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Sib. Zh. Vychisl. Mat., 2016, Volume 19, Number 2, Pages 223–233 (Mi sjvm614)  

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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.575.21.0084


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

Full text: PDF file (396 kB)
References: PDF file   HTML file

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

Citation in format AMSBIB
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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. 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  crossref  isi  scopus
    2. 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  crossref  isi  scopus
    3. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus
    4. 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
    5. 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  crossref  mathscinet  isi  scopus
    6. 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
    7. 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  crossref  mathscinet  isi  scopus
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