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On the existence of mosaic-skeleton approximations for discrete analogues of integral operators

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Abstract

Exterior three-dimensional Dirichlet problems for the Laplace and Helmholtz equations are considered. By applying methods of potential theory, they are reduced to equivalent Fredholm boundary integral equations of the first kind, for which discrete analogues, i.e., systems of linear algebraic equations (SLAEs) are constructed. The existence of mosaic-skeleton approximations for the matrices of the indicated systems is proved. These approximations make it possible to reduce the computational complexity of an iterative solution of the SLAEs. Numerical experiments estimating the capabilities of the proposed approach are described.

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Authors and Affiliations

  1. Computing Center, Far East Branch, Russian Academy of Sciences, Khabarovsk, 680000, Russia

    A. A. Kashirin & M. Yu. Taltykina

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  1. A. A. Kashirin
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  2. M. Yu. Taltykina
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Correspondence to A. A. Kashirin.

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Original Russian Text © A.A. Kashirin, M.Yu. Taltykina, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 9, pp. 1421–1432.

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Kashirin, A.A., Taltykina, M.Y. On the existence of mosaic-skeleton approximations for discrete analogues of integral operators. Comput. Math. and Math. Phys. 57, 1404–1415 (2017). https://doi.org/10.1134/S096554251709007X

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  • DOI: https://doi.org/10.1134/S096554251709007X

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