Studying the issue of acoustic wave scattering from a system of soft screens by the method of integral equations
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 t...
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| Format: | Article |
| Language: | English |
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Penza State University Publishing House
2025-03-01
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| Series: | Известия высших учебных заведений. Поволжский регион: Физико-математические науки |
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| author | V.O. Nesterov A.A. Tsupak |
| author_facet | V.O. Nesterov A.A. Tsupak |
| author_sort | V.O. Nesterov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c906f644d52e4a3585f23bb6daaefe7b |
| institution | OA Journals |
| issn | 2072-3040 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Penza State University Publishing House |
| record_format | Article |
| series | Известия высших учебных заведений. Поволжский регион: Физико-математические науки |
| spelling | doaj-art-c906f644d52e4a3585f23bb6daaefe7b2025-08-20T02:08:00ZengPenza State University Publishing HouseИзвестия высших учебных заведений. Поволжский регион: Физико-математические науки2072-30402025-03-01410.21685/2072-3040-2024-4-3Studying the issue of acoustic wave scattering from a system of soft screens by the method of integral equations V.O. Nesterov0A.A. Tsupak1Penza State UniversityPenza State UniversityBackground. 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 problemacoustically soft screensintegral equationssobolev spacesgalerkin method |
| spellingShingle | V.O. Nesterov A.A. Tsupak Studying the issue of acoustic wave scattering from a system of soft screens by the method of integral equations Известия высших учебных заведений. Поволжский регион: Физико-математические науки diffraction problem acoustically soft screens integral equations sobolev spaces galerkin method |
| title | Studying the issue of acoustic wave scattering from a system of soft screens by the method of integral equations |
| title_full | Studying the issue of acoustic wave scattering from a system of soft screens by the method of integral equations |
| title_fullStr | Studying the issue of acoustic wave scattering from a system of soft screens by the method of integral equations |
| title_full_unstemmed | Studying the issue of acoustic wave scattering from a system of soft screens by the method of integral equations |
| title_short | Studying the issue of acoustic wave scattering from a system of soft screens by the method of integral equations |
| title_sort | studying the issue of acoustic wave scattering from a system of soft screens by the method of integral equations |
| topic | diffraction problem acoustically soft screens integral equations sobolev spaces galerkin method |
| work_keys_str_mv | AT vonesterov studyingtheissueofacousticwavescatteringfromasystemofsoftscreensbythemethodofintegralequations AT aatsupak studyingtheissueofacousticwavescatteringfromasystemofsoftscreensbythemethodofintegralequations |