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Volumn 17, Issue 6, 2010, Pages 997-1019

Preconditioner updates for solving sequences of linear systems in matrix-free environment

Author keywords

Factorization updates; Incomplete factorizations; Inexact Newton Krylov methods; Matrix free environment; Preconditioned iterative methods

Indexed keywords


EID: 78649654096     PISSN: 10705325     EISSN: 10991506     Source Type: Journal    
DOI: 10.1002/nla.695     Document Type: Article
Times cited : (25)

References (48)
  • 1
    • 0004155392 scopus 로고
    • Iterative Methods for Linear and Nonlinear Equations
    • SIAM: Philadelphia, PA,
    • Kelley CT. Iterative Methods for Linear and Nonlinear Equations. SIAM: Philadelphia, PA, 1995.
    • (1995)
    • Kelley, C.T.1
  • 2
    • 17644411935 scopus 로고    scopus 로고
    • Solving Nonlinear Equations with Newton's Method
    • Fundamentals of Algorithms. SIAM: Philadelphia, PA,
    • Kelley CT. Solving Nonlinear Equations with Newton's Method. Fundamentals of Algorithms. SIAM: Philadelphia, PA, 2003.
    • (2003)
    • Kelley, C.T.1
  • 4
    • 0000109908 scopus 로고    scopus 로고
    • Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion
    • Mousseau VA, Knoll DA, Rider WJ. Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion. Journal of Computational Physics 2000; 160:743-765.
    • (2000) Journal of Computational Physics , vol.160 , pp. 743-765
    • Mousseau, V.A.1    Knoll, D.A.2    Rider, W.J.3
  • 5
    • 14044257293 scopus 로고    scopus 로고
    • Terascale Implicit Methods for Partial Differential Equations
    • Contemporary Mathematics, AMS: Providence, RI
    • Keyes D. Terascale Implicit Methods for Partial Differential Equations. Contemporary Mathematics, vol. 306. AMS: Providence, RI, 2001; 29-84.
    • (2001) , vol.306 , pp. 29-84
    • Keyes, D.1
  • 6
    • 0038115253 scopus 로고    scopus 로고
    • An efficient physics-based preconditioner for the fully implicit solution of small-scale thermally driven atmospheric flows
    • Reisner J, Mousseau VA, Wyszogrodzki AA, Knoll DA. An efficient physics-based preconditioner for the fully implicit solution of small-scale thermally driven atmospheric flows. Journal of Computational Physics 2003; 189:30-44.
    • (2003) Journal of Computational Physics , vol.189 , pp. 30-44
    • Reisner, J.1    Mousseau, V.A.2    Wyszogrodzki, A.A.3    Knoll, D.A.4
  • 7
    • 0348198275 scopus 로고    scopus 로고
    • Jacobian-free Newton-Krylov methods: a survey of approaches and applications
    • Knoll DA, Keyes D. Jacobian-free Newton-Krylov methods: a survey of approaches and applications. Journal of Computational Physics 2004; 193:357-397.
    • (2004) Journal of Computational Physics , vol.193 , pp. 357-397
    • Knoll, D.A.1    Keyes, D.2
  • 8
    • 37849018804 scopus 로고    scopus 로고
    • A method to reduce the spin-up time of ocean models
    • Bernsen E, Dijkstra HA, Wubs FW. A method to reduce the spin-up time of ocean models. Ocean Modelling 2008; 20:380-392.
    • (2008) Ocean Modelling , vol.20 , pp. 380-392
    • Bernsen, E.1    Dijkstra, H.A.2    Wubs, F.W.3
  • 9
    • 44649141252 scopus 로고    scopus 로고
    • A fast Newton-Krylov solver for seasonally varying global ocean biogeochemistry models
    • Li X, Primeau F. A fast Newton-Krylov solver for seasonally varying global ocean biogeochemistry models. Ocean Modelling 2008; 23:13-20.
    • (2008) Ocean Modelling , vol.23 , pp. 13-20
    • Li, X.1    Primeau, F.2
  • 10
    • 46849115990 scopus 로고    scopus 로고
    • Fast spin up of ocean biogeochemical models using matrix-free Newton-Krylov
    • Khatiwala S. Fast spin up of ocean biogeochemical models using matrix-free Newton-Krylov. Ocean Modelling 2008; 23:121-129.
    • (2008) Ocean Modelling , vol.23 , pp. 121-129
    • Khatiwala, S.1
  • 11
    • 0001651643 scopus 로고
    • Nonlinearly preconditioned Krylov subspace methods for discrete Newton algorithms
    • Chan T, Jackson K. Nonlinearly preconditioned Krylov subspace methods for discrete Newton algorithms. SIAM Journal on Scientific and Statistical Computing 1984; 5(3):533-542.
    • (1984) SIAM Journal on Scientific and Statistical Computing , vol.5 , Issue.3 , pp. 533-542
    • Chan, T.1    Jackson, K.2
  • 12
    • 0032209239 scopus 로고    scopus 로고
    • A fast, matrix-free implicit method for compressible flows on unstructured grids
    • Luo H, Baum JD, Löhner R. A fast, matrix-free implicit method for compressible flows on unstructured grids. Journal of Computational Physics 1998; 146(2):664-690.
    • (1998) Journal of Computational Physics , vol.146 , Issue.2 , pp. 664-690
    • Luo, H.1    Baum, J.D.2    Löhner, R.3
  • 13
    • 78649654405 scopus 로고
    • A matrix-free preconditioner applied to CFD. Technical Report No. 940, INRIA, France
    • Choquet R. A matrix-free preconditioner applied to CFD. Technical Report No. 940, INRIA, France, 1995.
    • (1995)
    • Choquet, R.1
  • 14
    • 33747619635 scopus 로고    scopus 로고
    • A Jacobian-free Newton-GMRES(m) method with adaptive preconditioner and its application for power flow calculations
    • Chen Y, Shen C. A Jacobian-free Newton-GMRES(m) method with adaptive preconditioner and its application for power flow calculations. IEEE Transactions on Power Systems 2006; 21(3):1096-1103.
    • (2006) IEEE Transactions on Power Systems , vol.21 , Issue.3 , pp. 1096-1103
    • Chen, Y.1    Shen, C.2
  • 15
    • 0034345411 scopus 로고    scopus 로고
    • Automatic preconditioning by limited memory quasi-Newton updating
    • electronic).
    • Morales JL, Nocedal J. Automatic preconditioning by limited memory quasi-Newton updating. SIAM Journal on Optimization 2000; 10(4):1079-1096 (electronic).
    • (2000) SIAM Journal on Optimization , vol.10 , Issue.4 , pp. 1079-1096
    • Morales, J.L.1    Nocedal, J.2
  • 17
    • 84966262179 scopus 로고
    • Updating quasi-Newton matrices with limited storage
    • Nocedal J. Updating quasi-Newton matrices with limited storage. Mathematical Computations 1980; 35(151):773-782.
    • (1980) Mathematical Computations , vol.35 , Issue.151 , pp. 773-782
    • Nocedal, J.1
  • 18
    • 0037711492 scopus 로고    scopus 로고
    • High-order finite difference schemes and Toeplitz based preconditioners for elliptic problems
    • electronic).
    • Serra Capizzano S, Tablino Possio C. High-order finite difference schemes and Toeplitz based preconditioners for elliptic problems. Electronic Transactions on Numerical Analysis 2000; 11:55-84 (electronic).
    • (2000) Electronic Transactions on Numerical Analysis , vol.11 , pp. 55-84
    • Serra Capizzano, S.1    Tablino Possio, C.2
  • 20
    • 12944291389 scopus 로고    scopus 로고
    • Preconditioned HSS methods for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation
    • Bertaccini D, Golub GH, Serra Capizzano S, Tablino Possio C. Preconditioned HSS methods for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation. Numerische Mathematik 2005; 99(3):441-484.
    • (2005) Numerische Mathematik , vol.99 , Issue.3 , pp. 441-484
    • Bertaccini, D.1    Golub, G.H.2    Serra Capizzano, S.3    Tablino Possio, C.4
  • 24
  • 25
    • 0033678178 scopus 로고    scopus 로고
    • A deflated version of the conjugate gradient algorithm
    • Iterative methods for solving systems of algebraic equations (Copper Mountain, CO, 1998)
    • Saad Y, Yeung M, Erhel J, Guyomarc'h F. A deflated version of the conjugate gradient algorithm. SIAM Journal on Scientific Computing 2000; 21(5):1742-1749. Iterative methods for solving systems of algebraic equations (Copper Mountain, CO, 1998).
    • (2000) SIAM Journal on Scientific Computing , vol.21 , Issue.5 , pp. 1742-1749
    • Saad, Y.1    Yeung, M.2    Erhel, J.3    Guyomarc'h, F.4
  • 28
    • 40449138046 scopus 로고    scopus 로고
    • Large scale topology optimization using preconditioned Krylov subspace recycling and continuous approximation of material distribution. In Multiscale and Functionally Graded Materials 2006 (M&FGM 2006), Paulino GH, Pindera M-J, Dodds Jr RH, Rochinha FA, Dave E, Chen L (eds), Oahu Island, Hawaii, 15-18 October 2006. AIP Conference Proceedings, 2008
    • de Sturler E, Le C, Wang S, Paulino G. Large scale topology optimization using preconditioned Krylov subspace recycling and continuous approximation of material distribution. In Multiscale and Functionally Graded Materials 2006 (M&FGM 2006), Paulino GH, Pindera M-J, Dodds Jr RH, Rochinha FA, Dave E, Chen L (eds), Oahu Island, Hawaii, 15-18 October 2006. AIP Conference Proceedings, 2008; 279-284.
    • de Sturler, E.1    Le, C.2    Wang, S.3    Paulino, G.4
  • 29
    • 0036223272 scopus 로고    scopus 로고
    • On the incomplete Cholesky decomposition of a class of perturbed matrices
    • (electronic). Copper Mountain Conference, 2000
    • Meurant G. On the incomplete Cholesky decomposition of a class of perturbed matrices. SIAM Journal on Scientific Computing 2001; 23(2):419-429 (electronic). Copper Mountain Conference, 2000.
    • (2001) SIAM Journal on Scientific Computing , vol.23 , Issue.2 , pp. 419-429
    • Meurant, G.1
  • 30
    • 4043133030 scopus 로고    scopus 로고
    • Approximate inverse preconditioning for shifted linear systems
    • Benzi M, Bertaccini D. Approximate inverse preconditioning for shifted linear systems. BIT 2003; 43(2):231-244.
    • (2003) BIT , vol.43 , Issue.2 , pp. 231-244
    • Benzi, M.1    Bertaccini, D.2
  • 31
    • 22744450197 scopus 로고    scopus 로고
    • Efficient preconditioning for sequences of parametric complex symmetric linear systems
    • Bertaccini D. Efficient preconditioning for sequences of parametric complex symmetric linear systems. Electronic Transactions on Numerical Mathematics 2004; 18:49-64.
    • (2004) Electronic Transactions on Numerical Mathematics , vol.18 , pp. 49-64
    • Bertaccini, D.1
  • 32
    • 52149094645 scopus 로고    scopus 로고
    • Efficient preconditioning of sequences of nonsymmetric linear systems
    • Duintjer Tebbens J, Tůma M. Efficient preconditioning of sequences of nonsymmetric linear systems. SIAM Journal on Scientific Computing 2007; 29(5):1918-1941.
    • (2007) SIAM Journal on Scientific Computing , vol.29 , Issue.5 , pp. 1918-1941
    • Duintjer Tebbens, J.1    Tůma, M.2
  • 33
    • 70350286251 scopus 로고    scopus 로고
    • Improving Triangular Preconditioner Updates for Nonsymmetric Linear Systems
    • Lecture Notes in Computer Science, Springer: New York,
    • Duintjer Tebbens J, Tůma M. Improving Triangular Preconditioner Updates for Nonsymmetric Linear Systems. Lecture Notes in Computer Science, vol. 4818. Springer: New York, 2008; 737-744.
    • (2008) , vol.4818 , pp. 737-744
    • Duintjer Tebbens, J.1    Tůma, M.2
  • 36
    • 0000421410 scopus 로고
    • Estimation of sparse Jacobian matrices and graph coloring problems
    • Coleman TF, Moré JJ. Estimation of sparse Jacobian matrices and graph coloring problems. SIAM Journal on Numerical Analysis 1983; 20:187-209.
    • (1983) SIAM Journal on Numerical Analysis , vol.20 , pp. 187-209
    • Coleman, T.F.1    Moré, J.J.2
  • 37
    • 28244465516 scopus 로고    scopus 로고
    • What color is your Jacobian? Graph coloring for computing derivatives
    • Gebremedhin AH, Manne F, Pothen A. What color is your Jacobian? Graph coloring for computing derivatives. SIAM Review 2005; 47:629-705.
    • (2005) SIAM Review , vol.47 , pp. 629-705
    • Gebremedhin, A.H.1    Manne, F.2    Pothen, A.3
  • 38
    • 0003378255 scopus 로고
    • Nonlinear Optimization, 1981 (Cambridge, 1981)
    • NATO Conference Series II: Systems Science. Academic Press: London,
    • Griewank A, Toint PL. On the unconstrained optimization of partially separable functions. Nonlinear Optimization, 1981 (Cambridge, 1981). NATO Conference Series II: Systems Science. Academic Press: London, 1982; 301-312.
    • (1982) On the unconstrained optimization of partially separable functions , pp. 301-312
    • Griewank, A.1    Toint, P.L.2
  • 39
    • 33845319245 scopus 로고    scopus 로고
    • Matrix-free preconditioning using partial matrix estimation
    • Cullum J, Tůma M. Matrix-free preconditioning using partial matrix estimation. BIT Numerical Mathematics 2006; 46:711-729.
    • (2006) BIT Numerical Mathematics , vol.46 , pp. 711-729
    • Cullum, J.1    Tůma, M.2
  • 40
    • 0003603813 scopus 로고
    • Computers and Intractability: A Guide to the Theory of NP-Completeness
    • Freeman & Co.: New York,
    • Garey MR, Johnson DS. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman & Co.: New York, 1979.
    • (1979)
    • Garey, M.R.1    Johnson, D.S.2
  • 43
    • 0016940739 scopus 로고
    • Comparative analysis of the Cuthill-McKee and the reverse Cuthill-McKee ordering algorithms for sparse matrices
    • Liu JWH, Sherman AH. Comparative analysis of the Cuthill-McKee and the reverse Cuthill-McKee ordering algorithms for sparse matrices. SIAM Journal on Numerical Analysis 1976; 13:198-213.
    • (1976) SIAM Journal on Numerical Analysis , vol.13 , pp. 198-213
    • Liu, J.W.H.1    Sherman, A.H.2
  • 44
    • 0033293791 scopus 로고    scopus 로고
    • Orderings for incomplete factorization preconditioning of nonsymmetric problems
    • Benzi M, Szyld DB, van Duin A. Orderings for incomplete factorization preconditioning of nonsymmetric problems. SIAM Journal on Scientific Computing 1999; 20(5):1652-1670.
    • (1999) SIAM Journal on Scientific Computing , vol.20 , Issue.5 , pp. 1652-1670
    • Benzi, M.1    Szyld, D.B.2    van Duin, A.3
  • 45
    • 0031651231 scopus 로고    scopus 로고
    • Computational experience with globally convergent descent methods for large sparse systems of nonlinear equations
    • Lukšan L, Vlček J. Computational experience with globally convergent descent methods for large sparse systems of nonlinear equations. Optimization Methods in Software 1998; 8(3-4):201-223.
    • (1998) Optimization Methods in Software , vol.8 , Issue.3-4 , pp. 201-223
    • Lukšan, L.1    Vlček, J.2
  • 46
    • 78649680364 scopus 로고    scopus 로고
    • UFO 2008-interactive system for universal functional optimization. Technical Report V-1040, downloadable from, ICS AS CR .
    • Lukšan L, Tůma M, Vlček J, Ramešová N, Šiška M, Hartman J, Matonoha C. UFO 2008-interactive system for universal functional optimization. Technical Report V-1040, downloadable from, ICS AS CR 2008.
    • (2008)
    • Lukšan, L.1    Tůma, M.2    Vlček, J.3    Ramešová, N.4    Šiška, M.5    Hartman, J.6    Matonoha, C.7
  • 47
    • 84985408358 scopus 로고
    • ILUT: a dual threshold incomplete LU factorization
    • Saad Y. ILUT: a dual threshold incomplete LU factorization. Numerical Linear Algebra with Applications 1994; 1(4):387-402.
    • (1994) Numerical Linear Algebra with Applications , vol.1 , Issue.4 , pp. 387-402
    • Saad, Y.1
  • 48
    • 68849103142 scopus 로고    scopus 로고
    • Iterative solvers within sequences of large linear systems in non-linear structural mechanics
    • Hartmann S, Duintjer Tebbens J, Quint K, Meister A. Iterative solvers within sequences of large linear systems in non-linear structural mechanics. ZAMM 2009; 89:711-728.
    • (2009) ZAMM , vol.89 , pp. 711-728
    • Hartmann, S.1    Duintjer Tebbens, J.2    Quint, K.3    Meister, A.4


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