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: 1948-3033

Smagin 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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[2] Ihlenburg, F. Finite element analysis of acoustic scattering. Springer-Verlag New York Inc.; 1998: 226.

[3] Clayton, R., Engquist, B. Absorbing boundary conditions for acoustic and elastic wave equations. Bull. Seismol. Soc. Amer. 1977; 67(6):1529–1540.

[4] Berenger, J.-P. A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 1994; 114(2):185–200.

[5] Liu, Q.-H., Tao J. The perfectly matched layer for acoustic waves in absorptive media. J. Acoust. Soc. Am. 1997; 102(4):2072–2082.

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[7] Smagin, S.I. Integral'nye uravneniya zadach difraktsii [Integral equations for diffraction problems]. Vladivostok: Dalnauka; 1995: 203. (In Russ.)

[8] Kashirin, A.A., Smagin, S.I. Generalized solutions of the integral equations of a scalar diffraction problem. Differential Equations. 2006; 42(1):88–100.

[9] Colton, D., Kress, R. Integral Equation Methods in Scattering Theory. New York: John Wiley and Sons; 1983: 271.

[10] Tsetsokho, V.A., Voronin, V.V., Smagin, S.I. On the solution of diffraction problems using simple layer potentials. Doklady Akademii Nauk SSSR. 1988; 302(2):323–327. (In Russ.)

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[14] Kashirin, A.A. Issledovanie i chislennoe reshenie integral'nykh uravneniy trekhmernykh statsionarnykh zadach difraktsii akusticheskikh voln: Dis. ... kand. fiz.-mat. nauk [Investigation and numerical solution of integral equations for three-dimensional stationary diffraction problems of acoustic waves].Khabarovsk: VTs DVO RAN; 2006: 118. (In Russ.)

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[17] Voronin, V.V., Tsetsokho, V.A. An Interpolation Method for Solving an Integral Equation of the First Kind with a Logarithmic Singularity. Doklady Akademii Nauk SSSR. 1974; 216(6):1209–1211. (In Russ.)

[18] Atkinson, K.E. A discrete Galerkin method for first kind integral equations with a logarithmic kernel. J. Integral Equations Appl. 1988; 1(3):343–364.

[19] Smagin, S.I. Numerical solution of the integral equation of the first kind with a weak singularity for the density of a simple layer potential. USSR Computational Mathematics and Mathematical Physics. 1988; 28(6):41–49.

[20] Kashirin, A.A., Smagin, S.I. Potential-based numerical solution of Dirichlet problems for the Helmholtz equation. Computational Mathematics and Mathematical Physics. 2012; 52(8):1173–1185.

[21] Brebbia, C.A., Telles, J.C.F., Wrobel, L.C. Boundary Element Techniques: Theory and Applications in Engineering. Berlin: Springer-Verlag; 1984: 464.

[22] Kashirin, A.A., Smagin, S.I. Numerical solution of integral equations for a scalar diffraction problem. Doklady Mathematics. 2014; 90(2):549–552.

[23] Kashirin, A.A., Smagin, S.I., Taltykina, M.Yu. Mosaic-skeleton method as applied to the numerical solution of three-dimensional Dirichlet problems for the Helmholtz equation in integral form. Computational Mathematics and Mathematical Physics. 2016; 56(4):612–625.

[24] Beale, J.T. A grid-based boundary integral method for elliptic problems in three dimensions. SIAM J. Numer. Anal. 2004; 42(2):599–620.

[25] Tausch, J. A spectral method for the fast solution of boundary integral formulations of elliptic problems. Integral Methods in Science and Engineering / C. Constanda, Z. Nashed, D. Rollins. (Eds). Boston: Birkhauser; 2006: 289–297.

[26] Saad, Y., Schultz, M. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. and Stat. Comput. 1986; 7(3):856–869.

[27] Laliena, A.R., Rapun, M.-L., Sayas F.-J. Symmetric boundary integral formulations for Helmholtz transmission problems. Appl. Num. Math. 2009; 59(11):2814–2823.

[28] Kleefeld, A. The transmission problem for the Helmholtz equation in R3. Comput. Methods Appl. Math. 2012; 12(3):330–350.

[29] McLean, W. Strongly elliptic systems and boundary integral equations. Cambridge: Cambridge University Press; 2000: 372.

[30] Ershov, N.E., Illarionova, L.V., Smagin, S.I. Numerical solution of a 3D stationary problem for diffraction of acoustic waves. Computational technologies. 2010; 15(1):60–76. (In Russ.)

[31] Tikhonov, A.N., Samarskii, A.A. Equations of Mathematical Physics. New York: Dover;2011: 800.

[32] Watson, G. N. Treatise on the Theory of Bessel Functions. Cambridge: Cambridge Univ. Press; 1952: 804.