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Two-frequency decomposition

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Summary.

In this paper, we present a preconditioner for large systems of linear equations based on the block decomposition for block-tridiagonal matrices. This decomposition is in many respects similar to the frequency-filtering method of Wittum [18] and also to the frequency-filtering decomposition of Wagner [4]–[6]. In contrast to these methods, our approach requires no pointwise filtering conditions but, as in [1], only averaged ones; this simplifies the implementation without any loss of efficiency. Theoretical analysis of the model problem leads to the convergence rate . Numerical experiments demonstrate similar convergence behaviour for a wider class of problems.

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References

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Authors and Affiliations

  1. Department of Mathematics, Kaliningrad State University, A. Nevsky 14, 236041, Kaliningrad, Russia

    A. Buzdin

  2. IWR – Technische Simulation, Universität Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg

    G. Wittum

Authors
  1. A. Buzdin
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  2. G. Wittum
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Correspondence to G. Wittum.

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Mathematics Subject Classification (2000): 65F10, 65N22

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Buzdin, A., Wittum, G. Two-frequency decomposition. Numer. Math. 97, 269–295 (2004). https://doi.org/10.1007/s00211-003-0459-8

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  • DOI: https://doi.org/10.1007/s00211-003-0459-8

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