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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, Number 9, Pages 81–96 (Mi ivm9399)  
This article is cited in 3 scientific papers (total in 3 papers)

Topological methods in one numerical scheme of solving three-dimensional continuum mechanics problems

E. I. Yakovleva, D. T. Chekmarevb

a National Research University Higher School of Economics, 25/12 Bol'shaya Pecherskaya str., Nizhny Novgorod, 603155 Russia
b Nizhny Novgorod State University, 23 Gagarin Ave., Nizhny Novgorod, 603950 Russia
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Abstract: We discuss finite element numerical schemes for solving the continuum mechanics problems. Previously a method of acceleration of calculations was developed which uses the simplicial mesh inscribed in the original cubic cell partition of a three-dimensional body. In this work we show that the obstacle to the construction of this design may be described in terms of homology groups modulo 2. The main goal of the work is to develop a method of removing this obstacle. The achievement of the goal is based on efficient algorithms for computing bases of the homology groups which are dual with respect to the intersection form.
Keywords: computational topology, polyhedron, cell complex, homology group, manifold, intersection form, continuum mechanics, finite element method.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00312_а
HSE Basic Research Program
Received: 14.07.2017
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, Volume 62, Issue 9, Pages 72–85
DOI: https://doi.org/10.3103/S1066369X18090086
Bibliographic databases:
Document Type: Article
UDC: 514.86:515.146:519.63
Language: Russian
Citation: E. I. Yakovlev, D. T. Chekmarev, “Topological methods in one numerical scheme of solving three-dimensional continuum mechanics problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 9, 81–96; Russian Math. (Iz. VUZ), 62:9 (2018), 72–85
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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