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, Volume 50, Issue 2, pp 127–148 | Cite as

Multilevel Gauss-Seidel-algorithms for full and sparse grid problems

  • M. Griebel
  • C. Zenger
  • S. Zimmer
Article

Abstract

We present grid-oriented and newly developed point-oriented robust multilevel methods for full and sparse grid discretizations. Especially the point-oriented multilevel methods are very well suited for parallelization and behave robust for anisotropic model problems. They can be generalized easily to domain-oriented multilevel methods with the same properties.

AMS (MOS) Subject Classifications

65F10 65N20 65N30 

Key words

Anisotropic problems block-Gauss-Seidel iteration Gauss-Seidel iteration hierarchical basis multigrid methods partial differential equations point-oriented methods semidefinite system sparse grids 

Multilevel Gauß-Seidel-Algorithmen für Voll- und Dünngitterprobleme

Zasammenfassung

Wir stellen gitterorientierte und neu entwickelte punktorientierte robuste Multilevelverfahren für Voll- und Dünngitterdiskretisierungen vor. Besonders die punktorientierten Multilevelmethoden sind sehr gut zu parallelisieren und erweisen sich als robust für anisotrope Modellprobleme. Sie erlauben eine einfache Erweiterung auf gebietsorientierte Multilevelmethoden mit denselben Eigenschaften.

Wir berichten die Ergebnisse numerischer Experimente für die Reduktionszahlen dieser neuen Algorithmen.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • M. Griebel
    • 1
  • C. Zenger
    • 1
  • S. Zimmer
    • 1
  1. 1.Stefan Zimmer Institut für InformatikTechnische Universität MünchenMünchen 2Federal Republic of Germany

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