Geodesic
Grid-characteristic method on unstructured tetrahedral meshes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 5, pp. 821-832 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] Kondaurov V. I., Fortov V. E., Osnovy termomekhaniki kondensirovannoi sredy, MFTI, M., 2002

[2] Magomedov K. M., Kholodov A. S., Setochno-kharakteristicheskie chislennye metody, Nauka, M., 1988 | MR

[3] Petrov I. B., Lobanov A. I., Lektsii po vychislitelnoi matematike, Internet-un-t informats. tekh., M., 2006

[4] Petrov I. B., Favorskaya A. V., “Biblioteka po interpolyatsii vysokikh poryadkov na nestrukturirovannykh treugolnykh i tetraedralnykh setkakh”, Informats. tekhnologii, 2011, no. 9, 30–32

[5] Petrov I. B., Kholodov A. S., “Chislennoe issledovanie nekotorykh dinamicheskikh zadach mekhaniki deformiruemogo tverdogo tela setochno-kharakteristicheskim metodom”, Zh. vychisl. matem. i matem. fiz., 24:5 (1984), 722–739 | MR

[6] Petrov I. B., Kholodov A. S., “O regulyarizatsii razryvnykh chislennykh reshenii uravnenii giperbolicheskogo tipa”, Zh. vychisl. matem. i matem. fiz., 24:8 (1984), 1172–1188 | MR

[7] Petrov I. B., Tormasov A. G., Kholodov A. S., “Ob ispolzovanii gibridizirovannykh setochno-kharakteristicheskikh skhem dlya chislennogo resheniya trekhmernykh zadach dinamiki deformiruemogo tverdogo tela”, Zh. vychisl. matem. i matem. fiz., 30:8 (1990), 1237–1244 | MR

[8] Petrov I. B., Chelnokov F. B., “Chislennoe issledovanie volnovykh protsessov i protsessov razrusheniya v mnogosloinykh pregradakh”, Zh. vychisl. matem. i matem. fiz., 43:10 (2003), 1562–1579 | MR

[9] Agapov P. I., Belotserkovskii O. M., Petrov I. B., “Chislennoe modelirovanie posledstvii mekhanicheskogo vozdeistviya na mozg cheloveka pri cherepno-mozgovoi travme”, Zh. vychisl. matem. i matem. fiz., 46:9 (2006), 1711–1720 | MR

[10] Matyushev N. G., Petrov I. B., “Matematicheskoe modelirovanie deformatsionnykh i volnovykh protsessov v mnogosloinykh konstruktsiyakh”, Zh. vychisl. matem. i matem. fiz., 49:9 (2009), 1–7 | MR

[11] Kvasov I. E., Petrov I. B., “Chislennoe modelirovanie volnovykh protsessov v geologicheskikh sredakh v zadachakh seismorazvedki vysokoproizvoditelnykh EVM”, Zh. vychisl. matem. i matem. fiz., 52:2 (2012), 330–341 | MR

[12] Kvasov I. E., Petrov I. B., Sannikov A. V., Favorskaya A. V., “Kompyuternoe modelirovanie prostranstvennykh dinamicheskikh protsessov setochno-kharakteristicheskim metodom na nestrukturirovannykh tetraedralnykh setkakh”, Informats. tekhnologii, 2011, no. 9, 28–30

[13] Kvasov I. E., Petrov I. B., Sannikov A. V., Favorskaya A. V., “Setochno-kharakteristicheskii metod vysokoi tochnosti na tetraedralnykh ierarkhicheskikh setkakh s kratnym shagom po vremeni”, Kompyuternye issledovaniya i modelirovanie, 3:1 (2012), 161–171

[14] Favorskaya A. V., Petrov I. B., Kvasov I. E., Sannikov A. V., “Setochno-kharakteristicheskii metod s interpolyatsiei vysokikh poryadkov na tetraedralnykh ierarkhicheskikh setkakh s kratnym shagom po vremeni”, Matem. modelirovanie, 25:2 (2013), 42–52

[15] Levyant V. B., Petrov I. B., Kvasov I. E., “Chislennoe modelirovanie volnovogo otklika ot subvertikalnykh makrotreschin, veroyatnykh flyuidoprovodyaschikh kanalov”, Tekhnologii seismorazvedki, 2011, no. 4, 4–29

[16] Levyant V. B., Petrov I. B., Muratov M. V., “Chislennoe modelirovanie volnovykh otklikov ot sistemy (klastera) subvertikalnykh makrotreschin”, Tekhnologii seismorazvedki, 2012, no. 1, 5–21