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This article is cited in 7 scientific papers (total in 7 papers)
The study of increased order grid-characteristic methods on unstructured grids
A. V. Favorskaya, I. B. Petrov
Moscow Institute of Physics and Technology (State University), 9 Inststitutskii per., Dolgoprudny, Moscow region, 141700, Russia
Abstract:
We study the grid-characteristic methods for solving hyperbolic systems using a high order interpolation on unstructured tetrahedral and triangular grids for approximation. We consider the interpolation with orders from the first to the fifth included. Also, one-dimensional finite difference schemes appropriate for the considered methods are given. We study these schemes in terms of stability. The grid-characteristic method on unstructured triangular and tetrahedral grids are successfully used for solving the seismic prospecting problems, including, seismic prospecting in the conditions of the Arctic shelf and permafrost, as well as for solving seismic problems, problems of dynamic deformation and destruction, studying anisotropic composite materials.
Key words:
grid-characteristic method, numerical simulation, unstructured grids, high order interpolation.
DOI:
https://doi.org/10.15372/SJNM20160208
 Full text:
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English version:
Numerical Analysis and Applications, 2016, 9:2, 171–178
Bibliographic databases:
   
UDC:
517.9
Received: 06.02.2015
Revised: 13.05.2015
Citation:
A. V. Favorskaya, I. B. Petrov, “The study of increased order grid-characteristic methods on unstructured grids”, Sib. Zh. Vychisl. Mat., 19:2 (2016), 223–233; Num. Anal. Appl., 9:2 (2016), 171–178
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http://mi.mathnet.ru/eng/sjvm614 http://mi.mathnet.ru/eng/sjvm/v19/i2/p223
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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A. Favorskaya, I. Petrov, A. Grinevskiy, “Numerical simulation of fracturing in geological medium”, Knowledge-Based and Intelligent Information & Engineering Systems, Procedia Computer Science, 112, eds. C. ZanniMerk, C. Frydman, C. Toro, Y. Hicks, R. Howlett, L. Jain, Elsevier Science BV, 2017, 1216–1224
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V A. Favorskaya, M. S. Zhdanov, I N. 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
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A. V. Favorskaya, S. V. Kabisov, I. B. Petrov, “Modeling of ultrasonic waves in fractured rails with an explicit approach”, Dokl. Math., 98:1 (2018), 401–404
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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
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A. V. Favorskaya, “Interpolation on unstructured tetrahedral grids”, 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, 45–73
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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
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A. V. Favorskaya, M. S. Zhdanov, “Migration of elastic fields based on Kirchhoff and Rayleigh integrals”, 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, 241–265
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