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Matem. Mod., 2015, Volume 27, Number 3, Pages 96–108 (Mi mm3584)  

This article is cited in 8 scientific papers (total in 8 papers)

Discontinuous Galerkin method for numerical simulation of dynamic processes in solids

V. A. Miryaha, A. V. Sannikov, I. B. Petrov

Moscow Institute of Physics and Technology

Abstract: The aim of this paper is applying of Discontinuous Galerkin Method to deformation and destruction problems of elastoplastic bodies as well as to hydroelastic problems. Two-sided crack model for destruction, Prandtl–Reuss elastoplastic model, dynamic contact of bodies, wave propagation through coupled elastic-acoustic media for marine seismology, comparison of reflected waves in fluid-filled and infinite thin crack models and underwater objects detection are described. Method was implemented for HPC infrastructure.

Keywords: Discontinuous Galerkin Method, mechanics of deformable solids, HPC, wave problems in coupled elastic-acoustic media, marine seismology, fluid-filled crack, dynamic contact of bodies, destruction.

Funding Agency Grant Number
Russian Science Foundation 14-11-00434


Full text: PDF file (845 kB)
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English version:
Mathematical Models and Computer Simulations, 2015, 7:5, 446–455

Document Type: Article
UDC: 519.63
Received: 01.09.2014

Citation: V. A. Miryaha, A. V. Sannikov, I. B. Petrov, “Discontinuous Galerkin method for numerical simulation of dynamic processes in solids”, Matem. Mod., 27:3 (2015), 96–108; Math. Models Comput. Simul., 7:5 (2015), 446–455

Citation in format AMSBIB
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\by V.~A.~Miryaha, A.~V.~Sannikov, I.~B.~Petrov
\paper Discontinuous Galerkin method for numerical simulation of dynamic processes in solids
\jour Matem. Mod.
\yr 2015
\vol 27
\issue 3
\pages 96--108
\mathnet{http://mi.mathnet.ru/mm3584}
\elib{http://elibrary.ru/item.asp?id=23421485}
\transl
\jour Math. Models Comput. Simul.
\yr 2015
\vol 7
\issue 5
\pages 446--455
\crossref{https://doi.org/10.1134/S2070048215050087}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84941913022}


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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. 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
    2. V. A. Biryukov, V. A. Miryaha, I. B. Petrov, N. I. Khokhlov, “Simulation of elastic wave propagation in geological media: Intercomparison of three numerical methods”, Comput. Math. Math. Phys., 56:6 (2016), 1086–1095  mathnet  crossref  crossref  isi  elib
    3. M. A. Zaitsev, S. A. Karabasov, “Skhema Kabare dlya chislennogo resheniya zadach deformirovaniya uprugoplasticheskikh tel”, Matem. modelirovanie, 29:11 (2017), 53–70  mathnet  elib
    4. O. O'Reilly, E. M. Dunham, J. Nordstrom, “Simulation of wave propagation along fluid-filled cracks using high-order summation-by-parts operators and implicit-explicit time stepping”, SIAM J. Sci. Comput., 39:4 (2017), B675–B702  crossref  mathscinet  zmath  isi  scopus
    5. V. A. Biryukov, V. A. Miryakha, I. B. Petrov, “Analysis of the dependence of the global load on the mechanical parameters of ice under interaction between an ice field and construction”, Dokl. Phys., 62:6 (2017), 328–331  crossref  isi  scopus
    6. V. A. Miryakha, A. V. Sannikov, V. A. Biryukov, I. B. Petrov, “Modelirovanie eksperimentov po issledovaniyu prochnostnykh kharakteristik lda razryvnym metodom Galerkina”, Matem. modelirovanie, 30:2 (2018), 110–118  mathnet  elib
    7. I. B. Petrov, “Problemy modelirovaniya prirodnykh i antropogennykh protsessov v Arkticheskoi zone Rossiiskoi Federatsii”, Matem. modelirovanie, 30:7 (2018), 103–136  mathnet
    8. V. A. Miryakha, I. B. Petrov, “Modelirovanie razryvnym metodom Galerkina vozdeistviya ledyanogo polya na vertikalnuyu tsilindricheskuyu oporu”, Matem. modelirovanie, 30:9 (2018), 111–134  mathnet
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