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Article information
2019 , Volume 24, ¹ 6, p.40-49
Kashirin A.A., Smagin S.I.
A numerical method for solving the boundary integral equations of the three-dimensional scalar diffraction problem
Purpose. The article addresses developing efficient algorithms for numerical solution of the diffraction problem for stationary acoustic waves by three-dimensional homogeneous inclusions on the spectrum of integral operators. Methods. By using the combinations of single- and double-layer potentials, two Fredholm boundary integral equations of the first kind with one unknown function are obtained for them. For discretization the equations, a special method of averaging integral operators with weak singularities in the kernels is applied. For a numerical solution on the spectrum of integral operators, a solution interpolation method is proposed. Outcomes. The obtained integral equations are approximated by systems of linear algebraic equations with easily calculated coefficients, which are then solved numerically by the generalized minimal residual method (GMRES). The computing experiments for numerical solution of the three-dimensional diffraction problem have been carried out on the spectrum of integral operators. Conclusions. Computational experiments have shown that the proposed approach is highly accurate in finding approximate solutions to the problems in question on the spectrum of integral operators. It can be used to solve other problems of mathematical physics formulated in the form of boundary integral equations.
[full text] [link to elibrary.ru]
Keywords: diffraction problem, Helmholtz equation, boundary integral equation, spectrum, numerical method
doi: 10.25743/ICT.2019.24.6.006.
Author(s):
Kashirin Alexey Alekseevich
PhD. , Associate Professor
Position: Senior Research Scientist
Office: Computer Center FEB RAS
Address: Russia, Khabarovsk, 65, Kim Yu Chen str.
E-mail: elomer@mail.ru
SPIN-code: 1948-3033Smagin Sergey Ivanovich
Dr. , Correspondent member of RAS, Professor
Position: Director
Office: Computer Center FEB RAS
Address: 680000, Russia, Khabarovsk
Phone Office: (4212) 22 72 67
E-mail: smagin@ccfebras.ru
SPIN-code: 2419-4990 References:
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Bibliography link:
Kashirin A.A., Smagin S.I. A numerical method for solving the boundary integral equations of the three-dimensional scalar diffraction problem // Computational technologies. 2019. V. 24. ¹ 6. P. 40-49
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