Geodesic
Computation of wave processes in nonuniform 3D constructions
Matematičeskoe modelirovanie, Tome 21 (2009) no. 5, pp. 3-9

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The purpose of the given article is research of character of the return wavefront caused by dispersion of elastic energy from cavity and crack zones in massive rocks. Numerical solutions of elastic wave transmission close to nonuniformities (cavities and cracks, characteristic for considered rocks) and also in housing and industrial constructions having essential nonumiformities (internal cavities – rooms) have been obtained. Grid-characteristic method with formulation of boundary conditions on an interface between rock and cavity (or crack), and also on free surfaces in an explicit form is used in this article. The offered numerical method has a great generality and is suitable for research of processes of a flow about macroscopical barriers by seismic waves when it is impossible to neglect effects of shielding and diffraction. 
@article{MM_2009_21_5_a0,
     author = {I. E. Kvasov and I. B. Petrov and F. B. Chelnokov},
     title = {Computation of wave processes in nonuniform {3D} constructions},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--9},
     publisher = {mathdoc},
     volume = {21},
     number = {5},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2009_21_5_a0/}
}
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I. E. Kvasov; I. B. Petrov; F. B. Chelnokov. Computation of wave processes in nonuniform 3D constructions. Matematičeskoe modelirovanie, Tome 21 (2009) no. 5, pp. 3-9. http://geodesic.mathdoc.fr/item/MM_2009_21_5_a0/