Numerical solution of a three-dimensional stationary problem of the diffraction of elastic waves
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 3, pp. 486-502
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Three-dimensional problems concerning the propagation of stationary elastic oscillations in media with three-dimensional inclusions are solved numerically. By applying potential theory methods, the original problem is stated as a system of two singular vector integral equations for the unknown internal and external densities of auxiliary sources of waves. An approximate solution of the original problem is obtained by approximating the integral equations by a system of linear algebraic equations, which is then solved numerically. The underlying algorithm has the property of self-regularization, due to which a numerical solution is found without using cumbersome regularizing algorithms. Results of test computations and numerical experiments are presented that characterize the capabilities of this approach as applied to the diffraction of elastic waves in three-dimensional settings.
@article{ZVMMF_2010_50_3_a7,
author = {N. E. Ershov and L. V. Illarionova},
title = {Numerical solution of a three-dimensional stationary problem of the diffraction of elastic waves},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {486--502},
publisher = {mathdoc},
volume = {50},
number = {3},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_3_a7/}
}
TY - JOUR AU - N. E. Ershov AU - L. V. Illarionova TI - Numerical solution of a three-dimensional stationary problem of the diffraction of elastic waves JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2010 SP - 486 EP - 502 VL - 50 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_3_a7/ LA - ru ID - ZVMMF_2010_50_3_a7 ER -
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N. E. Ershov; L. V. Illarionova. Numerical solution of a three-dimensional stationary problem of the diffraction of elastic waves. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 3, pp. 486-502. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_3_a7/