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The Sommerfeld Integral in Problems of Simulating the Diffraction of Acoustic Waves Using a Triangular Lattice

  • CLASSICAL PROBLEMS OF LINEAR ACOUSTICS AND WAVE THEORY
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Abstract

Analytical solutions are obtained for two problems for a discrete analogue of the Helmholtz equation on a triangular lattice: (1) the problem of radiation from a point source on a plane; (2) the problem of diffraction on a half-line with Dirichlet boundary conditions. It is shown that in these problems, the complete field can be represented as an integral of an algebraic function over a family of contours located on some complex manifold. The solution to the first problem is found as an integral of some differential form over this manifold, and the asymptotics of the far field for this solution is obtained. The second problem is solved using an analogue of the Sommerfeld integral. It is checked that the obtained solution coincides with the solution of this problem by the Wiener–Hopf method.

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Funding

The study was supported by the Russian Foundation for Basic Research (project no. 19-29-06048).

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Authors and Affiliations

  1. Moscow State University, 119991, Moscow, Russia

    O. I. Makarov, A. V. Shanin & A. I. Korolkov

Authors
  1. O. I. Makarov
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  2. A. V. Shanin
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  3. A. I. Korolkov
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Correspondence to O. I. Makarov.

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Makarov, O.I., Shanin, A.V. & Korolkov, A.I. The Sommerfeld Integral in Problems of Simulating the Diffraction of Acoustic Waves Using a Triangular Lattice. Acoust. Phys. 69, 143–158 (2023). https://doi.org/10.1134/S1063771023600080

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  • DOI: https://doi.org/10.1134/S1063771023600080

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