Geodesic
Grid-characteristic method on unstructured tetrahedral meshes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 5, pp. 821-832

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The goal of this paper is to develop a grid-characteristic method intended for high-performance computer systems and implemented on unstructured tetrahedral hierarchical meshes with the use of a multiple time step and high-order interpolation, including interpolation with a limiter, piecewise parabolic interpolation, and monotone interpolation. The method is designed for simulating complex three-dimensional dynamical processes in heterogeneous media. It involves accurately stated contact conditions and produces physically correct solutions of problems in seismology and seismic exploration. Hierarchical meshes make it possible to take into account numerous inhomogeneous inclusions (cracks, cavities, etc.) and to solve problems in a real-life formulation. The grid-characteristic method enables the use of a multiple time step. As a result, the computation time is considerably reduced and the efficiency of the method is raised. The method is parallelized on a computer cluster with an optimal use of system resources. 
@article{ZVMMF_2014_54_5_a9,
     author = {M. V. Muratov and I. B. Petrov and A. V. Sannikov and A. V. Favorskaya},
     title = {Grid-characteristic method on unstructured tetrahedral meshes},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {821--832},
     publisher = {mathdoc},
     volume = {54},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_5_a9/}
}
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M. V. Muratov; I. B. Petrov; A. V. Sannikov; A. V. Favorskaya. Grid-characteristic method on unstructured tetrahedral meshes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 5, pp. 821-832. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_5_a9/