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Quadrature Formula for the Direct Value of the Double-Layer Potential

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Abstract

In this paper, a quadrature formula is derived for the direct value of a double-layer potential with the continuous density defined on a closed or open surface. Double-layer potentials for the Laplace and Helmholtz equations are considered. The derived quadrature formula can be used for the numerical solution of boundary value problems for the Laplace and Helmholtz equations by the potential method and boundary integral equations. The proposed quadrature formula has a significantly higher accuracy than the standard quadrature formula, which is confirmed by our numerical tests performed in Matlab. Time-consuming analytical computations in this work are carried out using the Symbolic Math Toolbox computer algebra system based on Matlab.

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Authors and Affiliations

  1. Moscow State University, 119991, Moscow, Russia

    I. O. Reznichenko

  2. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, 125047, Moscow, Russia

    P. A. Krutitskii

Authors
  1. I. O. Reznichenko
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  2. P. A. Krutitskii
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Correspondence to I. O. Reznichenko or P. A. Krutitskii.

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Translated by Yu. Kornienko

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Reznichenko, I.O., Krutitskii, P.A. Quadrature Formula for the Direct Value of the Double-Layer Potential. Program Comput Soft 48, 227–233 (2022). https://doi.org/10.1134/S0361768822030094

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  • DOI: https://doi.org/10.1134/S0361768822030094

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