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Title Numerical analysis of multi-crack large-scale plane problems with adaptive cross approximation and hierarchical matrices
Authors Yeremenko, H.A.
Keywords numerical analysis
чисельний аналіз
численный анализ
hierarchical matrices
ієрархічні матриці
иерархические матрицы
cracks
тріщини
трещины
Type Conference Papers
Date of Issue 2015
URI http://essuir.sumdu.edu.ua/handle/123456789/40678
Publisher Sumy State University
License
Citation Yeremenko, H.A. Numerical analysis of multi-crack large-scale plane problems with adaptive cross approximation and hierarchical matrices [Текст] / H.A. Yeremenko; EL adviser A.M.Diadechko // Соціально-гуманітарні аспекти розвитку сучасного суспільства : матеріали Всеукраїнської наукової конференції викладачів, аспірантів, співробітників та студентів, м. Суми, 23-24 квітня 2015 року. - Суми : СумДУ, 2015. - С. 304-305.
Abstract The problem of interaction of large number of cracks in a plate is considered by the method of singular integral equations (SIE). The corresponding system of SIE is solved by using Gauss–Chebyshev quadratures, which results in a large system of linear algebraic equations. The solution of the latter employs the adaptive cross approximation (ACA) technique that has not previously been applied for studying multi-crack large-scale plane problems. Therefore, several benchmarks problems with large number of cracks modelling periodical arrangements have been tested to investigate performance of the method; these include arrays of collinear cracks, parallel cracks, and double network of parallel cracks. Comparisons with analytical and numerical periodical solutions available for the mentioned cases reveal high accuracy and fast performance of the method. It is also applied for studying effective characteristics of bodies with up to 20,000 cracks and for accurate modelling of interaction of a macrocrack with thousands of microcracks.
Appears in Collections: Наукові видання (ІФСК)

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