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Grid- and Point-Oriented Multilevel Algorithms

  • Michael Griebel
Chapter
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)

Abstract

Instead of the usual basis, we use a generating system for the discretization of PDEs that contains not only the basis functions of the finest level of discretization but additionally the basis functions of all coarser levels of discretization. The Galerkin-approach now results in a semidefinite system of linear equations to be solved. Standard iterative GS-methods for this system turn out to be equivalent to elaborated multigrid methods for the fine grid system.

Beside Gauss-Seidel methods for the level-wise ordered semidefinite system, we study block Gauss-Seidel methods for the point-wise ordered semidefinite system. These new algorithms show the same properties as conventional multigrid methods with respect to their convergence behavior and efficiency. Additionally, they possess superior properties with respect to parallelization.

We report the results of numerical experiments regarding the reduction rates of different variants of these algorithms.

Key words

partial differential equations multilevel methods multigrid methods Gauss-Seidel iteration block Gauss-Seidel iteration semidefinite system 

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Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1993

Authors and Affiliations

  • Michael Griebel
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenMünchen 2Deutschland

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