메뉴 건너뛰기




Volumn 24, Issue 4, 1997, Pages 501-512

Multigrid with inexact minimal residual smoothing acceleration

Author keywords

Conjugate gradient type methods; Minimal residual smoothing; Multigrid method; Subspace minimization

Indexed keywords

COMPUTATIONAL COMPLEXITY; CONVERGENCE OF NUMERICAL METHODS; PROBLEM SOLVING;

EID: 0031234826     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(97)00010-X     Document Type: Article
Times cited : (4)

References (30)
  • 1
    • 84966233568 scopus 로고
    • Multi-level adaptive solution to boundary-value problems
    • A. Brandt, Multi-level adaptive solution to boundary-value problems, Math. Comp. 31 (1977) 333-396.
    • (1977) Math. Comp. , vol.31 , pp. 333-396
    • Brandt, A.1
  • 2
    • 0000559094 scopus 로고
    • Inadequacy of first-order upwind difference scheme for some recirculating flows
    • A. Brandt and I. Yavneh, Inadequacy of first-order upwind difference scheme for some recirculating flows, J. Comput. Phys. 93 (1991) 128-143.
    • (1991) J. Comput. Phys. , vol.93 , pp. 128-143
    • Brandt, A.1    Yavneh, I.2
  • 3
    • 0000221506 scopus 로고
    • Accelerated multigrid convergence and high-Reynolds recirculating flows
    • A. Brandt and I. Yavneh, Accelerated multigrid convergence and high-Reynolds recirculating flows, SIAM J. Sci. Comput. 14 (1993) 607-626.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 607-626
    • Brandt, A.1    Yavneh, I.2
  • 4
    • 0041666799 scopus 로고
    • Hybrid procedures for solving linear systems
    • C. Brezinski and M. Redivo-Zaglia, Hybrid procedures for solving linear systems, Numer. Math. 67 (1994) 1-19.
    • (1994) Numer. Math. , vol.67 , pp. 1-19
    • Brezinski, C.1    Redivo-Zaglia, M.2
  • 6
    • 25444452938 scopus 로고
    • QMR: A quasi-minimal residual method for non-Hermitian linear systems
    • R.W. Freund and N.M. Nachtigal, QMR: a quasi-minimal residual method for non-Hermitian linear systems, Numer. Math. 60 (1991) 315-339.
    • (1991) Numer. Math. , vol.60 , pp. 315-339
    • Freund, R.W.1    Nachtigal, N.M.2
  • 7
    • 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) 470-482.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 470-482
    • Freund, R.W.1
  • 8
    • 0021207821 scopus 로고
    • A single cell high order scheme for the convection-diffusion equation with variable coefficients
    • M.M. Gupta, R.P. Manohar and J.W. Stephenson, A single cell high order scheme for the convection-diffusion equation with variable coefficients, Internat J. Numer. Methods Fluids 4 (1984) 641-651.
    • (1984) Internat J. Numer. Methods Fluids , vol.4 , pp. 641-651
    • Gupta, M.M.1    Manohar, R.P.2    Stephenson, J.W.3
  • 10
    • 0002814189 scopus 로고
    • Solution of systems of linear equations by minimized iterations
    • C. Lanczos, Solution of systems of linear equations by minimized iterations, J. Res. Nat. Bur. Stand. 49 (1952) 33-53.
    • (1952) J. Res. Nat. Bur. Stand. , vol.49 , pp. 33-53
    • Lanczos, C.1
  • 11
    • 0004550557 scopus 로고
    • Steplength optimization and linear multigrid methods
    • A. Reusken, Steplength optimization and linear multigrid methods, Numer. Math. 58 (1991) 819-838.
    • (1991) Numer. Math. , vol.58 , pp. 819-838
    • Reusken, A.1
  • 12
    • 0001326593 scopus 로고
    • Efficient solution of finite difference and finite element equations
    • D.J. Paddon and H. Holstein, eds., Clarendon Press, Oxford
    • J. Ruge and K. Stüben, Efficient solution of finite difference and finite element equations, in: D.J. Paddon and H. Holstein, eds., Multigrid Methods for Integral and Differential Equations (Clarendon Press, Oxford, 1985) 169-212.
    • (1985) Multigrid Methods for Integral and Differential Equations , pp. 169-212
    • Ruge, J.1    Stüben, K.2
  • 13
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual method for solving nonsymmetric linear systems
    • Y. Saad and M.H. Schultz, GMRES: a generalized minimal residual method for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput. 7 (1986) 856-869.
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 15
    • 0002716979 scopus 로고
    • CGS, a fast Lanczos-type solver for nonsymmetric linear systems
    • P. Sonneveld, CGS, a fast Lanczos-type solver for nonsymmetric linear systems, SIAM J. Sci. Statist. Comput. 10 (1989) 36-52.
    • (1989) SIAM J. Sci. Statist. Comput. , vol.10 , pp. 36-52
    • Sonneveld, P.1
  • 16
    • 0002621183 scopus 로고
    • Algebraic multigrid (AMG): Experience and comparisons
    • K. Stüben, Algebraic multigrid (AMG): experience and comparisons, Appl. Math. Comput. 13 (1983) 419-452.
    • (1983) Appl. Math. Comput. , vol.13 , pp. 419-452
    • Stüben, K.1
  • 17
    • 0040775188 scopus 로고
    • Fast multigrid solver
    • P. Vaněk, Fast multigrid solver, Appl. Math. 40 (1995) 1-20.
    • (1995) Appl. Math. , vol.40 , pp. 1-20
    • Vaněk, P.1
  • 18
    • 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. Statist. Comput. 13 (1992) 631-644.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 631-644
    • Van Der Vorst, H.A.1
  • 19
    • 0008375753 scopus 로고
    • Residual smoothing and peak/plateau behavior in Krylov subspace methods
    • H.F. Walker, Residual smoothing and peak/plateau behavior in Krylov subspace methods, Appl. Numer. Math. 19 (1995) 279-286.
    • (1995) Appl. Numer. Math. , vol.19 , pp. 279-286
    • Walker, H.F.1
  • 22
    • 0005423908 scopus 로고    scopus 로고
    • On red-black sor smoothing in multigrid
    • I. Yavneh, On red-black SOR smoothing in multigrid, SIAM J. Sci. Comput. 17 (1996) 180-192.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 180-192
    • Yavneh, I.1
  • 23
    • 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) 1-27.
    • (1990) J. Comput. Appl. Math. , vol.33 , pp. 1-27
    • De Zeeuw, P.M.1
  • 24
    • 16344371625 scopus 로고
    • Numerical study of a multigrid method with four smoothing methods for the incompressible Navier-stokes equations in general coordinates
    • P.W. Hemker and P. Wesseling, eds., Stichting Mathematisch Centrum, Amsterdam
    • S. Zeng and P. Wesseling, Numerical study of a multigrid method with four smoothing methods for the incompressible Navier-Stokes equations in general coordinates, in: P.W. Hemker and P. Wesseling, eds., Contributions to Multigrid (Stichting Mathematisch Centrum, Amsterdam, 1994) 203-218.
    • (1994) Contributions to Multigrid , pp. 203-218
    • Zeng, S.1    Wesseling, P.2
  • 25
    • 0038996848 scopus 로고    scopus 로고
    • Acceleration of five-point red-black Gauss-Seidel in multigrid for two dimensional Poisson equation
    • J. Zhang, Acceleration of five-point red-black Gauss-Seidel in multigrid for two dimensional Poisson equation, Appl. Math. Comput 80 (1996) 73-93.
    • (1996) Appl. Math. Comput , vol.80 , pp. 73-93
    • Zhang, J.1
  • 26
    • 85033130834 scopus 로고    scopus 로고
    • Minimal residual smoothing in multi-level iterative method
    • to appear
    • J. Zhang, Minimal residual smoothing in multi-level iterative method, Appl. Math. Comput., to appear.
    • Appl. Math. Comput.
    • Zhang, J.1
  • 27
    • 0042046489 scopus 로고    scopus 로고
    • A cost-effective multigrid projection operator
    • J. Zhang, A cost-effective multigrid projection operator, J. Comput. Appl. Math. 76 (1996) 325-333.
    • (1996) J. Comput. Appl. Math. , vol.76 , pp. 325-333
    • Zhang, J.1
  • 28
    • 85033151064 scopus 로고    scopus 로고
    • Residual scaling techniques in multigrid, I: Equivalence proof
    • to appear
    • J. Zhang, Residual scaling techniques in multigrid, I: equivalence proof, Appl. Math. Comput., to appear.
    • Appl. Math. Comput.
    • Zhang, J.1
  • 29
    • 0002545264 scopus 로고    scopus 로고
    • Accelerated multigrid high accuracy solution of the convection-diffusion equations with high reynolds number
    • J. Zhang, Accelerated multigrid high accuracy solution of the convection-diffusion equations with high Reynolds number, Numer. Methods Partial Differential Equations 13 (1997) 77-92.
    • (1997) Numer. Methods Partial Differential Equations , vol.13 , pp. 77-92
    • Zhang, J.1
  • 30
    • 0000848766 scopus 로고
    • Residual smoothing techniques for iterative methods
    • L. Zhou and H.F. Walker, Residual smoothing techniques for iterative methods, SIAM J. Sci. Comput. 15 (1994) 297-312.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 297-312
    • Zhou, L.1    Walker, H.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.