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Construction of direct and iterative decomposition methods

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Abstract

In order to solve boundary value problems with the Dirichlet-Dirichlet type conditions by decomposing the computational domain into subdomains joined without overlapping, the discrete Green’s functions are used to approximate the Poincaré-Steklov operator equation on the interface of the subdomains, which involves the difference of the normal derivatives of the solution on the opposite sides of the interface. Basing on this approach, some direct and iterative decomposition methods are constructed that are basically of a parallel nature. Examples of numerical computations demonstrate the accuracy and convergence of the algorithms.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia

    V. M. Sveshnikov

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    V. M. Sveshnikov

Authors
  1. V. M. Sveshnikov
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Correspondence to V. M. Sveshnikov.

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Original Russian Text © V.M. Sveshnikov, 2009, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2009, Vol. XII, No. 3, pp. 99–109.

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Sveshnikov, V.M. Construction of direct and iterative decomposition methods. J. Appl. Ind. Math. 4, 431–440 (2010). https://doi.org/10.1134/S1990478910030166

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  • DOI: https://doi.org/10.1134/S1990478910030166

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