메뉴 건너뛰기




Volumn 13, Issue 1, 2006, Pages 49-70

Algebraic multilevel preconditioning of finite element matrices using local Schur complements

Author keywords

Iterative methods; Local schur complements; Multilevel preconditioning

Indexed keywords


EID: 31644445132     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.462     Document Type: Article
Times cited : (44)

References (38)
  • 1
    • 0001326593 scopus 로고
    • Efficient solution of finite difference and finite element equations by algebraic multigrid (AMG)
    • Paddon DJ, Holstein H (eds). Clarendon Press: Oxford
    • Ruge JW, Stüben K. Efficient solution of finite difference and finite element equations by algebraic multigrid (AMG). In Multigrid Methods for Integral and Differential Equations, Paddon DJ, Holstein H (eds). Clarendon Press: Oxford, 1985; 169-212.
    • (1985) Multigrid Methods for Integral and Differential Equations , pp. 169-212
    • Ruge, J.W.1    Stüben, K.2
  • 4
    • 0036226531 scopus 로고    scopus 로고
    • Element-free AMGe: General algorithms for computing the interpolation weights in AMG
    • Henson VE, Vassilevski PS. Element-free AMGe: general algorithms for computing the interpolation weights in AMG. SIAM Journal on Scientific Computing 2001; 23:629-650.
    • (2001) SIAM Journal on Scientific Computing , vol.23 , pp. 629-650
    • Henson, V.E.1    Vassilevski, P.S.2
  • 6
    • 0000762041 scopus 로고
    • An approximate factorization procedure for solving self-adjoint elliptic difference equations
    • Dupont T, Kendall RP, Rachford HH. An approximate factorization procedure for solving self-adjoint elliptic difference equations. SIAM Journal on Numerical Analysis 1968; 5:559-573.
    • (1968) SIAM Journal on Numerical Analysis , vol.5 , pp. 559-573
    • Dupont, T.1    Kendall, R.P.2    Rachford, H.H.3
  • 7
    • 0001085784 scopus 로고    scopus 로고
    • ILUM: A multi-elimination ILU preconditioner for general sparse matrices
    • Saad Y. ILUM: a multi-elimination ILU preconditioner for general sparse matrices. SIAM Journal on Scientific and Statistical Computing 1996; 17:830-847.
    • (1996) SIAM Journal on Scientific and Statistical Computing , vol.17 , pp. 830-847
    • Saad, Y.1
  • 9
    • 0000279499 scopus 로고
    • The nested recursive two-level factorization method for nine-point difference matrices
    • Axelsson O, Eijkhout V. The nested recursive two-level factorization method for nine-point difference matrices. SIAM Journal on Scientific and Statistical Computing 1991; 12:1373-1400.
    • (1991) SIAM Journal on Scientific and Statistical Computing , vol.12 , pp. 1373-1400
    • Axelsson, O.1    Eijkhout, V.2
  • 10
    • 0042260619 scopus 로고    scopus 로고
    • Condition numbers of approximate Schur complements in two- And three-dimensional discretizations on hierarchically ordered grids
    • Kraus JK, Brand CW. Condition numbers of approximate Schur complements in two- and three-dimensional discretizations on hierarchically ordered grids. Computing 2000; 65:135-154.
    • (2000) Computing , vol.65 , pp. 135-154
    • Kraus, J.K.1    Brand, C.W.2
  • 11
    • 0034511247 scopus 로고    scopus 로고
    • Optimal order preconditioning of finite difference matrices
    • Notay Y. Optimal order preconditioning of finite difference matrices. SIAM Journal on Scientific Computing 2000; 21:1991-2007.
    • (2000) SIAM Journal on Scientific Computing , vol.21 , pp. 1991-2007
    • Notay, Y.1
  • 13
    • 38249042495 scopus 로고
    • A general incomplete block-matrix factorization method
    • Axelsson O. A general incomplete block-matrix factorization method. Linear Algebra and its Applications 1986; 74:179-190.
    • (1986) Linear Algebra and Its Applications , vol.74 , pp. 179-190
    • Axelsson, O.1
  • 17
    • 0033207377 scopus 로고    scopus 로고
    • A multilevel block incomplete factorization preconditioning
    • Notay Y. A multilevel block incomplete factorization preconditioning. Applied Numerical Mathematics 1999; 31:209-225.
    • (1999) Applied Numerical Mathematics , vol.31 , pp. 209-225
    • Notay, Y.1
  • 18
    • 0034397438 scopus 로고    scopus 로고
    • A robust algebraic multilevel preconditioner for non-symmetric M-matrices
    • Notay Y. A robust algebraic multilevel preconditioner for non-symmetric M-matrices. Numerical Linear Algebra with Applications 2000; 7:243-267.
    • (2000) Numerical Linear Algebra with Applications , vol.7 , pp. 243-267
    • Notay, Y.1
  • 20
    • 0000779223 scopus 로고
    • Algebraic multilevel preconditioning methods 1
    • Axelsson O, Vassilevski PS. Algebraic multilevel preconditioning methods 1. Numerische Mathematik 1989; 56:157-177.
    • (1989) Numerische Mathematik , vol.56 , pp. 157-177
    • Axelsson, O.1    Vassilevski, P.S.2
  • 22
    • 0001116752 scopus 로고
    • A black box generalized conjugate gradient solver with inner iterations and variablestep preconditioning
    • Axelsson O, Vassilevski PS. A black box generalized conjugate gradient solver with inner iterations and variablestep preconditioning. SIAM Journal on Matrix Analysis and Applications 1991; 12:625-644.
    • (1991) SIAM Journal on Matrix Analysis and Applications , vol.12 , pp. 625-644
    • Axelsson, O.1    Vassilevski, P.S.2
  • 23
    • 84985330885 scopus 로고
    • Variable-step multilevel preconditioning methods, 1: Self-adjoint and positive definite elliptic problems
    • Axelsson O, Vassilevski PS. Variable-step multilevel preconditioning methods, 1: self-adjoint and positive definite elliptic problems. Numerical Linear Algebra with Applications 1994; 1:75-101.
    • (1994) Numerical Linear Algebra with Applications , vol.1 , pp. 75-101
    • Axelsson, O.1    Vassilevski, P.S.2
  • 24
    • 0036453449 scopus 로고    scopus 로고
    • An algebraic preconditioning method for M-Matrices: Linear versus nonlinear multilevel iteration
    • Kraus JK. An algebraic preconditioning method for M-Matrices: linear versus nonlinear multilevel iteration. Numerical Linear Algebra with Applications 2002; 9:599-618.
    • (2002) Numerical Linear Algebra with Applications , vol.9 , pp. 599-618
    • Kraus, J.K.1
  • 25
    • 0032252492 scopus 로고    scopus 로고
    • Optimal V-cycle algebraic multilevel preconditioning
    • Notay Y. Optimal V-cycle algebraic multilevel preconditioning. Numerical Linear Algebra with Applications 1998; 5:441-459.
    • (1998) Numerical Linear Algebra with Applications , vol.5 , pp. 441-459
    • Notay, Y.1
  • 26
    • 0031101117 scopus 로고    scopus 로고
    • On two ways of stabilizing the hierarchical basis multilevel methods
    • Vassilevski PS. On two ways of stabilizing the hierarchical basis multilevel methods. SIAM Reiiew 1997; 39:18-53.
    • (1997) SIAM Reiiew , vol.39 , pp. 18-53
    • Vassilevski, P.S.1
  • 27
    • 0006743875 scopus 로고    scopus 로고
    • A unified framework for the construction of various algebraic multilevel preconditioning methods
    • Axelsson O, Bai Z. A unified framework for the construction of various algebraic multilevel preconditioning methods. Acta Mathematicae Applicatae Sinica 1999; 15:132-143.
    • (1999) Acta Mathematicae Applicatae Sinica , vol.15 , pp. 132-143
    • Axelsson, O.1    Bai, Z.2
  • 28
    • 85022608074 scopus 로고    scopus 로고
    • Hierarchical bases and the finite element method
    • Bank RE. Hierarchical bases and the finite element method. Acta Numerica 1996; 5:1-43.
    • (1996) Acta Numerica , vol.5 , pp. 1-43
    • Bank, R.E.1
  • 29
    • 0026219648 scopus 로고
    • The role of the strengthened CBS inequality in multilevel methods
    • Eijkhout V, Vassilevski PS. The role of the strengthened CBS inequality in multilevel methods. SIAM Review 1991; 33:405-419.
    • (1991) SIAM Review , vol.33 , pp. 405-419
    • Eijkhout, V.1    Vassilevski, P.S.2
  • 30
    • 84985370889 scopus 로고
    • Upper bound of the constant in the strengthened C.B.S. inequality for FEM 2D elasticity equations
    • Margenov SD. Upper bound of the constant in the strengthened C.B.S. inequality for FEM 2D elasticity equations. Numerical Linear Algebra with Applications 1994; 1:65-74.
    • (1994) Numerical Linear Algebra with Applications , vol.1 , pp. 65-74
    • Margenov, S.D.1
  • 31
    • 0012788594 scopus 로고
    • Nearly optimal iterative methods for solving finite element elliptic equations based on multilevel splitting of the matrix
    • Institute for Scientific Computation, University of Wyoming, Laramie, U.S.A.
    • Vassilevski PS. Nearly optimal iterative methods for solving finite element elliptic equations based on multilevel splitting of the matrix. Technical Report 1989-09, Institute for Scientific Computation, University of Wyoming, Laramie, U.S.A., 1989.
    • (1989) Technical Report , vol.1989 , Issue.9
    • Vassilevski, P.S.1
  • 32
    • 0032344210 scopus 로고    scopus 로고
    • Using approximate inverses in algebraic multilevel methods
    • Notay Y. Using approximate inverses in algebraic multilevel methods. Numerische Mathematik 1998; 80: 397-417.
    • (1998) Numerische Mathematik , vol.80 , pp. 397-417
    • Notay, Y.1
  • 33
    • 0036391779 scopus 로고    scopus 로고
    • Robust parameter-free algebraic multilevel preconditioning
    • Notay Y. Robust parameter-free algebraic multilevel preconditioning. Numerical Linear Algebra with Applications 2002; 9:409-428.
    • (2002) Numerical Linear Algebra with Applications , vol.9 , pp. 409-428
    • Notay, Y.1
  • 35
    • 31644446351 scopus 로고    scopus 로고
    • An agglomeration-based multilevel-topology concept with application to 3D-FE meshes
    • Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Austria
    • Kraus JK, Synka J. An agglomeration-based multilevel-topology concept with application to 3D-FE meshes. Technical Report 2004-08, Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Austria, 2004.
    • (2004) Technical Report , vol.2004 , Issue.8
    • Kraus, J.K.1    Synka, J.2
  • 36
    • 0142109867 scopus 로고    scopus 로고
    • On the existence problem of incomplete factorisation methods
    • UT-CS-99-435, Computer Science Department, University of Tennessee, U.S.A.
    • Eijkhout V. On the existence problem of incomplete factorisation methods. Lapack Working Note 144, UT-CS-99-435, Computer Science Department, University of Tennessee, U.S.A., 1999.
    • (1999) Lapack Working Note , vol.144
    • Eijkhout, V.1
  • 38
    • 0033293990 scopus 로고    scopus 로고
    • On the additive version of the algebraic multilevel iteration method for anisotropic elliptic problems
    • Axelsson O, Padiy A. On the additive version of the algebraic multilevel iteration method for anisotropic elliptic problems. SIAM Journal on Scientific Computing 1999; 20:1807-1830.
    • (1999) SIAM Journal on Scientific Computing , vol.20 , pp. 1807-1830
    • Axelsson, O.1    Padiy, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.