Studying the issue of acoustic wave scattering from a system of soft screens by the method of integral equations 

Vladislav O. Nesterov, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia) 
Aleksey A. Tsupak, Candidate of physical and mathematical sciences, associate professor, associate professor of the sub-department of mathematics and supercomputer
modeling, Penza State University (40 Krasnaya street, Penza, Russia) E-mail: altsupak@yandex.ru

Background. The aim of the work is a theoretical and numerical study of the scalar problem of diffraction on the system of acoustically soft screens. Material and methods: a rigorous mathematical formulation of the diffraction problem is considered; the Galerkin method is used to numerically solve the system of integral equations of the diffraction problem. Results. Theorems on the existence and uniqueness of the solution to the diffraction problem are proved; in particular, ellipticity and continuous invertibility of the operator of the integral equations system are established; convergence of the Galerkin method is proved. Conclusions. Important results on the solvability of the diffraction problem have been obtained; a projection method for its numerical solution is theoretically justified and implemented.

diffraction problem, acoustically soft screens, integral equations, Sobolev spaces, Galerkin method

Nesterov V.O., Tsupak A.A. Studying the issue of acoustic wave scattering from a system of soft screens by the method of integral equations. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki = University proceedings. Volga region. Physical and mathematical sciences. 2024;(4):35–45.
(In Russ.). doi: 10.21685/2072-3040-2024-4-3