-
1
-
-
0003733850
-
-
Technical report ANL-95/11-Revision 2.0.22, Argonne National Laboratory, Argonne, IL
-
S. BALAY, W. D. GROPP, L. C. MCINNES, AND B. F. SMITH, PETSc 2.0 User's Manual, Technical report ANL-95/11-Revision 2.0.22, Argonne National Laboratory, Argonne, IL, 1998; available online from http://www.mcs.anl.gov/petsc.
-
(1998)
PETSc 2.0 User's Manual
-
-
Balay, S.1
Gropp, W.D.2
Mcinnes, L.C.3
Smith, B.F.4
-
2
-
-
0039896302
-
Algebraic theory of multiplicative Schwarz methods
-
to appear
-
M. BENZI, A. FROMMER, R. NABBEN, AND D. B. SZYLD, Algebraic theory of multiplicative Schwarz methods, Numer. Math., to appear.
-
Numer. Math.
-
-
Benzi, M.1
Frommer, A.2
Nabben, R.3
Szyld, D.B.4
-
3
-
-
0031485176
-
Existence and uniqueness of splittings for stationary iterative methods with applications to alternating methods
-
M. BENZI AND D. B. SZYLD, Existence and uniqueness of splittings for stationary iterative methods with applications to alternating methods, Numer. Math., 76 (1997), pp. 309-321.
-
(1997)
Numer. Math.
, vol.76
, pp. 309-321
-
-
Benzi, M.1
Szyld, D.B.2
-
4
-
-
0003658403
-
-
Academic Press, New York, SIAM, Philadelphia
-
A. BERMAN AND R. J. PLEMMONS, Nonnegative Matrices in the Mathematical Sciences, 3rd ed., Academic Press, New York, 1979, SIAM, Philadelphia, 1994.
-
(1979)
Nonnegative Matrices in the Mathematical Sciences, 3rd Ed.
-
-
Berman, A.1
Plemmons, R.J.2
-
5
-
-
0008765509
-
On the spectra of sums of orthogonal projections with applications to parallel computing
-
P. E. BJØRSTAD AND J. MANDEL, On the spectra of sums of orthogonal projections with applications to parallel computing, BIT, 31 (1991), pp. 76-88.
-
(1991)
BIT
, vol.31
, pp. 76-88
-
-
BjØrstad, P.E.1
Mandel, J.2
-
6
-
-
0000020556
-
To overlap or not to overlap: A note on a domain decomposition method for elliptic problems
-
P. E. BJØRSTAD AND O. B. WIDLUND, To overlap or not to overlap: A note on a domain decomposition method for elliptic problems, SIAM J. Sci. Statist. Comput., 10 (1989), pp. 1053-1061.
-
(1989)
SIAM J. Sci. Statist. Comput.
, vol.10
, pp. 1053-1061
-
-
BjØrstad, P.E.1
Widlund, O.B.2
-
7
-
-
0040426346
-
Analysis of non-overlapping domain decomposition algorithms with inexact solves
-
J. H. BRAMBLE, J. E. PASCIAK, AND A. T. VASSILEV, Analysis of non-overlapping domain decomposition algorithms with inexact solves, Math. Comp., 67 (1998), pp. 1-19.
-
(1998)
Math. Comp.
, vol.67
, pp. 1-19
-
-
Bramble, J.H.1
Pasciak, J.E.2
Vassilev, A.T.3
-
8
-
-
0003159321
-
Parallel, synchronous and asynchronous two-stage multisplitting methods
-
R. BRU, V. MIGALLÓN, J. PENADÉS, AND D. B. SZYLD, Parallel, synchronous and asynchronous two-stage multisplitting methods, Electron. Trans. Numer. Anal., 3 (1995), pp. 24-38.
-
(1995)
Electron. Trans. Numer. Anal.
, vol.3
, pp. 24-38
-
-
Bru, R.1
Migallón, V.2
Penadés, J.3
Szyld, D.B.4
-
9
-
-
0002645449
-
A minimum overlap restricted additive Schwarz pre-conditioner and applications to 3D flow simulations
-
X.-C. CAI, C. FARHAT, AND M. SARKIS, A minimum overlap restricted additive Schwarz pre-conditioner and applications to 3D flow simulations, Contemp. Math., 218 (1998), pp. 479-485.
-
(1998)
Contemp. Math.
, vol.218
, pp. 479-485
-
-
Cai, X.-C.1
Farhat, C.2
Sarkis, M.3
-
10
-
-
21344470841
-
Overlapping domain decomposition algorithms for general sparse matrices
-
X.-C. CAI AND Y. SAAD, Overlapping domain decomposition algorithms for general sparse matrices, Numer. Linear Algebra Appl., 3 (1996), pp. 221-237.
-
(1996)
Numer. Linear Algebra Appl.
, vol.3
, pp. 221-237
-
-
Cai, X.-C.1
Saad, Y.2
-
11
-
-
0033295858
-
A restricted additive Schwarz preconditioner for general sparse linear systems
-
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.
-
(1999)
SIAM J. Sci. Comput.
, vol.21
, pp. 792-797
-
-
Cai, X.-C.1
Sarkis, M.2
-
12
-
-
84974325009
-
Domain decomposition methods
-
T. F. CHAN AND T. P. MATHEW, Domain decomposition methods, Acta Numerica (1994), pp. 61-143.
-
(1994)
Acta Numerica
, pp. 61-143
-
-
Chan, T.F.1
Mathew, T.P.2
-
13
-
-
0032364135
-
Some comparison theorems for weak nonnegative splittings of bounded operators
-
J.-.J. CLIMENT AND C. PEREA, Some comparison theorems for weak nonnegative splittings of bounded operators, Linear Algebra Appl., 275/276 (1998), pp. 77-106.
-
(1998)
Linear Algebra Appl.
, vol.275-276
, pp. 77-106
-
-
Climent, J.-J.1
Perea, C.2
-
14
-
-
0000962866
-
Aufgaben monotoner Art
-
L. COLLATZ, Aufgaben monotoner Art, Arch. Math., 3 (1952), pp. 366-376.
-
(1952)
Arch. Math.
, vol.3
, pp. 366-376
-
-
Collatz, L.1
-
16
-
-
0002059273
-
Towards a unified theory of domain decomposition algorithms for elliptic problems
-
T. F. Chan, R. Glowinski, J. Periaux, and O. B. Widlund, eds., SIAM, Philadelphia
-
M. DRYJA AND O. B. WIDLUND, Towards a unified theory of domain decomposition algorithms for elliptic problems, in Proceedings of the Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, T. F. Chan, R. Glowinski, J. Periaux, and O. B. Widlund, eds., SIAM, Philadelphia, 1990, pp. 3-21.
-
(1990)
Proceedings of the Third International Symposium on Domain Decomposition Methods for Partial Differential Equations
, pp. 3-21
-
-
Dryja, M.1
Widlund, O.B.2
-
17
-
-
0001450532
-
Comparison of weak regular splittings and multisplitting methods
-
L. ELSNER, Comparison of weak regular splittings and multisplitting methods, Numer. Math., 56 (1989), pp. 283-289.
-
(1989)
Numer. Math.
, vol.56
, pp. 283-289
-
-
Elsner, L.1
-
18
-
-
0040443554
-
On the theory and practice of multisplitting methods in parallel computation
-
A. FROMMER AND G. MAYER, On the theory and practice of multisplitting methods in parallel computation, Computing, 49 (1992), pp. 63-74.
-
(1992)
Computing
, vol.49
, pp. 63-74
-
-
Frommer, A.1
Mayer, G.2
-
19
-
-
84985372550
-
A comparison result for multisplitting s and waveform relaxation methods
-
A. FROMMER AND B. POHL, A comparison result for multisplitting s and waveform relaxation methods, Numer. Linear Algebra Appl., 2 (1995), pp. 335-346.
-
(1995)
Numer. Linear Algebra Appl.
, vol.2
, pp. 335-346
-
-
Frommer, A.1
Pohl, B.2
-
20
-
-
0031497209
-
A unified representation and theory of algebraic additive Schwarz and multisplitting methods
-
A. FROMMER AND H. SCHWANDT, A unified representation and theory of algebraic additive Schwarz and multisplitting methods, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 893-912.
-
(1997)
SIAM J. Matrix Anal. Appl.
, vol.18
, pp. 893-912
-
-
Frommer, A.1
Schwandt, H.2
-
21
-
-
0002504054
-
Asynchronous weighted additive Schwarz methods
-
A. FROMMER, H. SCHWANDT, AND D. B. SZYLD, Asynchronous weighted additive Schwarz methods, Electron. Trans. Numer. Anal., 5 (1997), pp. 48-61.
-
(1997)
Electron. Trans. Numer. Anal.
, vol.5
, pp. 48-61
-
-
Frommer, A.1
Schwandt, H.2
Szyld, D.B.3
-
22
-
-
33845744599
-
H-splittings and two-stage iterative methods
-
A. FROMMER AND D. B. SZYLD, H-splittings and two-stage iterative methods, Numer. Math., 63 (1992), pp. 345-356.
-
(1992)
Numer. Math.
, vol.63
, pp. 345-356
-
-
Frommer, A.1
Szyld, D.B.2
-
23
-
-
0033465847
-
Weighted max norms, splittings, and overlapping additive Schwarz iterations
-
A. FROMMER AND D. B. SZYLD, Weighted max norms, splittings, and overlapping additive Schwarz iterations, Numer. Math., 83 (1999), pp. 259-278.
-
(1999)
Numer. Math.
, vol.83
, pp. 259-278
-
-
Frommer, A.1
Szyld, D.B.2
-
24
-
-
0033293064
-
Inexact preconditioned conjugate gradient method with inner-outer iteration
-
G. H. GOLUB AND Q. YE, Inexact preconditioned conjugate gradient method with inner-outer iteration, SIAM J. Sci. Comput., 21 (1999), pp. 1305-1320.
-
(1999)
SIAM J. Sci. Comput.
, vol.21
, pp. 1305-1320
-
-
Golub, G.H.1
Ye, Q.2
-
25
-
-
0003826505
-
-
Springer-Verlag, New York, Berlin, Heidelberg
-
W. HACKBUSCH, Iterative Solution of Large Sparse Systems of Equations, Springer-Verlag, New York, Berlin, Heidelberg, 1994.
-
(1994)
Iterative Solution of Large Sparse Systems of Equations
-
-
Hackbusch, W.1
-
26
-
-
0008813599
-
A two-level aggregation-based Newton-Krylov-Schwarz method for hydrology
-
D. E. Keyes, A. Ecer, J. Periaux, and N. Satofuka, eds., North-Holland, Amsterdam
-
E. W. JENKINS, R. C. BERGER, J. P. HALLBERG, S. E. HOWINGTON, C. T. KELLEY, J. H. SCHMIDT, A. K. STAGG, AND M. D. TOCCI, A two-level aggregation-based Newton-Krylov-Schwarz method for hydrology, in Parallel Computational Fluid Dynamics, D. E. Keyes, A. Ecer, J. Periaux, and N. Satofuka, eds., North-Holland, Amsterdam, pp. 257-264.
-
Parallel Computational Fluid Dynamics
, pp. 257-264
-
-
Jenkins, E.W.1
Berger, R.C.2
Hallberg, J.P.3
Howington, S.E.4
Kelley, C.T.5
Schmidt, J.H.6
Stagg, A.K.7
Tocci, M.D.8
-
27
-
-
21344458136
-
Two-stage multisplitting methods with overlapping blocks
-
M. T. JONES AND D. B. SZYLD, Two-stage multisplitting methods with overlapping blocks, Numer. Linear Algebra Appl., 3 (1996), pp. 113-124.
-
(1996)
Numer. Linear Algebra Appl.
, vol.3
, pp. 113-124
-
-
Jones, M.T.1
Szyld, D.B.2
-
28
-
-
84966225158
-
An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix
-
J. A. MEIJERINK AND H. VAN DER VORST, An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Math. Comp., 31 (1977), pp. 148-162.
-
(1977)
Math. Comp.
, vol.31
, pp. 148-162
-
-
Meijerink, J.A.1
Van Der Vorst, H.2
-
29
-
-
0001324833
-
Multi-splittings of matrices and parallel solution of linear systems
-
D. P. O'LEARY AND R. E. WHITE, Multi-splittings of matrices and parallel solution of linear systems, SIAM J. Alg. Disc. Meth., 6 (1985), pp. 630-640.
-
(1985)
SIAM J. Alg. Disc. Meth.
, vol.6
, pp. 630-640
-
-
O'Leary, D.P.1
White, R.E.2
-
32
-
-
84968508605
-
A simple approach to the Perron-Frobenius theory for positive operators on general partially-ordered finite-dimensional linear spaces
-
W. C. RHEINBOLDT AND J. S. VANDERGRAFT, A simple approach to the Perron-Frobenius theory for positive operators on general partially-ordered finite-dimensional linear spaces, Math. Comp., 27 (1973), pp. 139-145.
-
(1973)
Math. Comp.
, vol.27
, pp. 139-145
-
-
Rheinboldt, W.C.1
Vandergraft, J.S.2
-
33
-
-
0000954680
-
A flexible inner-outer preconditioned GMRES algorithm
-
Y. SAAD, A flexible inner-outer preconditioned GMRES algorithm, SIAM J. Sci. Comput., 14 (1993), pp. 461-469.
-
(1993)
SIAM J. Sci. Comput.
, vol.14
, pp. 461-469
-
-
Saad, Y.1
-
35
-
-
0041753967
-
-
Ph.D. thesis, Department of Mathematics, Technical University of Chemnitz, Chemnitz, Germany
-
U. SCHRADER, Invers-isotone Diskretisierungsmethoden für invers-isotone lineare und quasilineare Zwei-Punkt-Randwertaufgaben, Ph.D. thesis, Department of Mathematics, Technical University of Chemnitz, Chemnitz, Germany, 2000.
-
(2000)
Invers-isotone Diskretisierungsmethoden für Invers-isotone Lineare und Quasilineare Zwei-Punkt-Randwertaufgaben
-
-
Schrader, U.1
-
36
-
-
0003419897
-
-
Cambridge University Press, Cambridge, New York, Melbourne
-
B. F. SMITH, P. E. BJØRSTAD, AND W. D. GROPP, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press, Cambridge, New York, Melbourne, 1996.
-
(1996)
Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations
-
-
Smith, B.F.1
BjØrstad, P.E.2
Gropp, W.D.3
-
37
-
-
85140868405
-
A flexible quasi-minimal residual method with inexact preconditioning
-
to appear
-
D. B. SZYLD AND J. A. VOGEL, A flexible quasi-minimal residual method with inexact preconditioning, SIAM J. Sci. Comput., to appear.
-
SIAM J. Sci. Comput.
-
-
Szyld, D.B.1
Vogel, J.A.2
-
38
-
-
0030388574
-
Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
-
P. VANĚK, J. MANDEL, AND M. BREZINA, Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems, Computing, 56 (1996), pp. 179-196.
-
(1996)
Computing
, vol.56
, pp. 179-196
-
-
Vaněk, P.1
Mandel, J.2
Brezina, M.3
-
39
-
-
0002340103
-
Factorization and normalized iterative methods
-
R. E. Langer, ed., The University of Wisconsin Press, Madison, WI
-
R. S. VARGA, Factorization and normalized iterative methods, in Boundary Problems in Differential Equations, R. E. Langer, ed., The University of Wisconsin Press, Madison, WI, 1960, pp. 121-142.
-
(1960)
Boundary Problems in Differential Equations
, pp. 121-142
-
-
Varga, R.S.1
-
40
-
-
0003943048
-
-
Prentice-Hall, Englewood Cliffs, NJ, 2nd ed., Springer, Berlin
-
R. S. VARGA, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1962, 2nd ed., Springer, Berlin, 2000.
-
(1962)
Matrix Iterative Analysis
-
-
Varga, R.S.1
-
41
-
-
0001156347
-
Multisplitting with different weighting schemes
-
R. E. WHITE, Multisplitting with different weighting schemes, SIAM J. Matrix Anal. Appl., 10 (1989), pp. 481-493.
-
(1989)
SIAM J. Matrix Anal. Appl.
, vol.10
, pp. 481-493
-
-
White, R.E.1
|