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  • 1
    Digitale Medien
    Digitale Medien
    A semi-circulant preconditioner for the convection-diffusion equation (1998)
    Springer
    Numerische Mathematik 81 (1998), S. 211-248 
    Details
    ISSN: 0945-3245
    Schlagwort(e): Mathematics Subject Classification (1991): 65N22
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract. In this paper we define and analyze a semi-circulant preconditioner for the convection-diffusion equation. We derive analytical formulas for the eigenvalues and the eigenvectors of the preconditioned system of equations. We show that for mesh Péclet numbers less than 2, the rate of convergence depends only on the mesh Péclet number and the direction of the convective field and not on the spatial grid ratio or the number of unknowns.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s002110050390
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  • 2
    Digitale Medien
    Digitale Medien
    Toeplitz Preconditioners with Block Structure for First-order PDEs (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 21-44 
    Details
    ISSN: 1070-5325
    Schlagwort(e): first-order PDEs ; iterative methods ; preconditioners ; Toeplitz ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Preconditioners to nonsymmetric, nondiagonally dominant systems of equations are constructed and examined numerically. The preconditioners are based on a Toeplitz approach with a certain symmetry that we define. The inversion of the preconditioners is defined through a Fast Modified Sine Transform. As a model problem we study the systems of equations arising from a implicit time-discretization with a large time-step of a scalar hyperbolic PDE.
    Zusätzliches Material: 17 Ill.
    Materialart: Digitale Medien
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  • 3
    Digitale Medien
    Digitale Medien
    A fast modified sine transform for solving block-tridiagonal systems with Toeplitz blocks (1994)
    Springer
    Numerical algorithms 7 (1994), S. 375-389 
    Details
    ISSN: 1572-9265
    Schlagwort(e): Sine transform ; fast Fourier transform ; tridiagonal ; Toeplitz matrices
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this report we consider block-tridiagonal systems with Toeplitz blocks. Each block is of sizen×n consisting ofn c×n c matrices as entries, and there arem×m blocks in the system. The solution of those systems consists of 2n c m modified sine transforms and an intermediate solution ofn block-tridiagonal systems. Symmetries in the data vectors are exploited such that one modified sine transform can be computed in terms of one Fourier transform of half the length of the original one, hence requiringO(2.5nlog2 n) operations. Similarly, we only have to solve (n+1)/2 of the intermediate systems due to symmetry.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02140691
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