Geodesic
About application of number-theoretic grids in problems of acoustics
Čebyševskij sbornik, Tome 22 (2021) no. 3, pp. 368-382.

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The article discusses spherical diffraction problem monochromatic sound wave absolutely rigid sphere. To represent the scattered field, a representation in the form of a Kirchhoff integral is used. This leads to the need to solve the Fredholm integral equation of the second kind to determine the velocity potential in the scattered wave on the surface of the scatterer. It is shown that the use of quadrature formulas based on number-theoretic grids allows you to reduce the number of calculations for the approximate calculation of integrals, when solving the integral equation and when calculating the scattered field on the surface of the sphere and in the far field. This method was compared with the simple cell method, which takes into account the mechanical formulation of the problem and has the same order of accuracy. Estimation of the accuracy of calculating the pressure on the surface of the sphere and the form-function of the scattered field based on the solution of the integral equation was carried out by comparison with the analytical solution based on the expansion in spherical wave functions.
Keywords: diffraction, spherical sound wave, linear integral equations, interpolation, interpolation polynomials, quadrature formulas, periodization, Smolyak grids, parallelepiped grids. 
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N. N. Dobrovol'skii; S. A. Skobel'tsyn; L. A. Tolokonnikov; N. V. Larin. About application of number-theoretic grids in problems of acoustics. Čebyševskij sbornik, Tome 22 (2021) no. 3, pp. 368-382. http://geodesic.mathdoc.fr/item/CHEB_2021_22_3_a21/

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