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Quadrature Formula for a Double Layer Potential in the Case of the Helmholtz Equation

Abstract

A quadrature formula for a double layer potential is derived in the case of the Helmholtz equations with a continuous density given on a smooth closed or open surface. The quadrature formula ensures higher numerical accuracy than a standard quadrature formula, which has been confirmed by numerical tests. An advantage of the new formula is especially noticeable near the surface, where the standard formula diverges rapidly, while the new one ensures acceptable numerical accuracy for points separated from the surface by distances comparable to or larger than the integration step size.

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Funding

Reznichenko’s research was supported by the Moscow Center for Fundamental and Applied Mathematics, agreement no. 075-15-2019-1623 with the Ministry of Science and Higher Education of the Russian Federation.

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Correspondence to P. A. Krutitskii or I. O. Reznichenko.

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Translated by I. Ruzanova

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Krutitskii, P.A., Reznichenko, I.O. Quadrature Formula for a Double Layer Potential in the Case of the Helmholtz Equation. Comput. Math. and Math. Phys. 62, 411–426 (2022). https://doi.org/10.1134/S0965542522030095

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  • DOI: https://doi.org/10.1134/S0965542522030095

Keywords:

  • double layer potential
  • quadrature formula
  • Helmholtz equation