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Robustness of the additive and multiplicative frequency decomposition multi-level method

Die Robustheit des additiven und multiplikativen Frequenzzerlegungs-Mehrgitterverfahrens

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Abstract

Recently, we introduced a cheap modification of Hackbusch'sFrequency Decomposition multi-level method. In this paper, the multiplicative variant of this method is studied. Using the theory of Subspace Correction Methods robustness is proved of both the multiplicative and additive variant applied to anisotropic problems in an arbitrary number of space dimensions. Implementation of both variants is discussed and numerical results are given.

Zusammenfassung

Kürzlich haben wir eine effektive Modifizierung des Frequenzzerlegungs-Mehrgitterverfahrens vorgestellt. In diesem Artikel wird die multiplikative Variante dieses Verfahrens untersucht. Unter Verwendung der Theorie der Unterraumkorrekturverfahren wird die Robustheit sowohl für die multiplikative als auch für die additive Variante bei Anwendung auf anisotrope Probleme mit beliebiger Raumdimension bewiesen. Die Implementierung beider Varianten wird diskutiert und numerische Ergebnisse werden angegeben.

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References

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Stevenson, R.P. Robustness of the additive and multiplicative frequency decomposition multi-level method. Computing 54, 331–346 (1995). https://doi.org/10.1007/BF02238231

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Mathematical Subject Classifications (1991)

  • 65N55
  • 65N30

Key words

  • Frequency decomposition
  • multi-level method
  • finite elements
  • hierarchical basis
  • additive and multiplicative Schwarz methods
  • subspace decomposition
  • robustness