메뉴 건너뛰기




Volumn 34, Issue 2, 2012, Pages

An algebraic multigrid method with guaranteed convergence rate

Author keywords

Aggregation; Algebraic multigrid; Convergence analysis; Iterative methods; Multigrid; Preconditioner

Indexed keywords

AGGREGATES; ALGEBRA; LINEAR SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 84861387731     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/100818509     Document Type: Article
Times cited : (214)

References (35)
  • 2
    • 0000779223 scopus 로고
    • Algebraic multilevel preconditioning methods. i
    • O. Axelsson and P. S. Vassilevski, Algebraic multilevel preconditioning methods. I, Numer. Math., 56 (1989), pp. 157-177.
    • (1989) Numer. Math. , vol.56 , pp. 157-177
    • Axelsson, O.1    Vassilevski, P.S.2
  • 3
    • 0001573921 scopus 로고
    • Algebraic multilevel preconditioning methods II
    • O. Axelsson and P. S. Vassilevski, Algebraic multilevel preconditioning methods, II, SIAM J. Numer. Anal., 27 (1990), pp. 1569-1590.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 1569-1590
    • Axelsson, O.1    Vassilevski, P.S.2
  • 4
    • 0029488033 scopus 로고
    • Towards algebraic multigrid for elliptic problems of second order
    • D. Braess, Towards algebraic multigrid for elliptic problems of second order, Computing, 55 (1995), pp. 379-393.
    • (1995) Computing , vol.55 , pp. 379-393
    • Braess, D.1
  • 5
    • 0002438068 scopus 로고
    • Algebraic multigrid (AMG) for sparse matrix equations
    • D. J. Evans, ed., Cambridge University Press, Cambridge, UK
    • A. Brandt, S. F. McCormick, and J. W. Ruge, Algebraic multigrid (AMG) for sparse matrix equations, in Sparsity and Its Applications, D. J. Evans, ed., Cambridge University Press, Cambridge, UK, 1985, pp. 257-284.
    • (1985) Sparsity and Its Applications , pp. 257-284
    • Brandt, A.1    McCormick, S.F.2    Ruge, J.W.3
  • 8
    • 84859724300 scopus 로고    scopus 로고
    • An improved convergence analysis of smoothed aggregation algebraic multigrid
    • to appear.
    • M. Brezina, P. Vaněk, and P. S. Vassilevski, An improved convergence analysis of smoothed aggregation algebraic multigrid, Numer. Linear Algebra Appl., to appear.
    • Numer. Linear Algebra Appl.
    • Brezina, M.1    Vaněk, P.2    Vassilevski, P.S.3
  • 9
    • 0027641332 scopus 로고
    • Multi-level iterative technique and aggregation concept with semi-analytical preconditioning for solving boundary-value problems
    • V. E. Bulgakov, Multi-level iterative technique and aggregation concept with semi-analytical preconditioning for solving boundary value problems, Comm. Numer. Methods Engrg., 9 (1993), pp. 649-657. (Pubitemid 23688507)
    • (1993) Communications in Numerical Methods in Engineering , vol.9 , Issue.8 , pp. 649-657
    • Bulgakov, V.E.1
  • 12
    • 77953131795 scopus 로고    scopus 로고
    • Performance of parallel AMG-preconditioners in CFD-codes for weakly compressible flows
    • M. Emans, Performance of parallel AMG-preconditioners in CFD-codes for weakly compressible flows, Parallel Comput., 36 (2010), pp. 326-338.
    • (2010) Parallel Comput. , vol.36 , pp. 326-338
    • Emans, M.1
  • 13
    • 22144473175 scopus 로고    scopus 로고
    • On generalizing the algebraic multigrid framework
    • DOI 10.1137/S0036142903429742
    • R. D. Falgout and P. S. Vassilevski, On generalizing the algebraic multigrid framework, SIAM J. Numer. Anal., 42 (2004), pp. 1669-1693. (Pubitemid 41366170)
    • (2004) SIAM Journal on Numerical Analysis , vol.42 , Issue.4 , pp. 1669-1693
    • Falgout, R.D.1    Vassilevski, P.S.2
  • 15
    • 0036226531 scopus 로고    scopus 로고
    • Element-free AMGe: General algorithms for computing interpolation weights in AMG
    • DOI 10.1137/S1064827500372997, PII S1064827500372997
    • V. E. Henson and P. S. Vassilevski, Element-free AMGe: General algorithms for computing interpolation weights in AMG, SIAM J. Sci. Comput., 23 (2001), pp. 629-650. (Pubitemid 34308006)
    • (2002) SIAM Journal of Scientific Computing , vol.23 , Issue.2 , pp. 629-650
    • Henson, V.E.1    Vassilevski, P.S.2
  • 16
    • 0036211804 scopus 로고    scopus 로고
    • AMGe based on element agglomeration
    • DOI 10.1137/S1064827599361047, PII S1064827599361047
    • J. E. Jones and P. S. Vassilevski, AMGe based on element agglomeration, SIAM J. Sci. Comput., 23 (2001), pp. 109-133. (Pubitemid 34278152)
    • (2002) SIAM Journal of Scientific Computing , vol.23 , Issue.1 , pp. 109-133
    • Jones, J.E.1    Vassilevski, P.S.2
  • 17
    • 0037233450 scopus 로고    scopus 로고
    • A multigrid method based on graph matching for convectiondiffusion equations
    • H. Kim, J. Xu, and L. Zikatanov, A multigrid method based on graph matching for convectiondiffusion equations, Numer. Linear Algebra Appl., 10 (2003), pp. 181-195.
    • (2003) Numer. Linear Algebra Appl. , vol.10 , pp. 181-195
    • Kim, H.1    Xu, J.2    Zikatanov, L.3
  • 18
    • 0032634013 scopus 로고    scopus 로고
    • Energy optimization of algebraic multigrid bases
    • J. Mandel, M. Brezina, and P. Vaněk, Energy optimization of algebraic multigrid bases, Computing, 62 (1999), pp. 205-228.
    • (1999) Computing , vol.62 , pp. 205-228
    • Mandel, J.1    Brezina, M.2    Vaněk, P.3
  • 19
    • 55549139507 scopus 로고    scopus 로고
    • Analysis of aggregation-based multigrid
    • A. C. Muresan and Y. Notay, Analysis of aggregation-based multigrid, SIAM J. Sci. Comput., 30 (2008), pp. 1082-1103.
    • (2008) SIAM J. Sci. Comput. , vol.30 , pp. 1082-1103
    • Muresan, A.C.1    Notay, Y.2
  • 20
    • 79954552462 scopus 로고    scopus 로고
    • Algebraic analysis of aggregation-based multigrid
    • A. Napov and Y. Notay, Algebraic analysis of aggregation-based multigrid, Numer. Linear Algebra Appl., 18 (2011), pp. 539-564.
    • (2011) Numer. Linear Algebra Appl. , vol.18 , pp. 539-564
    • Napov, A.1    Notay, Y.2
  • 22
    • 77955681191 scopus 로고    scopus 로고
    • An aggregation-based algebraic multigrid method
    • Y. Notay, An aggregation-based algebraic multigrid method, Electron. Trans. Numer. Anal., 37 (2010), pp. 123-146.
    • (2010) Electron. Trans. Numer. Anal. , vol.37 , pp. 123-146
    • Notay, Y.1
  • 25
    • 0001885411 scopus 로고
    • Algebraic multigrid
    • S. F. McCormick, ed., SIAM, Philadelphia
    • J. W. Ruge and K. Stüben, Algebraic multigrid, in Multigrid Methods, Frontiers Appl. Math. 3, S. F. McCormick, ed., SIAM, Philadelphia, 1987, pp. 73-130.
    • (1987) Multigrid Methods, Frontiers Appl. Math. , vol.3 , pp. 73-130
    • Ruge, J.W.1    Stüben, K.2
  • 26
    • 0003338384 scopus 로고    scopus 로고
    • An introduction to algebraic multigrid
    • Academic Press, San Diego, CA
    • K. Stüben, An introduction to algebraic multigrid, in Multigrid, Academic Press, San Diego, CA, 2001, pp. 413-532.
    • (2001) Multigrid , pp. 413-532
    • Stüben, K.1
  • 28
    • 0041034172 scopus 로고    scopus 로고
    • Convergence of algebraic multigrid based on smoothed aggregation
    • DOI 10.1007/s211-001-8015-y
    • P. Vaněk, M. Brezina, and J. Mandel, Convergence of algebraic multigrid based on smoothed aggregation, Numer. Math., 88 (2001), pp. 559-579. (Pubitemid 33573395)
    • (2001) Numerische Mathematik , vol.88 , Issue.3 , pp. 559-579
    • Vanek, P.1    Brezina, M.2    Mandel, J.3
  • 29
    • 0030388574 scopus 로고    scopus 로고
    • Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
    • P. Vaněk, J. Mandel, and M. Brezina, Algebraic multigrid based on smoothed aggregation for second and fourth order elliptic problems, Computing, 56 (1996), pp. 179-196. (Pubitemid 126633416)
    • (1996) Computing (Vienna/New York) , vol.56 , Issue.3 , pp. 179-196
    • Vanek, P.1    Mandel, J.2    Brezina, M.3
  • 30
    • 0001547219 scopus 로고
    • Hybrid V-cycle algebraic multilevel preconditioners
    • P. S. Vassilevski, Hybrid V-cycle algebraic multilevel preconditioners, Math. Comp., 58 (1992), pp. 489-512.
    • (1992) Math. Comp. , vol.58 , pp. 489-512
    • Vassilevski, P.S.1
  • 32
    • 77249093542 scopus 로고    scopus 로고
    • General constrained energy minimization interpolation mappings for AMG
    • P. S. Vassilevski, General constrained energy minimization interpolation mappings for AMG, SIAM J. Sci. Comput., 32 (2010), pp. 1-13.
    • (2010) SIAM J. Sci. Comput. , vol.32 , pp. 1-13
    • Vassilevski, P.S.1
  • 33
    • 33750175378 scopus 로고    scopus 로고
    • Multiple vector preserving interpolation mappings in algebraic multigrid
    • DOI 10.1137/040618205
    • P. S. Vassilevski and L. T. Zikatanov, Multiple vector preserving interpolation mappings in algebraic multigrid, SIAM J. Matrix Anal. Appl., 27 (2006), pp. 1040-1055. (Pubitemid 44599415)
    • (2006) SIAM Journal on Matrix Analysis and Applications , vol.27 , Issue.4 , pp. 1040-1055
    • Vassilevski, P.S.1    Zikatanov, L.T.2
  • 34
    • 33750712884 scopus 로고    scopus 로고
    • AMGe - Coarsening strategies and application to the oseen equations
    • DOI 10.1137/040610350
    • M. Wabro, AMGe-Coarsening strategies and application to the Oseen equations, SIAM J. Sci. Comput., 27 (2006), pp. 2077-2097. (Pubitemid 44784229)
    • (2006) SIAM Journal of Scientific Computing , vol.27 , Issue.6 , pp. 2077-2097
    • Wabro, M.1
  • 35
    • 33750160340 scopus 로고    scopus 로고
    • On an energy minimizing basis for algebraic multigrid methods
    • J. Xu and L. Zikatanov, On an energy minimizing basis for algebraic multigrid methods, Comput. Vis. Sci., 7 (2004), p. 121-127.
    • (2004) Comput. Vis. Sci. , vol.7 , pp. 121-127
    • Xu, J.1    Zikatanov, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.