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Volumn 20, Issue 5, 1999, Pages 1652-1670

Orderings for incomplete factorization preconditioning of nonsymmetric problems

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; MATRIX ALGEBRA; PARTIAL DIFFERENTIAL EQUATIONS; VECTORS;

EID: 0033293791     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S1064827597326845     Document Type: Article
Times cited : (112)

References (50)
  • 1
    • 38249006029 scopus 로고
    • Vectorizable preconditioners for elliptic difference equations in three space dimensions
    • O. AXELSSON AND V. EIJKHOUT, Vectorizable preconditioners for elliptic difference equations in three space dimensions, J. Comput. Appl. Math., 27 (1991), pp. 299-321.
    • (1991) J. Comput. Appl. Math. , vol.27 , pp. 299-321
    • Axelsson, O.1    Eijkhout, V.2
  • 4
    • 0002812224 scopus 로고
    • Comparison of fast iterative methods for symmetric systems
    • G. A. BEHIE AND P. A. FORSYTH, JR., Comparison of fast iterative methods for symmetric systems, IMA J. Numer. Anal., 3 (1983), pp. 41-63.
    • (1983) IMA J. Numer. Anal. , vol.3 , pp. 41-63
    • Behie, G.A.1    Forsyth P.A., Jr.2
  • 5
    • 0001085854 scopus 로고
    • Incomplete factorization methods for fully implicit simulation of enhanced oil recovery
    • G. A. BEHIE AND P. A. FORSYTH, JR., Incomplete factorization methods for fully implicit simulation of enhanced oil recovery, SIAM J. Sci. Stat. Comput., 5 (1984), pp. 543-561.
    • (1984) SIAM J. Sci. Stat. Comput. , vol.5 , pp. 543-561
    • Behie, G.A.1    Forsyth P.A., Jr.2
  • 6
    • 0009092565 scopus 로고    scopus 로고
    • Threshold ordering for preconditioning nonsymmetric problems
    • G. Golub, S. Lui, F. Luk, and R. Plemmons, eds., Hong Kong, 1997, Springer, Singapore
    • M. BENZI, H. CHOI, AND D. B. SZYLD, Threshold ordering for preconditioning nonsymmetric problems, in Proceedings of the Workshop on Scientific Computing, G. Golub, S. Lui, F. Luk, and R. Plemmons, eds., Hong Kong, 1997, Springer, Singapore, 1997, pp. 159-165.
    • (1997) Proceedings of the Workshop on Scientific Computing , pp. 159-165
    • Benzi, M.1    Choi, H.2    Szyld, D.B.3
  • 8
    • 0024663831 scopus 로고
    • Parallel elliptic preconditioners: Fourier analysis and performance on the connection machine
    • T. F. CHAN, C.-C. J. KUO, AND C. TONG, Parallel elliptic preconditioners: Fourier analysis and performance on the connection machine, Comput. Phys. Comm., 53 (1989), pp. 237 252.
    • (1989) Comput. Phys. Comm. , vol.53 , pp. 237-252
    • Chan, T.F.1    Kuo, C.-C.J.2    Tong, C.3
  • 9
    • 0000300094 scopus 로고    scopus 로고
    • On preconditioned Krylov subspace methods for discrete convection-diffusion problems
    • M. P. CHERNESKY, On preconditioned Krylov subspace methods for discrete convection-diffusion problems, Numer. Methods Partial Differential Equations, 13 (1997), pp. 321-330.
    • (1997) Numer. Methods Partial Differential Equations , vol.13 , pp. 321-330
    • Chernesky, M.P.1
  • 10
    • 0029719756 scopus 로고    scopus 로고
    • Application of threshold partitioning of sparse matrices to Markov chains
    • Urbana-Champaign, IL, 1996, IEEE Computer Society Press, Los Alamitos, CA
    • H. CHOI AND D. B. SZYLD, Application of threshold partitioning of sparse matrices to Markov chains, in Proceedings of the IEEE International Computer Performance and Dependability Symposium, IPDS '96, Urbana-Champaign, IL, 1996, IEEE Computer Society Press, Los Alamitos, CA, 1996, pp. 158-165.
    • (1996) Proceedings of the IEEE International Computer Performance and Dependability Symposium, IPDS '96 , pp. 158-165
    • Choi, H.1    Szyld, D.B.2
  • 11
    • 0031332548 scopus 로고    scopus 로고
    • Experimental study of ILU preconditioned for indefinite matrices
    • E. CHOW AND Y. SAAD, Experimental study of ILU preconditioned for indefinite matrices, J. Comput. Appl. Math., 86 (1997), pp. 387-414.
    • (1997) J. Comput. Appl. Math. , vol.86 , pp. 387-414
    • Chow, E.1    Saad, Y.2
  • 12
    • 0002337314 scopus 로고
    • Weighted graph based ordering techniques for preconditioned conjugate gradient methods
    • S. S. CLIFT AND W.-P. TANG, Weighted graph based ordering techniques for preconditioned conjugate gradient methods, BIT, 35 (1995), pp. 30-47.
    • (1995) BIT , vol.35 , pp. 30-47
    • Clift, S.S.1    Tang, W.-P.2
  • 13
    • 0025858036 scopus 로고
    • An automatic ordering method for incomplete factorization iterative solvers
    • Paper SPE 21226, Anaheim, CA, Society of Petroleum Engineers, Richardson, TX
    • E. F. D'AZEVEDO, P. A. FORSYTH, JR., AND W.-P. TANG, An automatic ordering method for incomplete factorization iterative solvers, Paper SPE 21226, in Proceedings of the 1991 SPE Reservoir Simulation Symposium, Anaheim, CA, Society of Petroleum Engineers, Richardson, TX, 1991.
    • (1991) Proceedings of the 1991 SPE Reservoir Simulation Symposium
    • D'Azevedo, E.F.1    Forsyth P.A., Jr.2    Tang, W.-P.3
  • 14
    • 0000565358 scopus 로고
    • Ordering methods for preconditioned conjugate gradient methods applied to unstructured grid problems
    • E. F. D'AZEVEDO, P. A. FORSYTH, JR., AND W.-P. TANG, Ordering methods for preconditioned conjugate gradient methods applied to unstructured grid problems, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 944-961.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 944-961
    • D'Azevedo, E.F.1    Forsyth P.A., Jr.2    Tang, W.-P.3
  • 16
    • 0000674152 scopus 로고
    • On parallelism and convergence of incomplete LU factorizations
    • S. DOI, On parallelism and convergence of incomplete LU factorizations, Appl. Numer. Math., 7 (1991), pp. 417-436.
    • (1991) Appl. Numer. Math. , vol.7 , pp. 417-436
    • Doi, S.1
  • 20
    • 85037806594 scopus 로고    scopus 로고
    • The design and use of algorithms for permuting large entries to the diagonal of sparse matrices
    • to appear
    • I. S. DUFF AND J. KOSTER, The design and use of algorithms for permuting large entries to the diagonal of sparse matrices, SIAM J. Matrix Anal. Appl., to appear.
    • SIAM J. Matrix Anal. Appl.
    • Duff, I.S.1    Koster, J.2
  • 21
    • 0000602242 scopus 로고
    • The effect of ordering on preconditioned conjugate gradients
    • I. S. DUFF AND G. A. MEURANT, The effect of ordering on preconditioned conjugate gradients, BIT, 29 (1989), pp. 635-657.
    • (1989) BIT , vol.29 , pp. 635-657
    • Duff, I.S.1    Meurant, G.A.2
  • 22
    • 0027545264 scopus 로고
    • The effect of ordering on preconditioned GMRES algorithm, for solving the compressible Navier-Stokes equations
    • L. C. DUTTO, The effect of ordering on preconditioned GMRES algorithm, for solving the compressible Navier-Stokes equations, Internat. J. Numer. Methods Engrg., 36 (1993), pp. 457-497.
    • (1993) Internat. J. Numer. Methods Engrg. , vol.36 , pp. 457-497
    • Dutto, L.C.1
  • 23
    • 0028468827 scopus 로고
    • Parallelizable block diagonal preconditioners for the compressible Navier-Stokes equations
    • L. C. DUTTO, W. G. HABASHI, AND M. FORTIN, Parallelizable block diagonal preconditioners for the compressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 117 (1994) pp. 15-47.
    • (1994) Comput. Methods Appl. Mech. Engrg. , vol.117 , pp. 15-47
    • Dutto, L.C.1    Habashi, W.G.2    Fortin, M.3
  • 24
    • 0000877266 scopus 로고
    • Analysis of parallel incomplete point factorizations
    • V. EIJKHOUT, Analysis of parallel incomplete point factorizations, Linear Algebra Appl., 154/156 (1991), pp. 723-740.
    • (1991) Linear Algebra Appl. , vol.154-156 , pp. 723-740
    • Eijkhout, V.1
  • 25
    • 84966211825 scopus 로고
    • A stability analysis of incomplete LU factorizations
    • H. C. ELMAN, A stability analysis of incomplete LU factorizations, Math. Comp., 47 (1986), pp. 191-217.
    • (1986) Math. Comp. , vol.47 , pp. 191-217
    • Elman, H.C.1
  • 26
    • 0001330133 scopus 로고
    • Relaxed and stabilized incomplete factorizations for non-self-adjoint linear systems
    • H. C. ELMAN, Relaxed and stabilized incomplete factorizations for non-self-adjoint linear systems, BIT, 29 (1989), pp. 890-915.
    • (1989) BIT , vol.29 , pp. 890-915
    • Elman, H.C.1
  • 27
    • 0024663788 scopus 로고
    • Ordering techniques for the preconditioned conjugate gradient method on parallel computers
    • H. C. ELMAN AND E. AGRÓN, Ordering techniques for the preconditioned conjugate gradient method on parallel computers, Comput. Phys. Comm., 53 (1989), pp. 253-269.
    • (1989) Comput. Phys. Comm. , vol.53 , pp. 253-269
    • Elman, H.C.1    Agrón, E.2
  • 28
    • 0001031880 scopus 로고
    • A transpose-free quasi-minimal residual algorithm for non-hermitian linear systems
    • R. W. FREUND, A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems, SIAM J. Sci. Comput., 14 (1993), pp. 470-482.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 470-482
    • Freund, R.W.1
  • 30
    • 0343050487 scopus 로고    scopus 로고
    • Diagonal dominance and positive definiteness of upwind approximations for advection diffusion problems
    • D. F. Griffiths and G. A. Watson, eds., World Scientific, River Edge, NJ
    • G. GOLUB, D. SILVESTER, AND A. WATHEN, Diagonal dominance and positive definiteness of upwind approximations for advection diffusion problems, in Numerical Analysis. A. R. Mitchell 75th Birthday Volume, D. F. Griffiths and G. A. Watson, eds., World Scientific, River Edge, NJ, 1996, pp. 125-131.
    • (1996) Numerical Analysis. A. R. Mitchell 75th Birthday Volume , pp. 125-131
    • Golub, G.1    Silvester, D.2    Wathen, A.3
  • 31
    • 0019575119 scopus 로고
    • Don't suppress the wiggles - They're telling you something!
    • P. M. GRESHO AND R. L. LEE, Don't suppress the wiggles - they're telling you something!, Comput. & Fluids, 9 (1981), pp. 223-253.
    • (1981) Comput. & Fluids , vol.9 , pp. 223-253
    • Gresho, P.M.1    Lee, R.L.2
  • 33
    • 0024607955 scopus 로고
    • Conjugate gradient methods and ILU preconditioning of non-symmetric matrix systems with arbitrary sparsity patterns
    • H. P. LANGTANGEN, Conjugate gradient methods and ILU preconditioning of non-symmetric matrix systems with arbitrary sparsity patterns, Internat. J. Numer. Methods Fluids, 9 (1989), pp. 213-233.
    • (1989) Internat. J. Numer. Methods Fluids , vol.9 , pp. 213-233
    • Langtangen, H.P.1
  • 34
    • 0022077450 scopus 로고
    • Modification of the minimum degree algorithm by multiple elimination
    • J. W. LIU, Modification of the minimum degree algorithm by multiple elimination, ACM Trans. Math. Software, 11 (1985), pp. 141-153.
    • (1985) ACM Trans. Math. Software , vol.11 , pp. 141-153
    • Liu, J.W.1
  • 35
    • 84966225158 scopus 로고
    • An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix
    • J. A. MEIJERINK AND H. A. VAN DEE 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.A.2
  • 37
    • 0000649580 scopus 로고
    • Orderings for conjugate gradient preconditionings
    • J. M. ORTEGA, Orderings for conjugate gradient preconditionings, SIAM J. Optim., 1 (1991), pp. 565-582.
    • (1991) SIAM J. Optim. , vol.1 , pp. 565-582
    • Ortega, J.M.1
  • 38
    • 0023537269 scopus 로고
    • Multicolor ICCG methods for vector computers
    • E. L. POOLE AND J. M. ORTEGA, Multicolor ICCG methods for vector computers, SIAM J. Numer. Anal., 24 (1987), pp. 1394-1418.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 1394-1418
    • Poole, E.L.1    Ortega, J.M.2
  • 39
    • 0002598644 scopus 로고
    • Preconditioning techniques for nonsymmetric and indefinite linear systems
    • Y. SAAD, Preconditioning techniques for nonsymmetric and indefinite linear systems, J. Comput. Appl. Math., 24 (1988), pp. 89-105.
    • (1988) J. Comput. Appl. Math. , vol.24 , pp. 89-105
    • Saad, Y.1
  • 40
    • 0003550735 scopus 로고
    • Technical Report 90-20, Research Institute for Advanced Computer Science, NASA Ames Research Center, Moffett Field, CA
    • Y. SAAD, SPARSKIT: A Basic Tool Kit for Sparse Matrix Computations, Technical Report 90-20, Research Institute for Advanced Computer Science, NASA Ames Research Center, Moffett Field, CA, 1990.
    • (1990) SPARSKIT: A Basic Tool Kit for Sparse Matrix Computations
    • Saad, Y.1
  • 41
    • 84985408358 scopus 로고
    • ILUT: A dual threshold incomplete LU factorization
    • Y. SAAD, ILUT: A dual threshold incomplete LU factorization, Numer. Linear Algebra Appl., 1 (1994), pp. 387-402.
    • (1994) Numer. Linear Algebra Appl. , vol.1 , pp. 387-402
    • Saad, Y.1
  • 43
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Y. SAAD AND M. H. SCHULTZ, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 7 (1986), pp. 856-869.
    • (1986) SIAM J. Sci. Stat. Comput. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 44
    • 0021974665 scopus 로고
    • Incomplete LU preconditioners for conjugate-gradient-type iterative methods
    • Dallas, TX, Society of Petroleum Engineers, Richardson, TX
    • H. D. SIMON, Incomplete LU preconditioners for conjugate-gradient-type iterative methods, in Proceedings of the 1985 SPE Reservoir Simulation Symposium, Dallas, TX, Society of Petroleum Engineers, Richardson, TX, 1985, pp. 387-396.
    • (1985) Proceedings of the 1985 SPE Reservoir Simulation Symposium , pp. 387-396
    • Simon, H.D.1
  • 45
    • 0031129196 scopus 로고    scopus 로고
    • Orderings for parallel conjugate gradient preconditioners
    • S. A. STOTLAND AND J. M. ORTEGA, Orderings for parallel conjugate gradient preconditioners, SIAM J. Sci. Comput., 18 (1997), pp. 854-868.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 854-868
    • Stotland, S.A.1    Ortega, J.M.2
  • 47
    • 0002003127 scopus 로고
    • Iterative solution methods for certain sparse linear systems with a non-symmetric matrix arising from PDE-problems
    • H. A. VAN DER VORST, Iterative solution methods for certain sparse linear systems with a non-symmetric matrix arising from PDE-problems, J. Comput. Phys., 44 (1981), pp. 1-19.
    • (1981) J. Comput. Phys. , vol.44 , pp. 1-19
    • Van Der Vorst, H.A.1
  • 48
    • 0000005482 scopus 로고
    • Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems
    • H. A. VAN DER VORST, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 13 (1992), pp. 631-644.
    • (1992) SIAM J. Sci. Stat. Comput. , vol.13 , pp. 631-644
    • Van Der Vorst, H.A.1
  • 49
    • 0019359208 scopus 로고
    • A conjugate gradient truncated direct method for the iterative solution of the reservoir simulation pressure equation
    • J. W. WATTS III, A conjugate gradient truncated direct method for the iterative solution of the reservoir simulation pressure equation, Soc. Petroleum Engineers J., 21 (1981), pp. 345-353.
    • (1981) Soc. Petroleum Engineers J. , vol.21 , pp. 345-353
    • Watts J.W. III1


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