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Zh. Vychisl. Mat. Mat. Fiz., 1984, Volume 24, Number 5, Pages 722–739 (Mi zvmmf4392)  

This article is cited in 48 scientific papers (total in 49 papers)

Numerical investigation of certain dynamical problems of the mechanics of a deformable solid body by the grid-characteristic method

I. B. Petrov, A. S. Kholodov


Full text: PDF file (2100 kB)

English version:
USSR Computational Mathematics and Mathematical Physics, 1984, 24:3, 61–73

Bibliographic databases:

UDC: 519.6:539.3
MSC: Primary 74S30; Secondary 65M25, 74S99
Received: 17.06.1982
Revised: 04.03.1983

Citation: I. B. Petrov, A. S. Kholodov, “Numerical investigation of certain dynamical problems of the mechanics of a deformable solid body by the grid-characteristic method”, Zh. Vychisl. Mat. Mat. Fiz., 24:5 (1984), 722–739; U.S.S.R. Comput. Math. Math. Phys., 24:3 (1984), 61–73

Citation in format AMSBIB
\Bibitem{PetKho84}
\by I.~B.~Petrov, A.~S.~Kholodov
\paper Numerical investigation of certain dynamical problems of the mechanics of a~deformable solid body by the grid-characteristic method
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1984
\vol 24
\issue 5
\pages 722--739
\mathnet{http://mi.mathnet.ru/zvmmf4392}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=747124}
\zmath{https://zbmath.org/?q=an:0551.73080}
\transl
\jour U.S.S.R. Comput. Math. Math. Phys.
\yr 1984
\vol 24
\issue 3
\pages 61--73
\crossref{https://doi.org/10.1016/0041-5553(84)90044-2}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. B. Petrov, I. G. Tormasov, A. S. Kholodov, “On the use of hybrid grid-characteristic schemes for the numerical solution of three-dimensional problems in the dynamics of a deformable solid”, U.S.S.R. Comput. Math. Math. Phys., 30:4 (1990), 191–196  mathnet  crossref  mathscinet  zmath
    2. N. N. Balanovskii, A. V. Bubnov, A. S. Obukhov, I. B. Petrov, “Raschet dinamicheskikh protsessov v glazu pri lazernoi ekstraktsii katarakty”, Matem. modelirovanie, 15:11 (2003), 37–44  mathnet  zmath
    3. I. B. Petrov, F. B. Chelnokov, V. V. Chibrikov, “Chislennoe issledovanie volnovykh protsessov v perforirovannykh deformiruemykh sredakh”, Matem. modelirovanie, 15:10 (2003), 89–94  mathnet  zmath
    4. I. B. Petrov, F. B. Chelnokov, “Numerical analysis of wave processes and fracture in layered targets”, Comput. Math. Math. Phys., 43:10 (2003), 1503–1519  mathnet  mathscinet  zmath
    5. F. B. Chelnokov, “Yavnoe predstavlenie setochno-kharakteristicheskikh skhem dlya uravnenii uprugosti v dvumernom i trekhmernom prostranstvakh”, Matem. modelirovanie, 18:6 (2006), 96–108  mathnet  mathscinet  zmath
    6. I. B. Petrov, “Modelirovanie deformatsionnykh protsessov v slozhnykh konstruktsiyakh pri ikh intensivnom dinamicheskom nagruzhenii”, Matem. modelirovanie, 18:5 (2006), 91–110  mathnet  zmath
    7. N. S. Matsievskii, I. B. Petrov, F. B. Chelnokov, “Chislennoe issledovanie dinamicheskogo povedeniya slozhnykh konstruktsii pri ikh soudarenii na pryamougolnykh i treugolnykh setkakh”, Matem. modelirovanie, 19:9 (2007), 105–113  mathnet  mathscinet  zmath
    8. Elena V. Kuchunova, Vladimir M. Sadovskii, “Vychislitelnyi algoritm dlya rascheta volnovykh polei v blochnykh sredakh na mnogoprotsessornykh vychislitelnykh sistemakh”, Zhurn. SFU. Ser. Matem. i fiz., 1:2 (2008), 210–220  mathnet
    9. I. E. Kvasov, I. B. Petrov, F. B. Chelnokov, “Raschet volnovykh protsessov v neodnorodnykh prostranstvennykh konstruktsiyakh”, Matem. modelirovanie, 21:5 (2009), 3–9  mathnet  zmath
    10. N. G. Matyushev, I. B. Petrov, “Mathematical simulation of deformation and wave processes in multilayered structures”, Comput. Math. Math. Phys., 49:9 (2009), 1615–1621  mathnet  crossref  zmath  isi
    11. I. E. Kvasov, S. A. Pankratov, I. B. Petrov, “Computational modeling of seysmoresponse in multilayered geologic medium by grid-characteristic method”, Math. Models Comput. Simul., 3:2 (2011), 196–204  mathnet  crossref
    12. I. E. Kvasov, S. A. Pankratov, I. B. Petrov, “Computation of dynamic processes in continuous media with a crack initiated by the near-surface disturbance using grid-characteristic method”, Math. Models Comput. Simul., 3:3 (2011), 399–409  mathnet  crossref
    13. V. I. Golubev, I. E. Kvasov, I. B. Petrov, “Influence of natural disasters on ground facilities”, Math. Models Comput. Simul., 4:2 (2012), 129–134  mathnet  crossref
    14. I. E. Kvasov, I. B. Petrov, “Numerical study of anisotropy of wave responses from fractured reservoir by grid-characteristic method”, Math. Models Comput. Simul., 4:3 (2012), 336–343  mathnet  crossref
    15. Golubev V.I., Kvasov I.E., Khokhlov N.I., Petrov I.B., “Chislennoe modelirovanie seismostoikosti zhilykh i promyshlennykh nazemnykh sooruzhenii”, 2011, 215–218  elib
    16. Khokhlov N.I., Golubev V.I., Kvasov I.E., Petrov I.B., “Chislennoe modelirovanie voln releya i lyava setochno-kharakteristicheskim metodom”, 2011, 219–223  elib
    17. Khokhlov N.I., Petrov I.B., “Modelirovanie seismicheskikh yavlenii setochno-kharakteristicheskim metodom”, Trudy Moskovskogo fiziko-tekhnicheskogo instituta, 3:3 (2011), 159–167  elib
    18. I. E. Kvasov, I. B. Petrov, “High-performance computer simulation of wave processes in geological media in seismic exploration”, Comput. Math. Math. Phys., 52:2 (2012), 302–313  mathnet  crossref  zmath  adsnasa  isi  elib  elib
    19. M. V. Muratov, I. B. Petrov, “Simulation of wave responses from subvertical macrofracture systems using grid-characteristic method”, Math. Models Comput. Simul., 5:5 (2013), 479–491  mathnet  crossref  mathscinet
    20. Igor Menshov, Alexander Mischenko, Alexey Serejkin, “Numerical modeling elasto-plastic flows by using a Godunov method with moving Eulerian grids”, Math. Models Comput. Simul., 6:2 (2014), 127–141  mathnet  crossref  mathscinet
    21. V. I. Golubev, I. B. Petrov, N. I. Khokhlov, “Numerical simulation of seismic activity by the grid-characteristic method”, Comput. Math. Math. Phys., 53:10 (2013), 1523–1533  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    22. K. A. Beklemysheva, I. B. Petrov, A. V. Favorskaya, “Numerical simulation of processes in rigid deformable media in the presence of dynamic contacts using grid-characteristic method”, Math. Models Comput. Simul., 6:3 (2014), 294–304  mathnet  crossref
    23. I. B. Petrov, N. I. Khokhlov, “Modeling of 3D seismic problems using high-performance computing”, Math. Models Comput. Simul., 6:4 (2014), 342–350  mathnet  crossref
    24. M. V. Muratov, I. B. Petrov, A. V. Sannikov, A. V. Favorskaya, “Grid-characteristic method on unstructured tetrahedral meshes”, Comput. Math. Math. Phys., 54:5 (2014), 837–847  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    25. I. B. Petrov, A. V. Favorskaya, N. I. Khokhlov, V. A. Miryaha, A. V. Sannikov, V. I. Golubev, “The monitoring state of a moving train using high performance systems and modern computational methods”, Math. Models Comput. Simul., 7:1 (2015), 51–61  mathnet  crossref
    26. I. B. Petrov, A. V. Vasyukov, K. A. Beklemysheva, A. S. Ermakov, A. S. Dzyuba, V. I. Golovan, “Chislennoe modelirovanie dinamicheskikh protsessov pri nizkoskorostnom udare po kompozitnoi stringernoi paneli”, Matem. modelirovanie, 26:9 (2014), 96–110  mathnet
    27. A. V. Vasyukov, A. S. Ermakov, I. B. Petrov, A. P. Potapov, A. V. Favorskaya, A. V. Shevtsov, “Combined grid-characteristic method for the numerical solution of three-dimensional dynamical elastoplastic problems”, Comput. Math. Math. Phys., 54:7 (2014), 1176–1189  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    28. Kvasov D.E. Sergeyev Ya.D., “Deterministic Approaches For Solving Practical Black-Box Global Optimization Problems”, Adv. Eng. Softw., 80:SI (2015), 58–66  crossref  isi  elib
    29. V. I. Golubev, I. B. Petrov, N. I. Khokhlov, K. I. Shul'ts, “Numerical computation of wave propagation in fractured media by applying the grid-characteristic method on hexahedral meshes”, Comput. Math. Math. Phys., 55:3 (2015), 509–518  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    30. K. A. Beklemysheva, A. V. Vasyukov, I. B. Petrov, “Numerical simulation of dynamic processes in biomechanics using the grid-characteristic method”, Comput. Math. Math. Phys., 55:8 (2015), 1346–1355  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    31. V. A. Biryukov, M. V. Muratov, I. B. Petrov, A. V. Sannikov, A. V. Favorskaya, “Application of the grid-characteristic method on unstructured tetrahedral meshes to the solution of direct problems in seismic exploration of fractured layers”, Comput. Math. Math. Phys., 55:10 (2015), 1733–1742  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    32. Khokhlov N., Yavich N., Malovichko M., Petrov I., “Solution of Large-Scale Seismic Modeling Problems”, 4Th International Young Scientist Conference on Computational Science, Procedia Computer Science, 66, eds. Sloot P., Boukhanovsky A., Athanassoulis G., Klimentov A., Elsevier Science BV, 2015, 191–199  crossref  isi
    33. Petrov I.B., Favorskaya A.V., Shevtsov A.V., Vasyukov A.V., Potapov A.P., Ermakov A.S., “Combined Method For the Numerical Solution of Dynamic Three-Dimensional Elastoplastic Problems”, Dokl. Math., 91:1 (2015), 111–113  crossref  mathscinet  zmath  isi  elib
    34. D. I. Petrov, I. B. Petrov, A. V. Favorskaya, N. I. Khokhlov, “Numerical solution of seismic exploration problems in the Arctic region by applying the grid-characteristic method”, Comput. Math. Math. Phys., 56:6 (2016), 1128–1141  mathnet  crossref  crossref  isi  elib
    35. I. E. Kvasov, V. B. Leviant, I. B. Petrov, “Numerical study of wave propagation in porous media with the use of the grid-characteristic method”, Comput. Math. Math. Phys., 56:9 (2016), 1620–1630  mathnet  crossref  crossref  isi  elib
    36. D. P. Grigorevykh, N. I. Khokhlov, I. B. Petrov, “Raschet dinamicheskogo razrusheniya v tverdykh deformiruemykh telakh”, Matem. modelirovanie, 29:4 (2017), 45–58  mathnet  elib
    37. M. A. Zaitsev, S. A. Karabasov, “Skhema Kabare dlya chislennogo resheniya zadach deformirovaniya uprugoplasticheskikh tel”, Matem. modelirovanie, 29:11 (2017), 53–70  mathnet  elib
    38. Golubev V.I. Gilyazutdinov R.I. Petrov I.B. Khokhlov N.I. Vasyukov A.V., “Simulation of Dynamic Processes in Three-Dimensional Layered Fractured Media With the Use of the Grid-Characteristic Numerical Method”, J. Appl. Mech. Tech. Phys., 58:3 (2017), 539–545  crossref  isi
    39. I. B. Petrov, “Vychislitelnye problemy modelirovaniya prirodnykh i industrialnykh protsessov v Arkticheskoi zone Rossiiskoi Federatsii”, Chebyshevskii sb., 18:3 (2017), 428–443  mathnet  crossref
    40. V. I. Golubev, N. I. Khokhlov, “Otsenka anizotropii seismicheskogo otklika ot treschinovatykh geologicheskikh ob'ektov”, Kompyuternye issledovaniya i modelirovanie, 10:2 (2018), 231–240  mathnet  crossref
    41. V. A. Gasilov, A. S. Grushin, A. S. Ermakov, O. G. Olkhovskaya, I. B. Petrov, “Modelirovanie razrusheniya polimernykh materialov pod deistviem intensivnykh potokov energii”, Matem. modelirovanie, 30:7 (2018), 61–78  mathnet
    42. I. B. Petrov, “Problemy modelirovaniya prirodnykh i antropogennykh protsessov v Arkticheskoi zone Rossiiskoi Federatsii”, Matem. modelirovanie, 30:7 (2018), 103–136  mathnet
    43. A. O. Kazakov, “On the calculation of border and contact nodes by grid-characteristic method on non-periodic tetrahedral grids”, Num. Anal. Appl., 11:4 (2018), 298–310  mathnet  crossref  crossref  isi  elib
    44. A. I. Lobanov, “Nauchnye i pedagogicheskie shkoly Aleksandra Sergeevicha Kholodova”, Kompyuternye issledovaniya i modelirovanie, 10:5 (2018), 561–579  mathnet  crossref
    45. D. S. Moiseeva, A. A. Motorin, E. L. Stupitskii, “Chislennye issledovaniya parametrov vozmuschennoi oblasti, obrazuyuscheisya v nizhnei ionosfere pod deistviem napravlennogo potoka radioizlucheniya ot nazemnogo istochnika”, Kompyuternye issledovaniya i modelirovanie, 10:5 (2018), 679–708  mathnet  crossref
    46. A. V. Vasyukov, I. B. Petrov, “Grid-characteristic method on tetrahedral unstructured meshes with large topological inhomogeneities”, Comput. Math. Math. Phys., 58:8 (2018), 1259–1269  mathnet  crossref  crossref  isi  elib
    47. V. I. Golubev, O. Ya. Voinov, I. B. Petrov, “Seismic imaging of fractured elastic media on the basis of the grid-characteristic method”, Comput. Math. Math. Phys., 58:8 (2018), 1309–1315  mathnet  crossref  crossref  isi  elib
    48. I. B. Petrov, M. V. Muratov, “Primenenie setochno-kharakteristicheskogo metoda v reshenii pryamykh zadach seismorazvedki treschinovatykh plastov (obzornaya statya)”, Matem. modelirovanie, 31:4 (2019), 33–56  mathnet  crossref  elib
    49. M. V. Muratov, I. B. Petrov, “Application of mathematical fracture models to simulation of exploration seismology problems by the grid-characteristic method”, Kompyuternye issledovaniya i modelirovanie, 11:6 (2019), 1077–1082  mathnet  crossref
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