algorithms for
convection-diffusion equations, East-West J. Numer. Math., 6 (1998).

X.-C. Cai, W. D. Gropp, D. E. Keyes, and M. D. Tidriri, Parallel
implicit methods for aerodynamics, Seventh International Conference on
Domain Decomposition Methods for Partial Differential Equations, D.
Keyes, J. Xu, eds., AMS, 1994.

X.-C. Cai and M. Dryja, Domain decomposition methods for monotone
nonlinear elliptic problems, Seventh International Conference on Domain
Decomposition Methods for Partial Differential Equations, D. Keyes, J.
Xu, eds., AMS, 1994.

X.-C. Cai, W. D. Gropp, D. E. Keyes, and M. D. Tidriri,
Newton-Krylov-Schwarz methods in CFD, Proceedings of the International
Workshop on the Navier-Stokes Equations, Notes in Numerical Fluid
Mechanics, R. Rannacher, eds. Vieweg Verlag, Braunschweig, 1994.

X.-C. Cai, The use of pointwise interpolation in domain decomposition
methods with non-nested meshes, SIAM J. Sci. Comput., 16 (1995), pp.
250-256.

X.-C. Cai, A family of overlapping Schwarz algorithms for nonsymmetric
and indefinite elliptic problems, in Domain-Based Parallelism and
Problem Decomposition Methods in Computational Science and Engineering,
D. Keyes and Y. Saad and D. Truhlar, eds., SIAM, 1994.

X.-C. Cai, W. D. Gropp, and D. E. Keyes, A comparison of some domain
decomposition and ILU preconditioned iterative methods for nonsymmetric
elliptic problems, Numer. Lin. Alg. Applics., 1 (1994), pp. 477-504.

B. Bialecki, X.-C. Cai, M. Dryja, and G. Fairweather, Schwarz
algorithms for orthogonal spline collocation problems, Sixth Conference
on Domain Decomposition Methods for Partial Differential Equations, A.
Quarteroni and J. Periaux and Y. A. Kuznetsov and O. B. Widlund, eds.,
AMS, 1994.

X.-C. Cai and Y. Saad, Overlapping domain decomposition algorithms for
general sparse matrices, TR 93-027, Army High Performance Computing
Research Center, University of Minnesota, 1993.

B. Bialecki and X.-C. Cai, $H^1$-norm error bounds for piecewise
Hermite bicubic orthogonal spline collocation schemes for elliptic
boundary value problems, SIAM J. Numer. Anal., 31 (1994), pp.
1128-1146.

X.-C. Cai, Multiplicative Schwarz methods for parabolic problems, SIAM
J. Sci. Comput., 15 (1994), pp. 587-603.

X.-C. Cai, An optimal two-level overlapping domain decomposition method
for elliptic problems in two and three dimensions, SIAM J. Sci.
Comput., 14 (1993), pp. 239-247.

X.-C. Cai and O. Widlund, Multiplicative Schwarz algorithms for
nonsymmetric and indefinite Elliptic Problems, SIAM J. Numer. Anal., 30
(1993), pp. 936--952.

X.-C. Cai and O. Widlund, Domain decomposition algorithms for
indefinite elliptic problems, SIAM J. Sci. Stat. Comp., 13 (1992), pp.
243-258.

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

Date: Mon, 5 Jun 2000 23:10:52 +0300 (IDT)
From: Yair Shapira 
Subject: References (Shapira)

Multigrid for Locally Refined Meshes.
SIAM J. Sci. Comput. 21, pp. 1168--1190.

Model-Case Analysis of an Algebraic Multilevel Method.
Numer. Linear Algebra Appl. 6 (1999), pp. 655--685.

Analysis of Matrix-Dependent Multigrid Algorithms.
Numer. Linear Algebra Appl. 5 (1998), pp. 165--201.

Parallelizable Approximate Solvers for Recursions
Arising in Preconditioning.
Linear Algebra Appl. 274 (1998), 211--237.

Multigrid Methods for 3-D Definite and Indefinite Problems.
Appl. Numer. Math. 26 (1998), 377--398.

Coloring Update Methods.  BIT 38, 1998, pp. 180--188.

Algebraic Interpretation of Continued Fractions.
J. Comput. Appl. Math. 78 (1997), pp. 3--8.

Note on the Multigrid W-Cycle.
J. Comput. Appl. Math. 85 (1997), pp. 351--353.

Algebraic Domain Decomposition Method for Unstructured Grids.
In Ninth International Conference on Domain Decomposition Methods,
Bjorstad, P., Espedal, M. and Keyes, D. (eds.),
Domain Decomposition press, Bergen, Norway (1999), pp. 205--214.

Shapira, Y.; Israeli, M.; and Sidi, A.:
Towards Automatic Multigrid Algorithms
for SPD, Nonsymmetric and Indefinite Problems.
SIAM J. Sci. Comput. 17 (1996), 439--453.

Sidi, A.; and Shapira, Y.: Upper Bounds for Convergence
Rates of Acceleration Methods with Initial Iterations.
Numer. Algorithms 18 (1998), 113--132.

Shapira, Y.; Sidi, A.; and Israeli, M.: Optimal Error Bounds for
Convergents of a Family of Continued Fractions.
J. Math. Anal. Appl. 197 (1996), 767--773.

Shapira, Y.; Israeli, M.; Sidi, A.; and Zrahia, U.:
Preconditioning Spectral Element Schemes
for Definite and Indefinite Problems.
Numer. Methods Partial Differential Equations 15 (1999), 535--543.

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

Date: Fri, 26 May 2000 15:34:58 -0700 (PDT)
From: "Panayot S. Vassilevski" 
Subject: List of Publications for Panayot S. Vassilevski

                                Journal Papers

1.  P. S. Vassilevski, "Finite difference schemes for one-dimensional
diffusion equation in Cartesian and cylindrical coordinates on unbounded
intervals", Differential Equations (Differentzial'nie Uravnenia) 19(1983),
1154-1171 (Russian).

2.  P. Vassilevski, "Multigridmethod in subspace and domain partitioning in
the discrete solution of elliptic problems", Lect. Notes in Math. (Springer)
1228(1986),301-314.

3.  O. Axelsson, V. Eijkhout, B. Polman, and P. S. Vassilevski, "Iterative
solution of singular perturbation 2nd order boundary value problems by use
of incomplete block-factorization methods", BIT 29(1989), 867-889.

4.  R. E. Ewing, R. D. Lazarov,and P. S. Vassilevski, "Localrefinement
techniques for elliptic problems on cell-centered grids, II:  Optimal order
two-grid iterative methods", Numer. Lin. Alg. with Appl. 1(1994), 337-368.

5.  O. Axelsson and P. S. Vassilevski, "Algebraic multilevel preconditioning
methods", I, Numer. Math. 56(1989), 157-177.

6.  R. D. Lazarov, P. S. Vassilevski, and S. D. Margenov, "Solving elliptic
problems by the domain decomposition methods using preconditioning matrices
derived by multilevel splittings of the finite element matrix", Lecture Notes
in Comput. Science (Springer) 297(1988), 826-835.

7.  P. S. Vassilevski, "Algorithms for construction of preconditioners based on
incomplete block - factorization of the matrix", Intern. J. Numer. Methods in
Engnr. 27(1989), 609-622.

8.  O. Axelsson and P. S. Vassilevski, "A black box generalized C G solver
with inner iterations and variable-step preconditioning",SIAM J. Matr. Anal.
Appl. 12(1991), 625-644.

9.  P. S. Vassilevski, "On some ways of approximating inverses of banded
matrices in connection with deriving preconditioners based on incomplete
block-factorizations", Computing 43(1990), 277-296.

10.  V. L. Eijkhout and P. S. Vassilevski, "The role of the strengthened
C.-B.-S.-inequality in multilevel methods", SIAM Review 33(1991), 405-419.

11.  V. Eijkhout and P. S. Vassilevski, "Positive definiteness aspects of
vectorizable preconditioners", Parallel Computing 10(1989), 93-100.

12.  O. Axelsson and P. S. Vassilevski, "A survey of multilevel preconditioned
iterative methods", BIT 29(1989), 769-793.

13.  O. Axelsson and P. S. Vassilevski, "Algebraic multilevel preconditioning
methods II", SIAM J. Numer. Anal. 27(1990), 1569-1590.

14.  P. S. Vassilevski and H. N. Djidjev, "Incomplete block - factorization
preconditioners for solving three-dimensional elliptic difference equations on
systolic processors", Int. J. Computer Mathematics 44(1992), 341-364.

15.  P. S. Vassilevski, "Hybrid V-cycle algebraic multilevel
preconditioners", Math. Comp. 58(1992), 489-512.

16.  R. E. Ewing, R. D. Lazarov and P. S. Vassilevski, "Local refinement
techniques for parabolic problems on grids with local refinement in time and
in space", Computing 45(1990), 193-215.

17.  O. Axelsson and P. S. Vassilevski, "Asymptotic work estimates for AMLI
methods", Applied Numer. Mathematics 7(1991), 437-451.

18.  R. E. Ewing, R. D. Lazarov,and P. S. Vassilevski, "Local refinement
techniques for elliptic problems on cell-centered grids", I:  Error analysis,
Math. Comp. 56(1991), 437-461.

19.  P. S. Vassilevski, S. I. Petrova, and R. D. Lazarov, "Finite difference
schemes on triangular cell-centered grids with local refinement", SIAM J. Sci.
Stat. Comp. 13(1992), 1287-1313.

20.  P. S. Vassilevski, "Multilevel preconditioners for elliptic problems by
substructuring", Appl. Math. Comput. 46(1991), 79-106.

21.  P. S. Vassilevski, "Indefinite ellipticproblems preconditioning", Commun.
in Appl. Numer. Methods 8(1992), 257-264.

22.  P. S. Vassilevskiand M. H. Etova, "Computation of constants in the
strengthened Cauchy inequality for elliptic problems with anisotropy", SIAM J.
Sci. Stat. Comp. 13(1992), 655-665.

23.  P. S. Vassilevski, "Preconditioning nonsymmetric and indefinite finite
element matrices", J. Numer. Linear Alg. with Appl. 1(1992), 59-76.

24.  R. E. Ewing, R. D. Lazarov and P. S. Vassilevski, "Local refinement
techniques for elliptic problems on cell-centered grids III:  Algebraic
multilevel BEPS preconditioners", Numer. Math. 59(1991), 431-452.

25.  O. Axelsson and P. S. Vassilevski, "Variable-step multilevel
preconditioning methods, I:  Symmetric positive definite elliptic problems",
Numer. Linear Algebra with Applications 1(1994), 75-101.

26.  O. P. Iliev, M. M. Makarov, and P. S. Vassilevski, "Performance of
certain iterative methods in solving implicit difference schemes for 2D
Navier-Stokes equations", Int. J. Numer. Meth. Engng. 33(1992), 1465-1480.

27.  R. E. Ewing, R. D. Lazarov, J. E. Pasciak, and P. S. Vassilevski, "Domain
decomposition type iterative techniques for parabolic problems on locally
refined grids", SIAM J. Numer. Anal. 30(1993), 1537-1557.

28.  R. E. Ewing, S. D. Margenov,and P. S. Vassilevski, "A multilevel technique
for solving the biharmonic equation", Mathematik a Balkanica 10(1996),
121-132.

29.  S. D. Margenov and P. S. Vassilevski, "Algebraic multilevel
preconditioning of anisotropic ellipticproblems", SIAM J. Sci. Comput.
15(1994), 1026-1037.

30.  P. S. Vassilevskiand J. W ang, "Multilevel iterative methods for mixed
finite element discretizations of elliptic problems", Numer. Math.
63(1992), 503-520.

31.  P. S. Vassilevski, S. I. Petrova, and R. D. Lazarov, "Preconditioning
elliptic problems on grids with multilevel local refinement", Mathematik a
Balkanica 8(1994), 179-196.

32.  R. E. Ewing, S. I. Petrova, and P. S. Vassilevski, "Two-level
local-refinement preconditioners for nonsymmetric and indefinite elliptic
problems",SIAM J. Sci. Comput. 15(1994), 149-163.

33.  R. E. Ewing, J. Shen, and P. S. Vassilevski, "Vectorizable
preconditioners for mixed finite element solution of second order elliptic
problems", Intern. J. on Computer Math. 44(1992), 313-327.

34.  P. S. Vassilevskiand J. Wang, "An application of the abstract multilevel
theory to nonconforming finite element methods", SIAM J. Numer. Anal.
32(1995), 235-248.

35.  R. D. Lazarov, I. D. Mishev and P. S. Vassilevski, "Finite volume methods
for convection diffusion problems", SIAM J. Numer. Anal. 33(1996), 31-55.

36.  T. F. Chan and P. S. Vassilevski, "A framework for block-ILU
factorizations using block-size reduction",Math. Comp. 64(1995), 129-156.

37.  P. S. Vassilevskiand R. D. Lazarov, "Preconditioning mixed finite element
saddle-point elliptic problems", Numer. Linear Alg. Appl. 3(1996), 1-20.

38.  W. Proskurowskiand P. S. Vassilevski, "Preconditioning capacitance matrix
problems in domain imbedding", SIAM J. Sci. Comput. 15(1994), 77-88.

39.  W. Proskurowskiand P. S. Vassilevski, "Preconditioning nonsymmetric and
indefinite capacitancematrix problems in domain imbedding", SIAM J. Sci.
Comput. 16(1995), 414-430.

40.  R. D. Lazarov, I. D. Mishev and P. S. Vassilevski, "Finite volume methods
with local refinement for convection diffusion problems", Computing
53(1994), 33-57.

41.  I. D. Lirkov, S. D. Margenov and P. S. Vassilevski, "Circulant incomplete
block-factorization preconditioners for elliptic problems", Computing 53(1994),
59-74.

42.  G. F. Carey, A. I. Pehliv anov and P. S. Vassilevski, "Least-squares
mixed finite element methods for non-selfadjoint elliptic problems, II:
Performance of block-ILU factorization methods", SIAM J. Sci. Comput.
16(1995), 1126-1136.

43.  T. Rusten, P. S. Vassilevski and R. Winther, "Interior penalty
preconditioners for mixed finite element approximations of elliptic
problems", Math. Comp. 65(1996), 447-466.

44.  R. E. Ewing, O. P. Iliev, S. D. Margenov, and P. S. Vassilevski,
"Numerical study of three multilevel preconditioners for solving 2D unsteady
Navier-Stokes equations", Comput. Methods Appl. Mech. Engrg. 121(1995)
177-186.

45.  A. I. Pehlivanov, G. F. Carey, and P. S. Vassilevski, "Least-squares
mixed finite element methods for non-selfadjoint elliptic problems", I:  Error
analysis, Numer. Math. 72(1996), 501-522.

46.  T. F. Chan, S. D. Margenov and P. S. Vassilevski, "Performance of
block-ILU factorization preconditioners based on block-size reduction for 2D
elasticity systems", SIAM J. Sci. Comput. 18(1997), 1355-1366.

47.  P. S. Vassilevski, "On two ways of stabilizing the HB multilevel
methods", SIAM Review 39(1997), 18-53.

48.  P. S. Vassilevskiand J. Wang, "Stabilizing the hierarchical basis by
approximate wavelets, I:  Theory", Numer. Linear Alg. Appl. 4(1997),
103-126.

49.  M. G. Neytchev a and P. S. Vassilevski, "Preconditioning of indefinite
and almost singular finite element elliptic equations", SIAM J. Sci. Comput.
19(1998), 1471-1485.

50.  P. S. Vassilevskiand J. W ang, "Stabilizing the hierarchical basis by
approximate wavelets, II:  Implementation and Numerical Results",SIAM J. Sci.
Comput. 20(1999), 490-514 (available electronically at
http://epubs.siam.org/sam-bin/dbq/toclist/SISC).

51.  So-Hsiang Chou, Do Y. Kwak, and P. S. Vassilevski, "Mixed covolume
methods for elliptic problems on triangular grids", SIAM J. Numer. Anal.
35(1998), 1850-1861.

52.  R. D. Lazarov, L. Tobiska and P. S. Vassilevski, "Streamline diffusion
least-squares mixed finite element methods for convection diffusion problems",
East-West J. of Numer. Math. 5(1997), 249-264.

53.  P. S. Vassilevski, "A block-factorization (algebraic) formulation of
multigrid and Schwarz methods", East-West J. Numer. Math. 6(1998), #1, pp.
65-79.

54.  T. Rusten, P. S. Vassilevski and R. Winther, "Domain embedding
preconditioners for mixed systems", Numer. Lin. Alg. with Appl. 5(1999),
321-345.

55.  J. H. Bramble, J. E. Pasciak and P. S. Vassilevski, "Computational scales
of Sobolev norms with application to preconditioning", Math. Comp. 69
(2000), 463-480.

56.  So-Hsiang Chouand P. S. Vassilevski, "A general mixed co-volume framework
for constructing conservative schemes for elliptic problems", Math. Comp.
68 (1999), 991-1011.

57.  So-Hsiang Chou and P. S. Vassilevski, "An upwinding cell-centered method
with piecewise constant velocity over covolumes", Numer. Meth. for PDEs
15(1999), 49-62.

58.  P. S. Vassilevskiand J. G. Wade, "A comparison of multilevel methods for
total variation regularization", Electronic Transaction on Numerical Analysis,
6(1997), 255-270.

59.  So-Hsiang Chou,Do Y. Kwak, and P. S. Vassilevski, "Mixed covolume methods
on rectangular grids for convection-diffusion problems", SIAM J. Sci.
Comput. 21(1999), 145-165.

                                Recent Reports

1.  S. I. Petrova, L. Tobiska and P. S. Vassilevski, "Algebraic multigrid
methods for nonconforming streamline diffusion finite element
discretizations of convection-diffusion prob- lems", (submitted).

2.  R. D. Lazarov, J. E. Pasciak and P. S. Vassilevski, "Iterative solution of
a combined mixed and standard Galerkin discretization method for elliptic
problems", submitted to NLA.

3.  J. E. Jones and P. S. Vassilevski, "AMGe based on element
agglomerations", SISC (to appear).

4.  V. E. Henson and P. S. Vassilevski, "Element-free AMGe:  General
algorithms for computing interpolation weights", 2000 (submitted).

5.  C. Kim, R. D. Lazarov, J. E. Pasciak, and P. S. Vassilevski, "Multiplier
spaces for the mortar finite element method in three dimensions", submitted,
2000.

6.  P. S. Vassilevski, "Sparse matrix element topology with application to AMG
and preconditioning", 2000 (in progress).

7.  P. S. Vassilevski, "A taxonomy of algebraic multilevel methods", 2000 (in
progress).

                     Other Reports and Proceeding Papers

1.  P. S. Vassilevski, "Some properties of Green functions of elliptic
difference operators", Proceedings,Conference on Numerical Methods and
Applications, Sofia 1984, Bulg. Acad. Sci. Press, Sofia, 1985, 613-618.

2.  P. S. Vassilevski and G. V. Dimitrov, "Numerical experiments based on a
fast algorithm for calculation of the electromagnetic potentials of a nerve
action potential", Proceedings, Conference on Numerical Methods and
Applications, Sofia, 1984, Bulg. Acad. Sci. Press, Sofia, 1985, 619-624.

3.  P. S. Vassilevski, "Poincare-Steklov operators for elliptic difference
problems and their application for deriving a priori estimates", in:
Numerical Methods and Software Packages for Solving Equations of Mathematical
Physics, (A. S. Alekseev, ed.), Siberian Branch of the USSR Academy of
Sciences, Computing Center, Novosibirsk, 1985, 10-30, Russian.

4.  P. S. Vassilevski, "A reformulation of the odd-even factorization
algorithm in solving separable elliptic problems", Report 8803, 1988, Dept.
Math., Univ. Nijmegen, The Netherlands.

5.  P. S. Vassilevski, "Multilevel preconditioning matrices and multigrid
V-cycle methods", Proceedings, IV GAMM Seminar on Robust Multigrid Methods,
Kiel, 1988, (W.Hackbusch, ed.), Notes on Numer. Fluid Mechanics, Vieweg,
Braunschweig, 23(1988) 200-208.

6.  P. S. Vassilevski, "Nearly optimal iterative methods for solving finite
element elliptic equations based on the multilevel splitting of the matrix",
Report #1989-09, Institute for Scientific Computation, Univ. Wyoming, Laramie,
USA.

7.  P. S. Vassilevski, "Optimal order multilevel domain decomposition
preconditioners", Report # 1990-32, EORI, Univ. Wyoming, Laramie, Wyoming,
USA, 1990.

8.  P. S. Vassilevski, R. D. Lazarov, and S. D. Margenov, "Vector and parallel
algorithms in iteration methods for elliptic problems", Proceedings of the
Eighteenth Spring Conference of the Union of Bulgarian Mathematicians, Albena,
April 6-10, 1989, Bulg. Acad. Sciences Press, Sofia, 1989, 40-51.

9.  R. E. Ewing, R. D. Lazarov, and P. S. Vassilevski, "Finite difference
schemes on grids with local refinement in time and in space for parabolic
problems.  Optimal order two-grid iterative methods", Proceedings, Sixth GAMM
Seminar on "Parallel Methods for PDEs", Kiel January 22-24, 1990, Notes in
Numer. Fluid Mechanics, Vieweg- Braunschweig, 1990, pp. 70-93.

10.  R. E. Ewing, R. D. Lazarov, T. F. Russel, and P. S. Vassilevski,
"Local refinement via domain decomposition for mixed finite element methods
with rectangular Raviart-Thomas elements", Proceedings ofthe Third Conference
on Domain Decomposition Methods,Houston, Texas, March 20-22, 1989,
SIAM, Philadelphia, 1990, pp. 98-114.

11.  O. Axelsson and P. S. Vassilevski, "Algebraic multilevel preconditioning
methods, III, Proceedings, Conference on Domain Decomposition Methods",
Moscow, 1990, SIAM, Philadelphia, 1991, pp. 163-177.

12.  R. E. Ewing, R. D. Lazarov, and P. S. Vassilevski, "Mixed finite element
solution of second order elliptic problems on grids with regular local
refinement", Proceedings of the Fourth Conference on Domain Decomposition
Methods, Moscow, May 1990, SIAM, Philadelphia, 1991, pp.206-212.

13.  R. E. Ewing, R. D. Lazarov, Peng Lu, and P. S. Vassilevski,
"Preconditioning indefinite systems arising from mixed finite element
discretization of second order elliptic problems", Proceedings, Conference on
PCG Methods, Nijmegen, June, 1989, Lecture Notes in Math., Springer,
1457(1990), 28-43.

14.  R. E. Ewing and P. S. Vassilevski, "Two-level iterative refinement
preconditioners", Proceedings of Fifth Conference on Domain Decomposition
Methods for PDEs, May 6-8, 1991, Norfolk, Virginia, SIAM, Philadelphia, 1992,
pp. 262-270.

15.  O. Axelsson and P. S. Vassilevski, "Variable-step multilevel
preconditioning methods, II:  Nonsymmetric and indefinite elliptic problems",
preprint, 1991.

16.  O. Axelsson and P. S. Vassilevski, "Constructionof variable-step
preconditioners for inner-outer iterative methods", Proceedings of IMACS
Conference on Iterative methods, April 1991, Brussels, Belgium, Iterative
Methods in Linear Algebra, (R. Beauwens and P. de Groen, eds.), North
Holland, 1992, pp. 1-14.

17.  R. E. Ewing, O. P. Iliev, S. D. Margenov, and P. S. Vassilevski, "A
multilevel technique for solving 2D unsteady Navier-Stokes equations",
Proceedings, Symposium on Adaptive Multilevel and Hierarchical Computational
Strategies, ASME Annual Meeting, Anaheim, Calif., Nov. 8-13, 1992, in:  (A. K.
Noor, ed.) AMD 157(1992), pp. 235-247.

18.  R. E. Ewing, J. E. Pasciak, and P. S. Vassilevski, "Hybrid hierarchical
multilevel methods for mixed finite element systems with penalty", preprint,
1991, EORI, University of Wyoming, Laramie, Wyoming, USA.

19.  I. D. Mishev, V. Austel, T. F. Chan, and P. S. Vassilevski, "Experiments
with algebraic multilevel preconditioners on connection machine", CAM Report
93-25, Department of Mathematics,UCLA, 1993.

20.  P. S. Vassilevski and O. Axelsson, "A two-levelstabilizing framework for
interface domain decomposition preconditioners", in:  Proceedings of the Third
International Conference O(h^3), Sofia, Bulgaria, August 21-August 26,
Sofia, Bulgaria, "Advances in Numerical Methods and Applications", (I.
T. Dimov, Bl. Sendov and P. S. Vassilevski, eds.), World Scientific,
Singapore, New Jersey, London, Hong Kong, 1994, pp. 196-202.

21.  P. S. Vassilevski, "On some applications of the H-stable wavelet-like
hierarchical finite element space decompositions", in:  The Mathematics of
Finite Elements and Applications, Highlights 1996, (J. R. Whiteman, ed.),
Chichester, 1997, J. Wiley & Sons, pp. 371-395.

22.  P. S. Vassilevski and J. Wang, "Wavelet-like methods in the design of
efflcient multilevel pre- conditioners for elliptic PDEs", Multiscale Wavelet
Methods for PDEs, (W. Dahmen, A. Kurdila and P. Oswald, eds.), Academic
Press, 1997, pp. 59-105.

23.  S. I. Petrova and P. S. Vassilevski, "A variational
parameters-to-estimate-free nonlinear solver", Proceedings of the First
Conference on Numerical Methods and Applications, June 24-27, 1996, Rousse,
Bulgaria, (L. Vulkov and P. Yalamov, eds.), Lecture Notes in Computer
Science 1196, Springer V erlag, pp. 396-405.

24.  T. F. Chan and P. S. Vassilevski, "Convergence analysis of block-ILU
factorization algorithms based on block-size reduction", CAM Report, 95-46,
Math. Dept., UCLA, 1995.

25.  E. Haug, T. Rusten, P. S. Vassilevski, and R. Winther, "Domain embedding
and the Dirichlet problem", in:  Large-Scale Scientific Computations of
Engineering and Environmental Problems, (M. Griebel, O. P. Iliev, S. D.
Margenov and P. S. Vassilevski, eds.), Friedr. Vieweg,
Braunschweig/Wiesbaden, Notes on Numer. Fluid Mechanics, vol. 62 (1998), pp.
66-77.

26.  S. D. Margenov and P. S. Vassilevski, "Algebraic two-level
preconditioning of non-conforming FEM systems", in:  Large-Scale Scientific
Computations of Engineering and Environmental Problems, (M. Griebel, O. P.
Iliev, S. D. Margenov and P. S. Vassilevski, eds.), Friedr. Vieweg,
Braunschweig/Wiesbaden, Notes on Numer. Fluid Mechanics, vol. 62 (1998), pp.
239-248.

27.  R. D. Lazarov, and P. S. Vassilevski, "Least-squares streamline diffusion
finite element approximations to singularly perturbed convection-diffusion
problems", to appear in the Proceedings of International workshop on
convection-diffusion problems, held in Lozenetz, 1998, Bulgaria.

28.  R. D. Lazarov, J. E. Pasciak, and P. S. Vassilevski, "Coupling mixed and
finite volume discretizations of convection-diffusion-reaction equations on
non-matching grids", in:  Finite Volumes for Complex Applica tions II, (R.
Vilsmeier, F. Benkhaldoun and D. Hanel), Hermes Science, Paris, 1999, pp.
51-68.

29.  R. D. Lazarov, J. E. Pasciak, and P. S. Vassilevski, "Mixed finite
element methods for elliptic problems on non-matching grids", Friedr.
Vieweg, Braunschweig/Wiesbaden, Notes on Numer. Fluid Mechanics, 2000 (to
appear).

30.  V. Dobrev and P. S. Vassilevski, "Non-mortar finite elements for elliptic
problems", Proceedings of the Fourth Intern. Conference on Numerical
Methods and Applications (NMA'98), "Recent Advances in Numerical Methods and
Applications" (O. Iliev, M. Kaschiev, S. Margenov, Bl. Sendov and P .S.
Vassilevski, eds.), World Scientific, Singapore, 1999, pp. 756-765.

31.So-Hsiang Chou and P. S. Vassilevski, "A note on the Kantorovich and
Wielandt inequalities",1997.

32.  R. E. Bank and P. S. Vassilevski, "The CG and GCG methods exploiting
auxiliary coarse space", 1998.

33.  J. H. Bramble and P. S. Vassilevski, "Wavelet-like extension operators in
non-overlapping domain decomposition algorithms", Math. Dept., Texas A & M
Univ., College Station,TX, 1996,

                             Short Communications

1.  P. S. Vassilevski, "Difference schemes for one-dimensional diffusion
equation on the whole line", Compt. rend. de l'Acad. bulg. Sci. 36(1983)
No 4, 425-428.

2.  P. S. Vassilevski, "Difference schemes for the diffusion equation in
cylindrical coordinates on an unbounded interval", Compt. rend. de l'Acad.
bulg. Sci. 36(1983), No 5, 579-582.

3.  P. S. Vassilevski, "Fast algorithm for solving a linear algebraic problem
with separable variables", Compt. rend. de l'Acad. bulg. Sci. 37(1984)
No 3, 305-308.

4.  P. S. Vassilevski, "Fast algorithms for solving discrete Poisson equation
in a rectangle", Compt. rend. de l'Acad. bulg. Sci. 38(1985), No 10,
1311-1314.

5.  P. S. Vassilevski, "Poincare-Steklov operators for elliptic difference
problems", Compt. rend. de l'Acad. bulg. Sci. 38(1985) No. 5, 543-546.

6.  P. S. Vassilevski, "Apriori estimates for elliptic difference problems in
subspaces and their applications", Compt. rend. de l'Acad. bulg. Sci.
38(1985), No 6, 695-698.

7.  P. S. Vassilevski, "A grid approximation of Poisson equation on region
partitioned into subregions", Compt. rend. de l'Acad. bulg. Sci. 39(1986)
No 2, 39-42.

8.  P. S. Vassilevski, "Convergenceestimates in solving Poisson equation on
regions partitioned into subregions", Compt. rend. de l'Acad. bulg. Sci.
39(1986) No 3, 37-40.

9.  P. S. Vassilevski, "An optimal stabilization of the marching algorithm",
Compt. rend. de l'Acad. bulg. Sci. 41(1988) No 7, 29-32.

10.  P. S. Vassilevskiand S. I. Petrova, "A note on construction of
preconditioners in solving 3D elliptic problems by substructuring", Compt.
rend. de l'Acad. bulg. Sci. 41(1988), No 7, 33-36.

11.  P. S. Vassilevski, "Algebraic multilevel preconditioners for elliptic
problems with condensation of the finite element stiffness matrix",
Compt.rend. de l'Acad. bulg. Sci. 43(1990) No. 6, 25-28.

12.  P. S. Vassilevski, "Algebraic multilevel preconditioners for nonsymmetric
problems", Compt. rend. de l'Acad. bulg. Sci. 43(1990), No. 9, 33-36.

Panayot S. Vassilevski
Center for Applied Scientific Computing
Lawrence-Livermore National Laboratory
Mail Stop L-560,
7000 East Avenue
Livermore, California 94550, USA
E-mail address:  panayot@llnl.gov            

    Editor's Note: I do not usually run a list this long, but there was a lot
    -------------  of interesting titles, so...

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End of MGNet Digest
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