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Numerical solution to a two-dimensional hypersingular integral equation and sound propagation in urban areas |
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| Authors: | V. A. Gutnikov V. Yu. Kiryakin I. K. Lifanov A. V. Setukha S. L. Stavtsev |
| Affiliation: | (1) Faculty of Ecology, Peoples’ Friendship University of Russia, Podol’skoe sh. 8/5, Moscow, 113093, Russia;(2) All-Russia Research Institute of Railroad Transportation, Federal Agency for Rail Transportation, Tret’ya Mytishchinskaya ul. 10, Moscow, 129626, Russia;(3) Department of Mathematics, Zhukovsky Air Force Engineering Academy, ul. Planetnaya 3, Moscow, 125190, Russia;(4) Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia |
| Abstract: | A mathematical model of sound propagation from a noise source in urban areas is constructed. The exterior Neumann problem for the scalar Helmholtz equation is reduced to a system of hypersingular integral equations. A numerical method for solving the system of integral equations is described. The convergence of the quadrature formulas underlying the numerical method is estimated. Numerical results are presented for particular applications. |
| Keywords: | acoustics problems hypersingular integral equations closed discrete vortical frames method estimates for quadrature formulas |
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