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Difference Decomposition Schemes Based on Splitting the Solution and Operator of the Problem

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Abstract

Domain decomposition methods are used for the approximate solution of boundary value problems for partial differential equations on parallel computing systems. The specifics of nonstationary problems is most completely taken into account when using noniterative domain decomposition schemes. Regionally additive schemes are constructed on the basis of various classes of splitting schemes. A new class of domain decomposition schemes with an additive representation of the solution on a new time level is distinguished that is based on splitting the domain into subdomains based on a partition of unity. An example of the Cauchy problem for first-order evolution equations with a positive self-adjoint operator in a finite-dimensional Hilbert space is considered. Unconditionally stable two- and three-level splitting schemes are constructed for the corresponding system of equations.

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Funding

This work was financially supported by the Russian Science Foundation, project 23-41-00037 (Secs. 1–3), https://rscf.ru/en/project/23-41-00037/ and project 23-71-30013 (Secs. 4–5),

https://rscf.ru/en/project/23-71-30013/.

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Authors and Affiliations

  1. Nuclear Safety Institute, Russian Academy of Sciences, Moscow, 115191, Russia

    P. N. Vabishchevich

  2. North-Eastern Federal University, Yakutsk, 677027, Russia

    P. N. Vabishchevich

Authors
  1. P. N. Vabishchevich
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Correspondence to P. N. Vabishchevich.

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Translated by V. Potapchouck

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Vabishchevich, P.N. Difference Decomposition Schemes Based on Splitting the Solution and Operator of the Problem. Diff Equat 59, 945–961 (2023). https://doi.org/10.1134/S001226612307008X

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  • DOI: https://doi.org/10.1134/S001226612307008X

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