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  • 65D32  (1)
  • SIMPLE algorithm  (1)
  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Numerical algorithms 18 (1998), S. 209-232 
    ISSN: 1572-9265
    Schlagwort(e): multivariate numerical quadrature ; Smolyak’s construction ; sparse grids ; complexity ; curse of dimension ; 65C20 ; 65D30 ; 65D32 ; 65M99 ; 65R20 ; 65U05 ; 65Y20
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We present new and review existing algorithms for the numerical integration of multivariate functions defined over d-dimensional cubes using several variants of the sparse grid method first introduced by Smolyak [49]. In this approach, multivariate quadrature formulas are constructed using combinations of tensor products of suitable one-dimensional formulas. The computing cost is almost independent of the dimension of the problem if the function under consideration has bounded mixed derivatives. We suggest the usage of extended Gauss (Patterson) quadrature formulas as the one‐dimensional basis of the construction and show their superiority in comparison to previously used sparse grid approaches based on the trapezoidal, Clenshaw–Curtis and Gauss rules in several numerical experiments and applications. For the computation of path integrals further improvements can be obtained by combining generalized Smolyak quadrature with the Brownian bridge construction.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 281-301 
    ISSN: 0271-2091
    Schlagwort(e): Navier-Stokes equations ; SIMPLE algorithm ; algebraic multigrid methods ; Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: The application of standard multigrid methods for the solution of the Navier-Stokes equations in complicated domains causes problems in two ways. First, coarsening is not possible to full extent since the geometry must be resolved by the coarsest grid used. Second, for semi-implicit time-stepping schemes, robustness of the convergence rates is usually not obtained for convection-diffusion problems, especially for higher Reynolds numbers. We show that both problems can be overcome by the use of algebraic multigrid (AMG), which we apply for the solution of the pressure and momentum equations in explicit and semi-implicit time-stepping schemes. We consider the convergence rates of AMG for several model problems and demonstrate the robustiness of the proposed scheme. © 1998 John Wiley & Sons, Ltd.
    Zusätzliches Material: 8 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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