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Solving Exterior Boundary Value Problems for the Laplace Equation

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Abstract

We propose methods for solving an exterior boundary value problem for the Laplace equation based on the main integral Green formula. The main technique is the one of setting an artificial integral boundary condition with iterative improvement. It is shown that iterative methods converge at the rate of a geometric progression. The applicability of the methods for solving exterior problems is confirmed by computational experiments in the two- and three-dimensional cases. The algorithm is also applied to problems with an operator of the mixed type.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Moscow, 125047, Russia

    M. P. Galanin & D. L. Sorokin

  2. Bauman Moscow State Technical University, Moscow, 105005, Russia

    M. P. Galanin & D. L. Sorokin

Authors
  1. M. P. Galanin
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  2. D. L. Sorokin
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Correspondence to M. P. Galanin or D. L. Sorokin.

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Translated by V. Potapchouck

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Galanin, M.P., Sorokin, D.L. Solving Exterior Boundary Value Problems for the Laplace Equation. Diff Equat 56, 890–899 (2020). https://doi.org/10.1134/S0012266120070083

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