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Volumn 26, Issue , 2007, Pages 330-349

Efficient deflation methods applied to 3-D bubbly flow problems

Author keywords

Bubbly flow problems; Conjugate gradient method; Deflation; Inner outer iterations; Poisson equation; Preconditioning; Symmetric positive semi definite matrices

Indexed keywords

BOUNDARY CONDITIONS; ITERATIVE METHODS; MATRIX ALGEBRA; POISSON EQUATION;

EID: 37649024547     PISSN: None     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (20)

References (33)
  • 1
    • 0031488469 scopus 로고    scopus 로고
    • Deflated and augmented Krylov subspace techniques
    • A. CHAPMAN AND Y. SAAD, Deflated and augmented Krylov subspace techniques, Numer. Linear Algebra Appl., 4 (1997), pp. 43-66.
    • (1997) Numer. Linear Algebra Appl , vol.4 , pp. 43-66
    • CHAPMAN, A.1    SAAD, Y.2
  • 3
    • 0001677218 scopus 로고
    • Black box multigrid
    • J. E. DENDY, JR., Black box multigrid, J. Comput. Phys., 48 (1982), pp. 366-386.
    • (1982) J. Comput. Phys , vol.48 , pp. 366-386
    • DENDY JR., J.E.1
  • 4
    • 0010957862 scopus 로고
    • An additive Schwarz algorithm for two and three dimensional finite element elliptic problems
    • Methods, T. F. Chan, R. Glowinski, J. Periaux, and O. B. Widlund, eds, SIAM, Philadelphia, PA
    • M. DRYJA, An additive Schwarz algorithm for two and three dimensional finite element elliptic problems, in Domain Decomposition Methods, T. F. Chan, R. Glowinski, J. Periaux, and O. B. Widlund, eds., SIAM, Philadelphia, PA, 1989, pp. 168-172.
    • (1989) Domain Decomposition , pp. 168-172
    • DRYJA, M.1
  • 5
    • 0002059273 scopus 로고
    • Towards a unified theory of domain decomposition algorithms for elliptic problems
    • Equations, T. F. Chan, R. Glowinski, J. Periaux, and O. B. Widlund, eds, SIAM, Philadelphia, PA
    • M. DRYJA AND O. B. WIDLUND, Towards a unified theory of domain decomposition algorithms for elliptic problems, 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, PA, 1990, pp. 3-21.
    • (1990) Third International Symposium on Domain Decomposition Methods for Partial Differential , pp. 3-21
    • DRYJA, M.1    WIDLUND, O.B.2
  • 6
    • 84990712164 scopus 로고
    • Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems
    • M. DRYJA AND O. B. WIDLUND, Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems, Comm. Pure Appl. Math., 48 (1995), pp. 121-155.
    • (1995) Comm. Pure Appl. Math , vol.48 , pp. 121-155
    • DRYJA, M.1    WIDLUND, O.B.2
  • 7
    • 0036227210 scopus 로고    scopus 로고
    • On the construction of deflation-based preconditioners
    • J. FRANK AND C. VUIK, On the construction of deflation-based preconditioners, SIAM J. Sci. Comput., 23 (2001), pp. 442-462.
    • (2001) SIAM J. Sci. Comput , vol.23 , pp. 442-462
    • FRANK, J.1    VUIK, C.2
  • 8
    • 0004236492 scopus 로고    scopus 로고
    • Third ed, The John Hopkins University Press, Baltimore
    • G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, Third ed., The John Hopkins University Press, Baltimore, 1996.
    • (1996) Matrix Computations
    • GOLUB, G.H.1    VAN LOAN, C.F.2
  • 9
    • 0033293064 scopus 로고    scopus 로고
    • 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
  • 10
    • 0004151494 scopus 로고
    • Cambridge University Press, USA Edition
    • R. HORN AND C. JOHNSON, Matrix Analysis, Cambridge University Press, USA Edition, 1990.
    • (1990) Matrix Analysis
    • HORN, R.1    JOHNSON, C.2
  • 11
    • 0001595571 scopus 로고
    • Preconditioned conjugate gradients for solving singular systems
    • E. F. KAASSCHIETER, Preconditioned conjugate gradients for solving singular systems, J. Comput. Appl. Math., 24 (1988), pp. 265-275.
    • (1988) J. Comput. Appl. Math , vol.24 , pp. 265-275
    • KAASSCHIETER, E.F.1
  • 12
    • 54649084720 scopus 로고    scopus 로고
    • Preconditioning of systems of linear algebraic equations by means of twofold deflation, I. Theory
    • L. YU. KOLOTILINA, Preconditioning of systems of linear algebraic equations by means of twofold deflation, I. Theory, J. Math. Sci., 89 (1998), pp. 1652-1689.
    • (1998) J. Math. Sci , vol.89 , pp. 1652-1689
    • YU. KOLOTILINA, L.1
  • 13
    • 0027558407 scopus 로고
    • Balancing domain decomposition
    • J. MANDEL, Balancing domain decomposition, Comm. Numer. Methods Engrg., 9 (1993), pp. 233-241.
    • (1993) Comm. Numer. Methods Engrg , vol.9 , pp. 233-241
    • MANDEL, J.1
  • 14
    • 37648999180 scopus 로고    scopus 로고
    • J. MANDEL, Hybrid domain decomposition with unstructured subdomains, in Domain Decomposition Methods in Science and Engineering, Sixth International Conference on Domain Decomposition, A. Quarteroni, J. Periaux, Y. A. Kuznetsov, and O. B. Widlund, eds., Contemp. Math., 157, Amer. Math. Soc., Providence, RI, 1994, pp. 103-112.
    • J. MANDEL, Hybrid domain decomposition with unstructured subdomains, in Domain Decomposition Methods in Science and Engineering, Sixth International Conference on Domain Decomposition, A. Quarteroni, J. Periaux, Y. A. Kuznetsov, and O. B. Widlund, eds., Contemp. Math., vol. 157, Amer. Math. Soc., Providence, RI, 1994, pp. 103-112.
  • 15
    • 0030518529 scopus 로고    scopus 로고
    • Balancing domain decomposition for problems with large jumps in coefficients
    • J. MANDEL AND M. BREZINA, Balancing domain decomposition for problems with large jumps in coefficients, Math. Comp., 216 (1996), pp. 1387-1401.
    • (1996) Math. Comp , vol.216 , pp. 1387-1401
    • MANDEL, J.1    BREZINA, M.2
  • 16
    • 0000299811 scopus 로고
    • Damped Jacobi preconditioning and coarse grid deflation for conjugate gradient iteration on parallel computers
    • L. MANSFIELD, Damped Jacobi preconditioning and coarse grid deflation for conjugate gradient iteration on parallel computers, SIAM J. Sci. Stat. Comput., 12 (1991), pp. 1314-1323.
    • (1991) SIAM J. Sci. Stat. Comput , vol.12 , pp. 1314-1323
    • MANSFIELD, L.1
  • 17
    • 84966225158 scopus 로고
    • An iterative solution for linear systems of which the coefficient matrix is a symmetric M-matrix
    • J. A. MEIJERINK AND H. A. VAN DER VORST, An iterative solution 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.A.2
  • 18
    • 0342602167 scopus 로고
    • A restarted GMRES method augmented with eigenvectors
    • R. B. MORGAN, A restarted GMRES method augmented with eigenvectors, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 1154-1171.
    • (1995) SIAM J. Matrix Anal. Appl , vol.16 , pp. 1154-1171
    • MORGAN, R.B.1
  • 19
    • 25444449003 scopus 로고    scopus 로고
    • A comparison of deflation and coarse grid correction applied to porous media flow
    • R. NABBEN AND C. VUIK, A comparison of deflation and coarse grid correction applied to porous media flow, SIAM J. Numer. Anal., 42 (2004), pp. 1631-1647.
    • (2004) SIAM J. Numer. Anal , vol.42 , pp. 1631-1647
    • NABBEN, R.1    VUIK, C.2
  • 20
    • 33748764169 scopus 로고    scopus 로고
    • A comparison of deflation and the balancing preconditioner
    • R. NABBEN AND C. VUIK, A comparison of deflation and the balancing preconditioner, SIAM J. Sci. Comput., 27 (2006), pp. 1742-1759.
    • (2006) SIAM J. Sci. Comput , vol.27 , pp. 1742-1759
    • NABBEN, R.1    VUIK, C.2
  • 21
    • 0023331865 scopus 로고
    • Deflation of conjugate gradients with applications to boundary value problems
    • R. A. NICOLAIDES, Deflation of conjugate gradients with applications to boundary value problems, SIAM J. Matrix Anal. Appl., 24 (1987), pp. 355-365.
    • (1987) SIAM J. Matrix Anal. Appl , vol.24 , pp. 355-365
    • NICOLAIDES, R.A.1
  • 24
    • 0033678178 scopus 로고    scopus 로고
    • A deflated version of the conjugate gradient algorithm
    • Y. SAAD, M. YEUNG, J. ERHEL, AND F. GUYOMARC'H, A deflated version of the conjugate gradient algorithm, SIAM J. Sci. Comput., 21 (2000), pp. 1909-1926.
    • (2000) SIAM J. Sci. Comput , vol.21 , pp. 1909-1926
    • SAAD, Y.1    YEUNG, M.2    ERHEL, J.3    GUYOMARC'H, F.4
  • 25
    • 21244436484 scopus 로고    scopus 로고
    • On the occurrence of superlinear convergence of exact and inexact Krylov subspace methods
    • V. SIMONCINI AND D. B. SZYLD, On the occurrence of superlinear convergence of exact and inexact Krylov subspace methods, SIAM Rev., 25 (2005), pp. 247-272.
    • (2005) SIAM Rev , vol.25 , pp. 247-272
    • SIMONCINI, V.1    SZYLD, D.B.2
  • 28
    • 34249822784 scopus 로고    scopus 로고
    • On deflation and singular symmetric positive semi-definite matrices
    • J. M. TANG AND C. VUIK, On deflation and singular symmetric positive semi-definite matrices, J. Comput. Appl. Math., 206 (2007), pp. 603-614.
    • (2007) J. Comput. Appl. Math , vol.206 , pp. 603-614
    • TANG, J.M.1    VUIK, C.2
  • 29
    • 37649001394 scopus 로고    scopus 로고
    • An efficient deflation method applied on 2-D and 3-D bubbly flow problems
    • 06-01, Delft University of Technology
    • J. M. TANG AND C. VUIK, An efficient deflation method applied on 2-D and 3-D bubbly flow problems, DUT Report 06-01, Delft University of Technology, 2006.
    • (2006) DUT Report
    • TANG, J.M.1    VUIK, C.2
  • 31
    • 0000035075 scopus 로고    scopus 로고
    • An efficient preconditioned CG method for the solution of a class of layered problems with extreme contrasts in the coefficients
    • C. VUIK, A. SEGAL, AND J. A. MEIJERINK, An efficient preconditioned CG method for the solution of a class of layered problems with extreme contrasts in the coefficients, J. Comput. Phys., 152 (1999), pp. 385-403.
    • (1999) J. Comput. Phys , vol.152 , pp. 385-403
    • VUIK, C.1    SEGAL, A.2    MEIJERINK, J.A.3
  • 32
    • 0035922236 scopus 로고    scopus 로고
    • The construction of projection vectors for a deflated ICCG method applied to problems with extreme contrasts in the coefficients
    • C. VUIK, A. SEGAL, J. A. MEIJERINK, AND G. T. WIJMA, The construction of projection vectors for a deflated ICCG method applied to problems with extreme contrasts in the coefficients, J. Comput. Phys., 172 (2001), pp. 426-450.
    • (2001) J. Comput. Phys , vol.172 , pp. 426-450
    • VUIK, C.1    SEGAL, A.2    MEIJERINK, J.A.3    WIJMA, G.T.4
  • 33
    • 0003090969 scopus 로고
    • Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
    • P. M. DE ZEEUW, Matrix-dependent prolongations and restrictions in a blackbox multigrid solver, J. Comput. Appl. Math., 33 (1990), pp. 1-27.
    • (1990) J. Comput. Appl. Math , vol.33 , pp. 1-27
    • DE ZEEUW, P.M.1


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