-
1
-
-
84966233568
-
Multi-level adaptive solutions to boundary-value problems
-
Brandt A. Multi-level adaptive solutions to boundary-value problems. Mathematics of Computation 1977 31(138):333-390.
-
(1977)
Mathematics of Computation
, vol.31
, Issue.138
, pp. 333-390
-
-
Brandt, A.1
-
2
-
-
84893764974
-
-
Algebraic multigrid (AMG) for automatic multigrid solution with application to geodetic computations. Technical Report, Institute for Computational Studies, Colorado State University
-
Brandt A, McCormick SF, Ruge JW. Algebraic multigrid (AMG) for automatic multigrid solution with application to geodetic computations. Technical Report, Institute for Computational Studies, Colorado State University, 1982.
-
(1982)
-
-
Brandt, A.1
McCormick, S.F.2
Ruge, J.W.3
-
3
-
-
0002438068
-
Algebraic multigrid (AMG) for sparse matrix equations
-
Evans DJ (ed.). Cambridge University Press: Cambridge
-
Brandt A, McCormick SF, Ruge JW. Algebraic multigrid (AMG) for sparse matrix equations. In Sparsity and Its Applications, Evans DJ (ed.). Cambridge University Press: Cambridge, 1984; 257-284.
-
(1984)
Sparsity and Its Applications
, pp. 257-284
-
-
Brandt, A.1
McCormick, S.F.2
Ruge, J.W.3
-
4
-
-
0001885411
-
Algebraic multigrid
-
Frontiers in Applied Mathematics. SIAM: Philadelphia, PA
-
Ruge JW, Stüben K. Algebraic multigrid. In Multigrid Methods, Vol.3, Frontiers in Applied Mathematics. SIAM: Philadelphia, PA, 1987; 73-130.
-
(1987)
Multigrid Methods
, vol.3
, pp. 73-130
-
-
Ruge, J.W.1
Stüben, K.2
-
6
-
-
77949646375
-
When does two-grid optimality carry over to the V-cycle?
-
Napov A, Notay Y. When does two-grid optimality carry over to the V-cycle? Numerical Linear Algebra with Applications 2010 17(2-3):273-290.
-
(2010)
Numerical Linear Algebra with Applications
, vol.17
, Issue.2-3
, pp. 273-290
-
-
Napov, A.1
Notay, Y.2
-
10
-
-
0034770470
-
Algebraic multigrid based on element interpolation (AMGe)
-
Brezina M, Cleary AJ, Falgout RD, Henson VE, Jones JE, Manteuffel TA, McCormick SF, Ruge JW. Algebraic multigrid based on element interpolation (AMGe). SIAM Journal on Scientific Computing 2000 22(5):1570-1592.
-
(2000)
SIAM Journal on Scientific Computing
, vol.22
, Issue.5
, pp. 1570-1592
-
-
Brezina, M.1
Cleary, A.J.2
Falgout, R.D.3
Henson, V.E.4
Jones, J.E.5
Manteuffel, T.A.6
McCormick, S.F.7
Ruge, J.W.8
-
13
-
-
0001822668
-
Multigrid methods: fundamental algorithms, model problem analysis and applications
-
Hackbusch W, Trottenberg U (eds), Lecture Notes in Mathematics. Springer-Verlag: Berlin
-
Stüben K, Trottenberg U. Multigrid methods: fundamental algorithms, model problem analysis and applications. In Multigrid Methods, Vol.960, Hackbusch W, Trottenberg U (eds), Lecture Notes in Mathematics. Springer-Verlag: Berlin, 1982; 1-176.
-
(1982)
Multigrid Methods
, vol.960
, pp. 1-176
-
-
Stüben, K.1
Trottenberg, U.2
-
14
-
-
0343959849
-
Algebraic formalisation of the multigrid method in the symmetric and positive definite case-a convergence estimation for the V-cycle
-
Institute of Mathematics and Its Applications Conference Series New Series. Oxford University Press: New York
-
Maitre JF, Musy F. Algebraic formalisation of the multigrid method in the symmetric and positive definite case-a convergence estimation for the V-cycle. In Multigrid Methods for Integral and Differential Equations (Bristol, 1983), Vol.3, Institute of Mathematics and Its Applications Conference Series New Series. Oxford University Press: New York, 1985; 213-223.
-
(1985)
Multigrid Methods for Integral and Differential Equations (Bristol, 1983)
, vol.3
, pp. 213-223
-
-
Maitre, J.F.1
Musy, F.2
-
15
-
-
0022107998
-
Sharp estimates for multigrid rates of convergence with general smoothing and acceleration
-
Bank RE, Douglas CC. Sharp estimates for multigrid rates of convergence with general smoothing and acceleration. SIAM Journal on Numerical Analysis 1985 22(4):617-633.
-
(1985)
SIAM Journal on Numerical Analysis
, vol.22
, Issue.4
, pp. 617-633
-
-
Bank, R.E.1
Douglas, C.C.2
-
16
-
-
0001685657
-
An algebraic interpretation of multigrid methods
-
McCormick SF. An algebraic interpretation of multigrid methods. SIAM Journal on Numerical Analysis 1982 19(3):548-560.
-
(1982)
SIAM Journal on Numerical Analysis
, vol.19
, Issue.3
, pp. 548-560
-
-
McCormick, S.F.1
-
17
-
-
0021417959
-
Multigrid methods for variational problems: further results
-
McCormick SF. Multigrid methods for variational problems: further results. SIAM Journal on Numerical Analysis 1984 21(2):255-263.
-
(1984)
SIAM Journal on Numerical Analysis
, vol.21
, Issue.2
, pp. 255-263
-
-
McCormick, S.F.1
-
18
-
-
0022107991
-
Multigrid methods for variational problems: general theory for the V-cycle
-
McCormick SF. Multigrid methods for variational problems: general theory for the V-cycle. SIAM Journal on Numerical Analysis 1985 22(4):634-643.
-
(1985)
SIAM Journal on Numerical Analysis
, vol.22
, Issue.4
, pp. 634-643
-
-
McCormick, S.F.1
-
19
-
-
0001927250
-
Algebraic multigrid theory: the symmetric case
-
July
-
Brandt A. Algebraic multigrid theory: the symmetric case. Applied Mathematics and Computation July1986 19: 23-56.
-
(1986)
Applied Mathematics and Computation
, vol.19
, pp. 23-56
-
-
Brandt, A.1
-
20
-
-
84966225192
-
Convergence estimates for product iterative methods with applications to domain decomposition
-
Bramble JH, Pasciak JE, Wang J, Xu J. Convergence estimates for product iterative methods with applications to domain decomposition. Mathematics of Computation 1991 57: 1-21.
-
(1991)
Mathematics of Computation
, vol.57
, pp. 1-21
-
-
Bramble, J.H.1
Pasciak, J.E.2
Wang, J.3
Xu, J.4
-
21
-
-
0036016141
-
The method of alternating projections and the method of subspace corrections in Hilbert space
-
Xu J, Zikatanov L. The method of alternating projections and the method of subspace corrections in Hilbert space. Journal of the American Mathematical Society 2002 15(3):573-597.
-
(2002)
Journal of the American Mathematical Society
, vol.15
, Issue.3
, pp. 573-597
-
-
Xu, J.1
Zikatanov, L.2
-
22
-
-
45549111807
-
Algebraic study of multigrid methods for symmetric, definite problems
-
Mandel J. Algebraic study of multigrid methods for symmetric, definite problems. Applied Mathematics and Computation 1988 25(1, part I):39-56.
-
(1988)
Applied Mathematics and Computation
, vol.25
, Issue.1 PART I
, pp. 39-56
-
-
Mandel, J.1
-
23
-
-
0008313962
-
Parallel multigrid methods
-
ICASE LaRC Interdisciplinary Series in Science and Engineering. Kluwer Acad. Publ.: Dordrecht
-
Jones JE, McCormick SF. Parallel multigrid methods. In Parallel Numerical Algorithms (Hampton, VA, 1994), Vol.4, ICASE LaRC Interdisciplinary Series in Science and Engineering. Kluwer Acad. Publ.: Dordrecht, 1997; 203-224.
-
(1997)
Parallel Numerical Algorithms (Hampton, VA, 1994)
, vol.4
, pp. 203-224
-
-
Jones, J.E.1
McCormick, S.F.2
-
24
-
-
0036532956
-
BoomerAMG: a parallel algebraic multigrid solver and preconditioner
-
Developments and trends in iterative methods for large systems of equations-in memoriam Rüdiger Weiss (Lausanne, 2000).
-
Henson VE, Yang UM. BoomerAMG: a parallel algebraic multigrid solver and preconditioner. Applied Numerical Mathematics. An IMACS Journal 2002 41(1):155-177. Developments and trends in iterative methods for large systems of equations-in memoriam Rüdiger Weiss (Lausanne, 2000).
-
(2002)
Applied Numerical Mathematics. An IMACS Journal
, vol.41
, Issue.1
, pp. 155-177
-
-
Henson, V.E.1
Yang, U.M.2
-
25
-
-
70249096845
-
Auxiliary space AMG for H(curl) problems
-
Langer U, Discacciati M, Keyes DE, Widlund OB, Zulehner W, Barth TJ, Griebel M, Keyes DE, Nieminen RM, Roose D, Schlick T (eds), Lecture Notes in Computational Science and Engineering. Springer Berlin: Heidelberg
-
Kolev TV, Vassilevski PS. Auxiliary space AMG for H(curl) problems. In Domain Decomposition Methods in Science and Engineering XVII, Vol.60, Langer U, Discacciati M, Keyes DE, Widlund OB, Zulehner W, Barth TJ, Griebel M, Keyes DE, Nieminen RM, Roose D, Schlick T (eds), Lecture Notes in Computational Science and Engineering. Springer Berlin: Heidelberg, 2008; 147-154.
-
(2008)
Domain Decomposition Methods in Science and Engineering XVII
, vol.60
, pp. 147-154
-
-
Kolev, T.V.1
Vassilevski, P.S.2
-
27
-
-
0142055288
-
An algebraic multigrid method for finite element discretizations with edge elements
-
Reitzinger S, Schöberl J. An algebraic multigrid method for finite element discretizations with edge elements. Numerical Linear Algebra with Applications 2002 9: 223-238.
-
(2002)
Numerical Linear Algebra with Applications
, vol.9
, pp. 223-238
-
-
Reitzinger, S.1
Schöberl, J.2
-
28
-
-
1842479841
-
Spectral AMGe (ρ AMGe)
-
Chartier T, Falgout RD, Henson VE, Jones J, Manteuffel T, McCormick S, Ruge J, Vassilevski PS. Spectral AMGe (ρ AMGe). SIAM Journal on Scientific Computing 2003 25(1):1-26.
-
(2003)
SIAM Journal on Scientific Computing
, vol.25
, Issue.1
, pp. 1-26
-
-
Chartier, T.1
Falgout, R.D.2
Henson, V.E.3
Jones, J.4
Manteuffel, T.5
McCormick, S.6
Ruge, J.7
Vassilevski, P.S.8
-
29
-
-
33645377668
-
Adaptive algebraic multigrid
-
Brezina M, Falgout R, MacLachlan S, Manteuffel T, McCormick S, Ruge J. Adaptive algebraic multigrid. SIAM Journal on Scientific Computing 2006 27(4):1261-1286.
-
(2006)
SIAM Journal on Scientific Computing
, vol.27
, Issue.4
, pp. 1261-1286
-
-
Brezina, M.1
Falgout, R.2
MacLachlan, S.3
Manteuffel, T.4
McCormick, S.5
Ruge, J.6
-
30
-
-
21244472010
-
Adaptive smoothed aggregation (αSA) multigrid
-
Brezina M, Falgout R, MacLachlan S, Manteuffel T, McCormick S, Ruge J. Adaptive smoothed aggregation (αSA) multigrid. SIAM Review 2005 47(2):317-346.
-
(2005)
SIAM Review
, vol.47
, Issue.2
, pp. 317-346
-
-
Brezina, M.1
Falgout, R.2
MacLachlan, S.3
Manteuffel, T.4
McCormick, S.5
Ruge, J.6
-
31
-
-
10244278127
-
Adaptive smoothed aggregation (αSA)
-
Brezina M, Falgout R, MacLachlan S, Manteuffel T, McCormick S, Ruge J. Adaptive smoothed aggregation (αSA). SIAM Journal on Scientific Computing 2004 25(6):1896-1920.
-
(2004)
SIAM Journal on Scientific Computing
, vol.25
, Issue.6
, pp. 1896-1920
-
-
Brezina, M.1
Falgout, R.2
MacLachlan, S.3
Manteuffel, T.4
McCormick, S.5
Ruge, J.6
-
32
-
-
0030388574
-
Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
-
Vaněk P, Mandel J, Brezina M. Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. Computing. Archives for Scientific Computing 1996 56(3):179-196.
-
(1996)
Computing. Archives for Scientific Computing
, vol.56
, Issue.3
, pp. 179-196
-
-
Vaněk, P.1
Mandel, J.2
Brezina, M.3
-
34
-
-
77953814525
-
Compatible relaxation and coarsening in algebraic multigrid
-
Brannick JJ, Falgout RD. Compatible relaxation and coarsening in algebraic multigrid. SIAM Journal on Scientific Computing 2010 32(3):1393-1416.
-
(2010)
SIAM Journal on Scientific Computing
, vol.32
, Issue.3
, pp. 1393-1416
-
-
Brannick, J.J.1
Falgout, R.D.2
-
37
-
-
79957581762
-
Bootstrap AMG
-
Brandt A, Brannick J, Kahl K, Livshits I. Bootstrap AMG. SIAM Journal on Scientific Computing 2011 33(2):612-632.
-
(2011)
SIAM Journal on Scientific Computing
, vol.33
, Issue.2
, pp. 612-632
-
-
Brandt, A.1
Brannick, J.2
Kahl, K.3
Livshits, I.4
-
39
-
-
0003810147
-
-
Mathematics and its Applications, Kluwer Academic Publishers Group: Dordrecht, Translated from the 1989 Russian original by N. B. Urusova and revised by the author.
-
Shaǐdurov VV. Multigrid Methods for Finite Elements, Mathematics and its Applications, Vol.318. Kluwer Academic Publishers Group: Dordrecht, 1995. Translated from the 1989 Russian original by N. B. Urusova and revised by the author.
-
(1995)
Multigrid Methods for Finite Elements
, vol.318
-
-
Shaǐdurov, V.V.1
-
40
-
-
84966216042
-
Convergence of multi-grid iterations applied to difference equations
-
April
-
Hackbusch W. Convergence of multi-grid iterations applied to difference equations. Mathematics of Computation April1980 34(150):425-440.
-
(1980)
Mathematics of Computation
, vol.34
, Issue.150
, pp. 425-440
-
-
Hackbusch, W.1
-
41
-
-
33846798182
-
A V-cycle multigrid for multilevel matrix algebras: proof of optimality
-
Aricò A, Donatelli M. A V-cycle multigrid for multilevel matrix algebras: proof of optimality. Numerische Mathematik 2007 105(4):511-547.
-
(2007)
Numerische Mathematik
, vol.105
, Issue.4
, pp. 511-547
-
-
Aricò, A.1
Donatelli, M.2
-
42
-
-
84893795196
-
-
On the convergence of multi-grid iteration. Technical Report 79-4, Mathematisches Institut, Universität zu Köln
-
Hackbusch W. On the convergence of multi-grid iteration. Technical Report 79-4, Mathematisches Institut, Universität zu Köln, 1979.
-
(1979)
-
-
Hackbusch, W.1
-
43
-
-
0005589275
-
Survey of convergence proofs for multigrid iteration
-
Frehse J, Pallasche D, Trottenberg U (eds). North Holland Publishing Company: Amsterdam, New York
-
Hackbusch W. Survey of convergence proofs for multigrid iteration. In Special Topics in Applied Mathematics, Frehse J, Pallasche D, Trottenberg U (eds). North Holland Publishing Company: Amsterdam, New York, 1980; 151-164.
-
(1980)
Special Topics in Applied Mathematics
, pp. 151-164
-
-
Hackbusch, W.1
-
45
-
-
22144438010
-
Algebraic multigrid and algebraic multilevel methods: a theoretical comparison
-
Notay Y. Algebraic multigrid and algebraic multilevel methods: a theoretical comparison. Numerical Linear Algebra with Applications 2005 12(5-6):419-451.
-
(2005)
Numerical Linear Algebra with Applications
, vol.12
, Issue.5-6
, pp. 419-451
-
-
Notay, Y.1
-
48
-
-
4043106376
-
Multigrid solvers and multilevel optimization strategies
-
Cong J, Shinnerl JR (eds), Combinatorial Optimization. Kluwer Academic Publishers: Dordrecht, The Netherlands
-
Brandt A, Ron D. Multigrid solvers and multilevel optimization strategies. In Multilevel Optimization in VLSICAD, Vol.14, Cong J, Shinnerl JR (eds), Combinatorial Optimization. Kluwer Academic Publishers: Dordrecht, The Netherlands, 2003; 1-69.
-
(2003)
Multilevel Optimization in VLSICAD
, vol.14
, pp. 1-69
-
-
Brandt, A.1
Ron, D.2
-
49
-
-
84861387731
-
An algebraic multigrid method with guaranteed convergence rate
-
Napov A, Notay Y. An algebraic multigrid method with guaranteed convergence rate. SIAM Journal on Scientific Computing 2012 34(2):A1079-A1109.
-
(2012)
SIAM Journal on Scientific Computing
, vol.34
, Issue.2
-
-
Napov, A.1
Notay, Y.2
-
50
-
-
84885013804
-
Algebraic multilevel preconditioners for the graph Laplacian based on matching in graphs
-
Brannick J, Chen Y, Kraus J, Zikatanov L. Algebraic multilevel preconditioners for the graph Laplacian based on matching in graphs. SIAM Journal on Numerical Analysis 2013 51(3):1805-1827.
-
(2013)
SIAM Journal on Numerical Analysis
, vol.51
, Issue.3
, pp. 1805-1827
-
-
Brannick, J.1
Chen, Y.2
Kraus, J.3
Zikatanov, L.4
-
51
-
-
77949647205
-
Operator-based interpolation for bootstrap algebraic multigrid
-
Manteuffel T, McCormick S, Park M, Ruge J. Operator-based interpolation for bootstrap algebraic multigrid. Numerical Linear Algebra with Applications 2010 17(2-3):519-537.
-
(2010)
Numerical Linear Algebra with Applications
, vol.17
, Issue.2-3
, pp. 519-537
-
-
Manteuffel, T.1
McCormick, S.2
Park, M.3
Ruge, J.4
-
52
-
-
84856586225
-
Relaxation-corrected bootstrap algebraic multigrid (rBAMG)
-
Brezina M, Ketelsen C, Manteuffel T, McCormick S, Park M, Ruge J. Relaxation-corrected bootstrap algebraic multigrid (rBAMG). Numerical Linear Algebra with Applications 2012 19(2):178-193.
-
(2012)
Numerical Linear Algebra with Applications
, vol.19
, Issue.2
, pp. 178-193
-
-
Brezina, M.1
Ketelsen, C.2
Manteuffel, T.3
McCormick, S.4
Park, M.5
Ruge, J.6
-
54
-
-
15944403194
-
Algebraic multigrid for higher-order finite elements
-
Heys JJ, Manteuffel TA, McCormick SF, Olson LN. Algebraic multigrid for higher-order finite elements. Journal of Computational Physics 2005 204(2):520-532.
-
(2005)
Journal of Computational Physics
, vol.204
, Issue.2
, pp. 520-532
-
-
Heys, J.J.1
Manteuffel, T.A.2
McCormick, S.F.3
Olson, L.N.4
|