메뉴 건너뛰기




Volumn 19, Issue 1, 2003, Pages 33-48

Multiplicative operator splittings in nonlinear diffusion: From spatial splitting to multiple timesteps

Author keywords

Additive operator splittings; Multiple timestep methods; Multiplicative operator splittings; Nonlinear diffusion

Indexed keywords

MATHEMATICAL OPERATORS; NONLINEAR FILTERING; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0041340839     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1024484920022     Document Type: Article
Times cited : (31)

References (36)
  • 1
    • 0036603206 scopus 로고    scopus 로고
    • A fundamental relationship between bilateral filtering, adaptive smoothing and the nonlinear diffusion equation
    • D. Barash, "A fundamental relationship between bilateral filtering, adaptive smoothing and the nonlinear diffusion equation," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 24, No. 7, 2002.
    • (2002) IEEE Transactions on Pattern Analysis and Machine Intelligence , vol.24 , Issue.7
    • Barash, D.1
  • 2
    • 0037439858 scopus 로고    scopus 로고
    • Inherent speedup limitations in multiple timestep/particle mesh ewald algorithms
    • D. Barash, L. Yang, X. Qian, and T. Schlick, "Inherent speedup limitations in multiple timestep/particle mesh ewald algorithms," Journal of Computational Chemistry, Vol. 24, No. 1, p. 77, 2002.
    • (2002) Journal of Computational Chemistry , vol.24 , Issue.1 , pp. 77
    • Barash, D.1    Yang, L.2    Qian, X.3    Schlick, T.4
  • 4
    • 0003524614 scopus 로고
    • Algebraic multigrid (AMG) for automatic multigrid solution with application to geodetic computations
    • Institute for Computational Studies, Fort Collins, CO
    • A. Brandt, S. McCormick, and J. Ruge, "Algebraic multigrid (AMG) for automatic multigrid solution with application to geodetic computations," Technical Report, Institute for Computational Studies, Fort Collins, CO, 1982.
    • (1982) Technical Report
    • Brandt, A.1    McCormick, S.2    Ruge, J.3
  • 5
    • 0026821645 scopus 로고
    • Image selective smoothing and edge detection by nonlinear diffusion
    • F. Catté, P.L. Lions, J.M. Morel, and T. Coll, "Image selective smoothing and edge detection by nonlinear diffusion," SIAM J. Numer. Anal., Vol. 29, No. 1, p. 182, 1992.
    • (1992) SIAM J. Numer. Anal. , vol.29 , Issue.1 , pp. 182
    • Catté, F.1    Lions, P.L.2    Morel, J.M.3    Coll, T.4
  • 6
    • 0042406872 scopus 로고    scopus 로고
    • The digital filter and nonlinear denoising
    • UCLA Computational and Applied Mathematics
    • T.F. Chan, S. Osher, and J. Shen, "The digital filter and nonlinear denoising," Technical Report CAM 99-34, UCLA Computational and Applied Mathematics, 1999.
    • (1999) Technical Report , vol.CAM 99-34
    • Chan, T.F.1    Osher, S.2    Shen, J.3
  • 7
    • 84963146276 scopus 로고
    • Generalized verlet algorithm for efficient molecular simulations with long-range interactions
    • H. Grubmüller, H. Heller, A. Windemuth, and K. Schulten, "Generalized verlet algorithm for efficient molecular simulations with long-range interactions," Mol. Sim., Vol. 6, p. 121, 1991.
    • (1991) Mol. Sim. , vol.6 , pp. 121
    • Grubmüller, H.1    Heller, H.2    Windemuth, A.3    Schulten, K.4
  • 12
    • 0037753379 scopus 로고
    • A parallel splitting up method and its application to Navier-Stokes equations
    • T. Lu, P. Neittaanmäki, and X.-C. Tai, "A parallel splitting up method and its application to Navier-Stokes equations," Applied Mathematics Letters, Vol. 4, No. 2, p. 25, 1991.
    • (1991) Applied Mathematics Letters , vol.4 , Issue.2 , pp. 25
    • Lu, T.1    Neittaanmäki, P.2    Tai, X.-C.3
  • 13
    • 0038091085 scopus 로고
    • A parallel splitting up method for partial differential equations and its application to Navier-Stokes equations
    • T. Lu, P. Neittaanmäki, and X.-C. Tai, "A parallel splitting up method for partial differential equations and its application to Navier-Stokes equations," RAIRO Mathematical Modelling and Numerical Analysis, Vol. 26, No. 6, p. 673, 1992.
    • (1992) RAIRO Mathematical Modelling and Numerical Analysis , vol.26 , Issue.6 , pp. 673
    • Lu, T.1    Neittaanmäki, P.2    Tai, X.-C.3
  • 14
    • 70350504025 scopus 로고
    • Splitting and alternating direction methods
    • P.G. Ciarlet and J.L. Lions (Eds.)
    • G.I. Marchuk, "Splitting and alternating direction methods," in Handbook of Numerical Analysis, P.G. Ciarlet and J.L. Lions (Eds.), Vol. 1, p. 197, 1990.
    • (1990) Handbook of Numerical Analysis , vol.1 , pp. 197
    • Marchuk, G.I.1
  • 15
    • 0002058827 scopus 로고
    • The numerical solution of parabolic and elliptic differential equations
    • D.W. Peaceman and H.H. Rachford, "The numerical solution of parabolic and elliptic differential equations," Journal Soc. Ind. Appl. Math, Vol. 3, p. 28, 1955.
    • (1955) Journal Soc. Ind. Appl. Math , vol.3 , pp. 28
    • Peaceman, D.W.1    Rachford, H.H.2
  • 17
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • L.I. Rudin, S. Osher, and F. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D., Vol. 60, p. 259, 1992.
    • (1992) Physica D. , vol.60 , pp. 259
    • Rudin, L.I.1    Osher, S.2    Fatemi, F.3
  • 18
    • 0035498040 scopus 로고    scopus 로고
    • Scale-based diffusive image filtering preserving boundary sharpness and fine structures
    • P.K. Saha and J.K. Udupa, "Scale-based diffusive image filtering preserving boundary sharpness and fine structures," IEEE Transactions on Medical Imaging, Vol. 20, No. 11, p. 1140, 2001.
    • (2001) IEEE Transactions on Medical Imaging , vol.20 , Issue.11 , pp. 1140
    • Saha, P.K.1    Udupa, J.K.2
  • 23
    • 0001518684 scopus 로고
    • On the construction and comparison of difference schemes
    • G. Strang, "On the construction and comparison of difference schemes," SIAM J. Numer. Anal., Vol. 5, No. 3, p. 506, 1968.
    • (1968) SIAM J. Numer. Anal. , vol.5 , Issue.3 , pp. 506
    • Strang, G.1
  • 24
    • 0009472127 scopus 로고
    • Accurate partial difference methods I: Linear cauchy problems
    • G. Strang, "Accurate partial difference methods I: Linear cauchy problems," Arch. Rational Mech. Anal., Vol. 12, p. 392, 1963.
    • (1963) Arch. Rational Mech. Anal. , vol.12 , pp. 392
    • Strang, G.1
  • 25
    • 0001471202 scopus 로고
    • Multiple time step methods in molecular dynamics
    • W.B. Streett, D.J. Tildesley, and G. Saville, "Multiple time step methods in molecular dynamics," Mol. Phys., Vol. 35, p. 639, 1978.
    • (1978) Mol. Phys. , vol.35 , pp. 639
    • Streett, W.B.1    Tildesley, D.J.2    Saville, G.3
  • 26
    • 0001144596 scopus 로고
    • A multiple time-step method for molecular dynamics simulations of fluids of chain molecules
    • R.D. Swindoll and J.M. Haile, "A multiple time-step method for molecular dynamics simulations of fluids of chain molecules," J. Chem. Phys., Vol. 53, p. 289, 1984.
    • (1984) J. Chem. Phys. , vol.53 , pp. 289
    • Swindoll, R.D.1    Haile, J.M.2
  • 29
    • 33646650705 scopus 로고
    • Reversible multiple time scale molecular dynamics
    • M.E. Tuckerman, B.J. Berne, and G.J. Martyna, "Reversible multiple time scale molecular dynamics," J. Chem. Phys., Vol. 97, p. 1990, 1992.
    • (1992) J. Chem. Phys. , vol.97 , pp. 1990
    • Tuckerman, M.E.1    Berne, B.J.2    Martyna, G.J.3
  • 30
    • 0001183716 scopus 로고
    • Simulation of macromolecules by multiple-timestep methods
    • M. Watanabe and M. Karplus, "Simulation of macromolecules by multiple-timestep methods," J. Phys. Chem., Vol. 99, No. 15, p. 5680, 1995.
    • (1995) J. Phys. Chem. , vol.99 , Issue.15 , pp. 5680
    • Watanabe, M.1    Karplus, M.2
  • 34
    • 0001768693 scopus 로고
    • Anisotropic diffusion filters for image processing based quality control
    • A. Fasano and M. Primicerio (Eds.), Teubner, Stuttgart
    • J. Weickert, "Anisotropic diffusion filters for image processing based quality control," in Proc. Seventh European Conf. on Mathematics in Industry, A. Fasano and M. Primicerio (Eds.), Teubner, Stuttgart, p. 355, 1994.
    • (1994) Proc. Seventh European Conf. on Mathematics in Industry , pp. 355
    • Weickert, J.1
  • 36
    • 0030283909 scopus 로고    scopus 로고
    • Behavioral analysis of anisotropic diffusion in image enhancement
    • Y. You, W. Xu, A. Tannenbaum, and M. Kaveh, "Behavioral analysis of anisotropic diffusion in image enhancement," IEEE Transactions on Image Processing, Vol. 5, No. 11, p. 1539, 1996.
    • (1996) IEEE Transactions on Image Processing , vol.5 , Issue.11 , pp. 1539
    • You, Y.1    Xu, W.2    Tannenbaum, A.3    Kaveh, M.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.