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Интеллектуальная Система Тематического Исследования НАукометрических данных |
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ON A GENERAL APPROACH FOR NUMERICAL SOLVING SINGULAR INTEGRAL EQUATIONS IN THE SCALAR PROBLEMS OF DIFFRACTION BY CURVILINEAR SMOOTH SCREENSстатья Тезисы
- Автор: Tsupak A.
- Журнал: Communications in Computer and Information Science
- Том: 1413
- Год издания: 2021
- Первая страница: 154
- Последняя страница: 160
- DOI: 10.1007/978-3-030-78759-2_13
- Аннотация: The problems of diffraction of monochromatic acoustic waves by smooth infinitely thin curvilinear sound-soft and sound-hard screens are considered. The singular integral equations of the diffraction problems are numerically solved using Galerkin method. A general approach for definition of basis functions with compact support is proposed in the case of arbitrary smooth (or piecewise smooth) parameterized screens. Several examples of such basis functions on non-planar screens are presented. It is shown that the basis functions possess the denseness property. Convergence of the Galerkin method is established in appropriate Sobolev spaces on manifolds with boundary. The parallel implementation of the Galerkin method is used. Several numerical tests are carried out; in particular, the approximate solutions of a test problem are compared with the known analytical solution. The proposed technique can be used for solving more complicated problems, i.e., problems of diffraction by systems of solids and screens, or by partially shielded solids without requiring consistency of grids on volumetric scatterers and surfaces.
- Добавил в систему: Цупак Алексей Александрович