SOLVING OF THE PROBLEM OF ACOUSTIC WAVE DIFFRACTION
ON A SYSTEM OF HARD SCREENS BY THE GALERKIN METHOD

Romanova Natal'ya Vladimirovna, Student, Penza State University (40 Krasnaya street, Penza, Russia), mmm@pnzgu.ru
Tsupak Aleksey Aleksandrovich, Candidate of physical and mathematical sciences, associate professor, sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), altsupak@yandex.ru

517.3

10.21685/2072-3040-2016-2-5

Background. The aim of this work is to numerically study the scalar problem of flat acoustic wave scattering by an obstacle of complex shape consisting of infinitely thin acoustically hard screens.
Material and methods. The problem is considered in the quasiclassical statement; the original boundary value problem for the Helmholtz equation in unbounded space is reduced to a system of integral equations over bounded manifolds of dimension 2. To find the numerical solution to the problem of diffraction, the Galerkin method is applied using piecewise linear basis functions.
Results. The projection method for solving the system of integral equations of the scalar diffraction problem was developed and implemented; several computational experiments were performed.
Conclusions. The proposed numerical method is an effective way to find approximate solutions to the scalar problems of diffraction on hard screens of arbitrary shape; it can also be used to solve problems of a wider range.

scalar diffraction problem, integral equations, acoustically hard screens, Galerkin method 

1. Medvedik M. Yu., Smirnov Yu. G., Tsupak A. A. Zhurnal vychislitel'noy matematiki i matematicheskoy fiziki [Journal of calculus mathematics and mathematical physics]. 2014, vol. 54, no. 8, pp. 1319–1331.
2. Smirnov Yu. G., Tsupak A. A. Differentsial'nye uravneniya [Differential equations]. 2014, vol. 50, no. 9, pp. 1164–1174.
3. Tsupak A. A. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fizikomatematicheskie nauki [University proceedings. Volga region. Physical and mathematical sciences]. 2014, no. 1 (29), pp. 30–38.
4. Tsupak A. A. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fizikomatematicheskie nauki [University proceedings. Volga region. Physical and mathematical sciences]. 2015, no. 3 (35), pp. 61–71.
5. Derevyanchuk E. D., Smol'kin E. Yu., Tsupak A. A. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki [University proceedings. Volga region. Physical and mathematical sciences]. 2014, no. 4 (32), pp. 57–68.
6. Marchuk G. I., Agoshkov V. I. Vvedenie v proektsionno-setochnye metody [Introduction into projection network methods]. Moscow: Nauka, 1981.
7. Stephan E. P. Integral equations and potential theory. 1987, vol. 10, pp. 236–257.