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

Sibirskii Zhurnal Vychislitel'noi Matematiki

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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2016, Volume 19, Number 2, Pages 223–233
DOI: https://doi.org/10.15372/SJNM20160208 (Mi sjvm614)

This article is cited in 16 scientific papers (total in 16 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

Full-text PDF (396 kB) Citations (16)

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DOI: https://doi.org/10.15372/SJNM20160208

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.

Funding agency	Grant number
Ministry of Education and Science of the Russian Federation	14.575.21.0084

Received: 06.02.2015
Revised: 13.05.2015

English version:
Numerical Analysis and Applications, 2016, Volume 9, Issue 2, Pages 171–178
DOI: https://doi.org/10.1134/S1995423916020087

Bibliographic databases:

Document Type: Article

UDC: 517.9

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/sjvm614

https://www.mathnet.ru/eng/sjvm/v19/i2/p223

This publication is cited in the following 16 articles:

I. V. Popov, “Modeling wave processes in elastic media based on conservative difference schemes”, Math. Models Comput. Simul., 13:6 (2021), 1160–1171
I. B. Petrov, A. V. Favorskaya, “Computation of seismic resistance of an ice island by the grid-characteristic method on combined grids”, Comput. Math. Math. Phys., 61:8 (2021), 1339–1352
A. V. Favorskaya, N. I. Khokhlov, I. B. Petrov, “Grid-characteristic method on joint structured regular and curved grids for modeling coupled elastic and acoustic wave phenomena in objects of complex shape”, Lobachevskii J. Math., 41:4, SI (2020), 512–525
Alena V. Favorskaya, Vasily I. Golubev, “Elastic and acoustic approximations for solving direct problems of human head ultrasonic study”, Procedia Computer Science, 176 (2020), 2566
Katerina Beklemysheva, Alexey Ermakov, Alena Favorskaya, “Numerical simulation of cone object destruction under a short high-energy pulse”, Procedia Computer Science, 159 (2019), 1095
A. V. Favorskaya, “Investigation the material properties of a plate by laser ultrasound using the analysis of multiple waves”, Computer Research and Modeling, 11:4 (2019), 653–673
Polina V. Stognii, Nikolay I. Khokhlov, Smart Innovation, Systems and Technologies, 133, Smart Modeling for Engineering Systems, 2019, 156
A. V. 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
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
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
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
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
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
Alena Favorskaya, “The use of multiple waves to obtain information on an underlying geological structure”, Procedia Computer Science, 126 (2018), 1110
A. V. Favorskaya, I. B. Petrov, “The use of full-wave numerical simulation for the investigation of fractured zones”, Math. Models Comput. Simul., 11:4 (2019), 518–530
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

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

Sibirskii Zhurnal Vychislitel'noi Matematiki

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