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  • 1
    Electronic Resource
    Electronic Resource
    An explicit fourth-order compact finite difference scheme for three-dimensional convection-diffusion equation (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 209-218 
    Details
    ISSN: 1069-8299
    Keywords: three-dimensional convection-diffusion equation ; fourth-order compact scheme ; iterative methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present an explicit fourth-order compact finite difference scheme for approximating the three-dimensional convection-diffusion equation with variable coefficients. This 19-point formula is defined on a uniform cubic grid. We compare the advantages and implementation costs of the new scheme with the standard 7-point scheme in the context of basic iterative methods. Numerical examples are used to verify the fourth-order convergence rate of the scheme and to show that the Gauss-Seidel iterative method converges for large values of the convection coefficients. Some algebraic properties of the coefficient matrices arising from different discretization schemes are compared. We also comment on the potential use of the fourth-order compact scheme with multilevel iterative methods. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 2
    Electronic Resource
    Electronic Resource
    On convergence and performance of iterative methods with fourth-order compact schemes (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 263-280 
    Details
    ISSN: 0749-159X
    Keywords: Convection-diffusion equation ; iterative methods ; fourth-order compact discretization schemes ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the convergence and performance of iterative methods with the fourth-order compact discretization schemes for the one- and two-dimensional convection-diffusion equations. For the one-dimensional problem, we investigate the symmetrizability of the coefficient matrix and derive an analytical formula for the spectral radius of the point Jacobi iteration matrix. For the two-dimensional problem, we conduct Fourier analysis to determine the error reduction factors of several basic iterative methods and comment on their potential use as the smoothers for the multilevel methods. Finally, we perform numerical experiments to verify our Fourier analysis results. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:263-280, 1998
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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