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Quadrature Formula for the Double Layer Potential with Differentiable Density

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Abstract

We derive a quadrature formula for the double layer potential with a differentiable density given on a smooth closed or open surface. Numerical tests show that this formula gives a higher accuracy of calculations near the surface where the potential density is given than the quadrature formulas in which the differentiability of the density is not taken into account and the density is only assumed to be continuous. The advantage of the quadrature formula in this paper is especially noticeable in the case where the potential density is represented by smooth oscillating functions, since it allows one to increase the accuracy of potential calculation without increasing the cost of computations.

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Authors and Affiliations

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

    P. A. Krutitskii

  2. Lomonosov Moscow State University, Moscow, 119991, Russia

    I. O. Reznichenko

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

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Translated by V. Potapchouck

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Krutitskii, P.A., Reznichenko, I.O. Quadrature Formula for the Double Layer Potential with Differentiable Density. Diff Equat 58, 1114–1125 (2022). https://doi.org/10.1134/S0012266122080122

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  • DOI: https://doi.org/10.1134/S0012266122080122

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