Geodesic
Application of number-theoretic grids in problems of sound diffraction by elastic bodies
Čebyševskij sbornik, Tome 23 (2022) no. 5, pp. 206-226

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The article considers the problem of a plane harmonic sound wave diffraction by an elastic ellipsoid. 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 displacement 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 acoustic pressure in near field. This method is compared with the calculation of integrals by the simple cell method, which has the same order of accuracy. The time of solving the problem is compared with the calculation of pressure in the vicinity of the ellipsoid based on the solution of an integral equation by two methods for calculating integrals.
Keywords: diffraction, sound waves, linear integral equations, quadrature formulas, periodization, Smolyak grids, parallelepiped grids. 
@article{CHEB_2022_23_5_a17,
     author = {N. N. Dobrovol'skii and S. A. Skobel'tsyn and L. A. Tolokonnikov and N. V. Larin},
     title = {Application of number-theoretic grids in problems of sound diffraction by elastic bodies},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {206--226},
     publisher = {mathdoc},
     volume = {23},
     number = {5},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2022_23_5_a17/}
}
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N. N. Dobrovol'skii; S. A. Skobel'tsyn; L. A. Tolokonnikov; N. V. Larin. Application of number-theoretic grids in problems of sound diffraction by elastic bodies. Čebyševskij sbornik, Tome 23 (2022) no. 5, pp. 206-226. http://geodesic.mathdoc.fr/item/CHEB_2022_23_5_a17/