Parallel Mosaic-Skeleton Algorithm for the Numerical Solution of a Three-Dimensional Scalar Scattering Problem in Integral Form

Abstract

A three-dimensional scalar stationary scattering problem is considered. It is formulated in the form of a weakly singular Fredholm boundary integral equation of the first kind with a single unknown function. The equation is approximated by a system of linear algebraic equations, which is then solved numerically by an iterative method. The mosaic-skeleton method is used at the stage of the approximate solution of this system in order to reduce the computational complexity of the approach.

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Funding

This work was supported by the Russian Foundation for Basic Research (project nos. 17-01-00682, 20-01-00450) and by the Far Eastern Branch of the Russian Academy of Sciences (basic research program, project no. 18-5-100).

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Correspondence to A. A. Kashirin or S. I. Smagin or M. Yu. Timofeenko.

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Translated by I. Ruzanova

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Kashirin, A.A., Smagin, S.I. & Timofeenko, M.Y. Parallel Mosaic-Skeleton Algorithm for the Numerical Solution of a Three-Dimensional Scalar Scattering Problem in Integral Form. Comput. Math. and Math. Phys. 60, 895–910 (2020). https://doi.org/10.1134/S0965542520050097

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Keywords:

  • scattering problem
  • integral equation
  • numerical solution
  • fast method
  • mosaic-skeleton method
  • incomplete cross approximation