Numerical solution to a two-dimensional hypersingular integral equation and sound propagation in urban areas

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. © 2007 Pleiades Publishing, Ltd.

Authors
Gutnikov V.A. 1 , Kiryakin V.Yu.2 , Lifanov I.K.3 , Setukha A.V.3 , Stavtsev S.L.4
Journal
Computational Mathematics and Mathematical Physics
Number of issue
12
Language
English
Pages
2002-2013
Status
Published
Link
External link
DOI
10.1134/S096554250712010X
Volume
47
Year
2007
Organizations
  • 1 Faculty of Ecology, Peoples' Friendship University of Russia, Podol'skoe sh. 8/5, Moscow 113093, Russian Federation
  • 2 All-Russia Research Institute of Railroad Transportation, Federal Agency for Rail Transportation, Tret'ya Mytishchinskaya ul. 10, Moscow 129626, Russian Federation
  • 3 Department of Mathematics, Zhukovsky Air Force Engineering Academy, ul. Planetnaya 3, Moscow 125190, Russian Federation
  • 4 Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow 119991, Russian Federation
Keywords
Acoustics problems; Closed discrete vortical frames method; Estimates for quadrature formulas; Hypersingular integral equations
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/3177/
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