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Computation of Asymptotic Spectral Distributions for Sequences of Grid Operators

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Abstract

The asymptotic spectral properties of matrices of grid operators on polygonal domains in the plane are studied in the case of refining triangular grids. Methods available for analyzing spectral distributions are largely based on tool of the theory of generalized locally Toeplitz sequences (GLT theory). In this paper, we show that the matrices of grid operators on nonrectangular domains do not form GLT sequences. A method for calculating spectral distributions in such cases is proposed. Generalizations of GLT sequences are introduced, and preconditioner based on them are proposed.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, 119991, Moscow, Russia

    S. V. Morozov & E. E. Tyrtyshnikov

  2. Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333, Moscow, Russia

    S. V. Morozov & E. E. Tyrtyshnikov

  3. University of Insubria, 22100, Como, Italy

    S. Serra-Capizzano

  4. Uppsala University, SE-751 05, Uppsala, Sweden

    S. Serra-Capizzano

  5. Siedlce University, 08-110, Siedlce, Poland

    E. E. Tyrtyshnikov

  6. Moscow Center for Fundamental and Applied Mathematics, 119234, Moscow, Russia

    E. E. Tyrtyshnikov

Authors
  1. S. V. Morozov
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  2. S. Serra-Capizzano
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  3. E. E. Tyrtyshnikov
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Corresponding authors

Correspondence to S. V. Morozov, S. Serra-Capizzano or E. E. Tyrtyshnikov.

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Translated by I. Ruzanova

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Morozov, S.V., Serra-Capizzano, S. & Tyrtyshnikov, E.E. Computation of Asymptotic Spectral Distributions for Sequences of Grid Operators. Comput. Math. and Math. Phys. 60, 1761–1777 (2020). https://doi.org/10.1134/S0965542520110093

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  • DOI: https://doi.org/10.1134/S0965542520110093

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