Abstract
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.
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Tsupak, A. (2021). On a General Approach for Numerical Solving Singular Integral Equations in the Scalar Problems of Diffraction by Curvilinear Smooth Screens. In: Balandin, D., Barkalov, K., Gergel, V., Meyerov, I. (eds) Mathematical Modeling and Supercomputer Technologies. MMST 2020. Communications in Computer and Information Science, vol 1413. Springer, Cham. https://doi.org/10.1007/978-3-030-78759-2_13
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DOI: https://doi.org/10.1007/978-3-030-78759-2_13
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