메뉴 건너뛰기




Volumn 242, Issue , 2013, Pages 715-725

A circulant preconditioner for fractional diffusion equations

Author keywords

CGNR method; Circulant preconditioner; Fast Fourier transform; Fractional diffusion equations; Shifted Gr nwald discretization; Toeplitz

Indexed keywords

CONJUGATE GRADIENT METHOD; DIFFUSION; FINITE DIFFERENCE METHOD; LINEAR SYSTEMS; MATRIX ALGEBRA; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 84875802403     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2013.02.025     Document Type: Article
Times cited : (238)

References (33)
  • 1
    • 34648831966 scopus 로고    scopus 로고
    • Fractional-order anisotropic diffusion for image denoising
    • Bai J., Feng X. Fractional-order anisotropic diffusion for image denoising. IEEE Trans. Image Proc. 2007, 16:2492-2502.
    • (2007) IEEE Trans. Image Proc. , vol.16 , pp. 2492-2502
    • Bai, J.1    Feng, X.2
  • 3
  • 5
    • 41449095257 scopus 로고    scopus 로고
    • Numerical solutions for fractional reaction-diffusion equations
    • Beumer B., Kovács M., Meerschaert M.M. Numerical solutions for fractional reaction-diffusion equations. Comput. Math. Appl. 2008, 55:2212-2226.
    • (2008) Comput. Math. Appl. , vol.55 , pp. 2212-2226
    • Beumer, B.1    Kovács, M.2    Meerschaert, M.M.3
  • 6
    • 0035679868 scopus 로고    scopus 로고
    • Anomalous diffusion and exit time distribution of particle tracers in plasma turbulence models
    • Carreras B.A., Lynch V.E., Zaslavsky G.M. Anomalous diffusion and exit time distribution of particle tracers in plasma turbulence models. Phys. Plasma 2001, 8:5096-5103.
    • (2001) Phys. Plasma , vol.8 , pp. 5096-5103
    • Carreras, B.A.1    Lynch, V.E.2    Zaslavsky, G.M.3
  • 8
    • 0030246195 scopus 로고    scopus 로고
    • Conjugate gradient methods for Toeplitz systems
    • Chan R., Ng M. Conjugate gradient methods for Toeplitz systems. SIAM Rev. 1996, 38:427-482.
    • (1996) SIAM Rev. , vol.38 , pp. 427-482
    • Chan, R.1    Ng, M.2
  • 9
    • 0001646777 scopus 로고
    • Toeplitz equations by conjugate gradients with circulant preconditioner
    • Chan R., Strang G. Toeplitz equations by conjugate gradients with circulant preconditioner. SIAM J. Sci. Stat. Comput. 1989, 10:104-119.
    • (1989) SIAM J. Sci. Stat. Comput. , vol.10 , pp. 104-119
    • Chan, R.1    Strang, G.2
  • 10
    • 0000853646 scopus 로고
    • An optimal circulant preconditioner for Toeplitz systems
    • Chan T. An optimal circulant preconditioner for Toeplitz systems. SIAM J. Sci. Stat. Comput. 1988, 9:766-771.
    • (1988) SIAM J. Sci. Stat. Comput. , vol.9 , pp. 766-771
    • Chan, T.1
  • 11
    • 59349113701 scopus 로고    scopus 로고
    • Finite element method for the space and time fractional Fokker-Planck equation
    • Deng W. Finite element method for the space and time fractional Fokker-Planck equation. SIAM J. Numer. Anal. 2008, 47:204-226.
    • (2008) SIAM J. Numer. Anal. , vol.47 , pp. 204-226
    • Deng, W.1
  • 12
    • 42649109055 scopus 로고    scopus 로고
    • Numerical approximation of a time dependent, nonlinear, space-fractional diffusion equation
    • Ervin V.J., Heuer N., Roop J.P. Numerical approximation of a time dependent, nonlinear, space-fractional diffusion equation. SIAM J. Numer. Anal. 2007, 45:572-591.
    • (2007) SIAM J. Numer. Anal. , vol.45 , pp. 572-591
    • Ervin, V.J.1    Heuer, N.2    Roop, J.P.3
  • 14
    • 17144427014 scopus 로고    scopus 로고
    • The accuracy and stability of an implicit solution method for the fractional diffusion equation
    • Langlands T.A.M., Henry B.I. The accuracy and stability of an implicit solution method for the fractional diffusion equation. J. Comput. Phys. 2005, 205:719-736.
    • (2005) J. Comput. Phys. , vol.205 , pp. 719-736
    • Langlands, T.A.M.1    Henry, B.I.2
  • 15
    • 1542425102 scopus 로고    scopus 로고
    • Numerical solution of the space fractional Fokker-Planck equation
    • Liu F., Anh V., Turner I. Numerical solution of the space fractional Fokker-Planck equation. J. Comput. Appl. Math. 2004, 166:209-219.
    • (2004) J. Comput. Appl. Math. , vol.166 , pp. 209-219
    • Liu, F.1    Anh, V.2    Turner, I.3
  • 17
    • 25444463578 scopus 로고    scopus 로고
    • Finite difference methods for two-dimensional fractional dispersion equation
    • Meerschaert M.M., Scheffler H.P., Tadjeran C. Finite difference methods for two-dimensional fractional dispersion equation. J. Comput. Phys. 2006, 211:249-261.
    • (2006) J. Comput. Phys. , vol.211 , pp. 249-261
    • Meerschaert, M.M.1    Scheffler, H.P.2    Tadjeran, C.3
  • 18
    • 4444368867 scopus 로고    scopus 로고
    • Finite difference approximations for fractional advection-dispersion flow equations
    • Meerschaert M.M., Tadjeran C. Finite difference approximations for fractional advection-dispersion flow equations. J. Comput. Appl. Math. 2004, 172:65-77.
    • (2004) J. Comput. Appl. Math. , vol.172 , pp. 65-77
    • Meerschaert, M.M.1    Tadjeran, C.2
  • 19
    • 28044468843 scopus 로고    scopus 로고
    • Finite difference approximations for two-sided space-fractional partial differential equations
    • Meerschaert M.M., Tadjeran C. Finite difference approximations for two-sided space-fractional partial differential equations. Appl. Numer. Math. 2006, 56:80-90.
    • (2006) Appl. Numer. Math. , vol.56 , pp. 80-90
    • Meerschaert, M.M.1    Tadjeran, C.2
  • 20
    • 46049119633 scopus 로고    scopus 로고
    • Implicit finite difference approximation for time fractional diffusion equations
    • Murio D.A. Implicit finite difference approximation for time fractional diffusion equations. Comput. Math. Appl. 2008, 56:1138-1145.
    • (2008) Comput. Math. Appl. , vol.56 , pp. 1138-1145
    • Murio, D.A.1
  • 22
    • 81455154296 scopus 로고    scopus 로고
    • Multigrid method for fractional diffusion equations
    • Pang H., Sun H. Multigrid method for fractional diffusion equations. J. Comput. Phys. 2012, 231:693-703.
    • (2012) J. Comput. Phys. , vol.231 , pp. 693-703
    • Pang, H.1    Sun, H.2
  • 24
    • 0036949980 scopus 로고    scopus 로고
    • Waiting-times and returns in high-frequency financial data: an empirical study
    • Raberto M., Scalas E., Mainardi F. Waiting-times and returns in high-frequency financial data: an empirical study. Physica A 2002, 314:749-755.
    • (2002) Physica A , vol.314 , pp. 749-755
    • Raberto, M.1    Scalas, E.2    Mainardi, F.3
  • 25
    • 0000885234 scopus 로고
    • Lévy dynamics of enhanced diffusion: application to turbulence
    • Shlesinger M.F., West B.J., Klafter J. Lévy dynamics of enhanced diffusion: application to turbulence. Phys. Rev. Lett. 1987, 58:1100-1103.
    • (1987) Phys. Rev. Lett. , vol.58 , pp. 1100-1103
    • Shlesinger, M.F.1    West, B.J.2    Klafter, J.3
  • 27
    • 64049113904 scopus 로고    scopus 로고
    • Finite difference approximates for a fractional advection diffusion problem
    • Sousa E. Finite difference approximates for a fractional advection diffusion problem. J. Comput. Phys. 2009, 228:4038-4054.
    • (2009) J. Comput. Phys. , vol.228 , pp. 4038-4054
    • Sousa, E.1
  • 28
    • 74249113616 scopus 로고    scopus 로고
    • Finite difference approximations for the fractional advection-diffusion equation
    • Su L., Wang W., Yang Z. Finite difference approximations for the fractional advection-diffusion equation. Phys. Lett. A 2009, 373:4405-4408.
    • (2009) Phys. Lett. A , vol.373 , pp. 4405-4408
    • Su, L.1    Wang, W.2    Yang, Z.3
  • 29
    • 31744438550 scopus 로고    scopus 로고
    • A second-order accurate numerical approximation for the fractional diffusion equation
    • Tadjeran C., Meerschaert M.M., Scheffler H.P. A second-order accurate numerical approximation for the fractional diffusion equation. J. Comput. Phys. 2006, 213:205-213.
    • (2006) J. Comput. Phys. , vol.213 , pp. 205-213
    • Tadjeran, C.1    Meerschaert, M.M.2    Scheffler, H.P.3
  • 30
    • 84860390012 scopus 로고    scopus 로고
    • An O(Nlog2N) alternating-direction finite difference method for two-dimensional fractional diffusion equations
    • Wang H., Wang K. An O(Nlog2N) alternating-direction finite difference method for two-dimensional fractional diffusion equations. J. Comput. Phys. 2011, 230:7830-7839.
    • (2011) J. Comput. Phys. , vol.230 , pp. 7830-7839
    • Wang, H.1    Wang, K.2
  • 31
    • 77955927812 scopus 로고    scopus 로고
    • log2N) finite difference method for fractional diffusion equations
    • log2N) finite difference method for fractional diffusion equations. J. Comput. Phys. 2010, 229:8095-8104.
    • (2010) J. Comput. Phys. , vol.229 , pp. 8095-8104
    • Wang, H.1    Wang, K.2    Sircar, T.3
  • 32
    • 79957886188 scopus 로고    scopus 로고
    • A fast characteristic finite difference method for fractional advection-diffusion equations
    • Wang K., Wang H. A fast characteristic finite difference method for fractional advection-diffusion equations. Adv. Water Resour. 2011, 34:810-816.
    • (2011) Adv. Water Resour. , vol.34 , pp. 810-816
    • Wang, K.1    Wang, H.2
  • 33
    • 0001554548 scopus 로고
    • Self-similar transport in incomplete chaos
    • Zaslavsky G.M., Stevens D., Weitzner H. Self-similar transport in incomplete chaos. Phys. Rev. E 1993, 48:1683-1694.
    • (1993) Phys. Rev. E , vol.48 , pp. 1683-1694
    • Zaslavsky, G.M.1    Stevens, D.2    Weitzner, H.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.