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Matem. Mod., 2013, Volume 25, Number 2, Pages 42–52 (Mi mm3330)  

This article is cited in 23 scientific papers (total in 23 papers)

Grid-characteristic method using high-order interpolation on tetrahedral hierarchical meshes with a multiple time step

I. B. Petrov, A. V. Favorskaya, A. V. Sannikov, I. E. Kvasov

Moscow Institute of Physics and Technology (State University)

Abstract: The purpose of this article is to develop a grid-characteristic method for high-performance computing systems using unstructured tetrahedral hierarchical meshes, a multiple time step and the high-order interpolation for simulating complex spatial dynamic processes in heterogeneous environments. This method has the precise formulation of contact conditions and is suitable for the physically correct solution of the seismology and seismic prospecting problems in complex heterogeneous environments. The use of the hierarchical meshes allows to take into account a large number of non-homogeneous inclusions (cracks, cavities, etc.). The use of this grid-characteristic method makes it possible to use the multiple time step and thereby increase productivity and significantly reduce the computation time. The methods developed for high-order interpolation on unstructured tetrahedral meshes can solve the problems of seismology and seismic prospecting with the approximation in space to the fifth degree inclusive.

Keywords: grid-characteristic method, tetrahedral grids, high-order interpolation, prospecting seismology, seismology, parallel algorithms, hierarchical grids.

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English version:
Mathematical Models and Computer Simulations, 2013, 5:5, 409–415

UDC: 519.63
Received: 22.02.2012

Citation: I. B. Petrov, A. V. Favorskaya, A. V. Sannikov, I. E. Kvasov, “Grid-characteristic method using high-order interpolation on tetrahedral hierarchical meshes with a multiple time step”, Matem. Mod., 25:2 (2013), 42–52; Math. Models Comput. Simul., 5:5 (2013), 409–415

Citation in format AMSBIB
\Bibitem{PetFavSan13}
\by I.~B.~Petrov, A.~V.~Favorskaya, A.~V.~Sannikov, I.~E.~Kvasov
\paper Grid-characteristic method using high-order interpolation on tetrahedral hierarchical meshes with a multiple time step
\jour Matem. Mod.
\yr 2013
\vol 25
\issue 2
\pages 42--52
\mathnet{http://mi.mathnet.ru/mm3330}
\transl
\jour Math. Models Comput. Simul.
\yr 2013
\vol 5
\issue 5
\pages 409--415
\crossref{https://doi.org/10.1134/S2070048213050104}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84920861134}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. 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
    3. V. I. Golubev, I. B. Petrov, N. I. Khokhlov, “Simulation of seismic processes inside the planet using hybrid grid-characteristic method”, Math. Models Comput. Simul., 7:5 (2015), 439–445  mathnet  crossref  elib
    4. V. A. Miryaha, A. V. Sannikov, I. B. Petrov, “Discontinuous Galerkin method for numerical simulation of dynamic processes in solids”, Math. Models Comput. Simul., 7:5 (2015), 446–455  mathnet  crossref  elib
    5. 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
    6. A. I. Sukhinov, D. S. Khachunts, A. E. Chistyakov, “A mathematical model of pollutant propagation in near-ground atmospheric layer of a coastal region and its software implementation”, Comput. Math. Math. Phys., 55:7 (2015), 1216–1231  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. 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
    8. A. V. Favorskaya, I. B. Petrov, D. I. Petrov, N. I. Khokhlov, “Numerical modeling of wave processes in layered media in the Arctic”, Math. Models Comput. Simul., 8:4 (2016), 348–357  mathnet  crossref  elib
    9. A. V. Favorskaya, I. B. Petrov, V. I. Golubev, N. I. Khokhlov, “Chislennoe modelirovanie setochno-kharakteristicheskim metodom vozdeistviya zemletryasenii na sooruzheniya”, Matem. modelirovanie, 27:12 (2015), 109–120  mathnet  elib
    10. M. V. Muratov, I. B. Petrov, I. E. Kvasov, “Chislennoe reshenie zadach seismorazvedki v zonakh treschinovatykh rezervuarov”, Matem. modelirovanie, 28:7 (2016), 31–44  mathnet  elib
    11. A. I. Sukhinov, A. E. Chistyakov, A. A. Semenyakina, A. V. Nikitina, “Chislennoe modelirovanie ekologicheskogo sostoyaniya Azovskogo morya s primeneniem skhem povyshennogo poryadka tochnosti na mnogoprotsessornoi vychislitelnoi sisteme”, Kompyuternye issledovaniya i modelirovanie, 8:1 (2016), 151–168  mathnet  crossref
    12. P. V. Stognii, D. I. Petrov, N. I. Khokhlov, I. B. Petrov, “Simulation of seismic processes in geological exploration of arctic shelf”, Russ. J. Numer. Anal. Math. Model., 32:6 (2017), 381–392  crossref  mathscinet  zmath  isi  scopus
    13. A. Favorskaya, I. Petrov, V. Golubev, N. Khokhlov, “Numerical simulation of earthquakes impact on facilities by grid characteristic method”, Knowledge-Based and Intelligent Information & Engineering Systems, Procedia Computer Science, 112, ed. C. Zanni-Merk, C. Frydman, C. Toro, Y. Hicks, R. Howlett, L. Jain, Elsevier Science BV, 2017, 1206–1215  crossref  isi  scopus
    14. A. Favorskaya, I. Petrov, A. Grinevskiy, “Numerical simulation of fracturing in geological medium”, Knowledge-Based and Intelligent Information & Engineering Systems, Procedia Computer Science, 112, ed. C. Zanni-Merk, C. Frydman, C. Toro, Y. Hicks, R. Howlett, L. Jain, Elsevier Science BV, 2017, 1216–1224  crossref  isi  scopus
    15. P. Stognii, D. Petrov, N. Khokhlov, A. Favorskaya, “Numerical modeling of influence of ice formations under seismic impacts based on grid-characteristic method”, Knowledge-Based and Intelligent Information & Engineering Systems, Procedia Computer Science, 112, ed. C. Zanni-Merk, C. Frydman, C. Toro, Y. Hicks, R. Howlett, L. Jain, Elsevier Science BV, 2017, 1497–1505  crossref  isi  scopus
    16. A. V. Favorskaya, I. B. Petrov, “Numerical modeling of dynamic wave effects in rock masses”, Dokl. Math., 95:3 (2017), 287–290  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    17. I. B. Petrov, “Problemy modelirovaniya prirodnykh i antropogennykh protsessov v Arkticheskoi zone Rossiiskoi Federatsii”, Matem. modelirovanie, 30:7 (2018), 103–136  mathnet
    18. P. V. Stognii, D. I. Petrov, N. I. Khokhlov, I. B. Petrov, “Chislennoe modelirovanie setochno-kharakteristicheskim metodom vliyaniya ledovykh obrazovanii na seismicheskie otkliki”, Matem. modelirovanie, 30:8 (2018), 107–115  mathnet
    19. V A. Favorskaya, M. S. Zhdanov, N. I. Khokhlov, I. B. Petrov, “Modelling the wave phenomena in acoustic and elastic media with sharp variations of physical properties using the grid-characteristic method”, Geophys. Prospect., 66:8 (2018), 1485–1502  crossref  isi  scopus
    20. A. V. Favorskaya, I. B. Petrov, “Theory and practice of wave processes modelling”, Innovations in Wave Processes Modelling and Decision Making: Grid-Characteristic Method and Applications, Smart Innovation Systems and Technologies, 90, eds. A. Favorskaya, I. Petrov, Springer-Verlag, Berlin, 2018, 1–6  crossref  mathscinet  isi  scopus
    21. A. V. Favorskaya, I. B. Petrov, “Grid-characteristic method”, Innovations in Wave Processes Modelling and Decision Making: Grid-Characteristic Method and Applications, Smart Innovation Systems and Technologies, 90, eds. A. Favorskaya, I. Petrov, Springer-Verlag, Berlin, 2018, 117–160  crossref  mathscinet  isi  scopus
    22. V. A. Gushchin, A. V. Nikitina, A. A. Semenyakina, A. I. Sukhinov, A. E. Chistyakov, “A model of transport and transformation of biogenic elements in the coastal system and its numerical implementation”, Comput. Math. Math. Phys., 58:8 (2018), 1316–1333  mathnet  crossref  crossref  isi  elib
    23. Petrov I.B. Muratov V M., “Mathematical Modeling of Spatial Wave Responses By Grid-Characteristic Method on Irregular Computational Meshes”, Lobachevskii J. Math., 40:4, SI (2019), 499–506  crossref  isi
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