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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

COMPUTATION OF CONVOLUTION OF FUNCTIONS WITHIN THE HAAR BASIS

Vestnik MGSU 8/2012
  • Mozgaleva Marina Leonidovna - Moscow State University of Civil Engineering (MSUCE) Candidate of Technical Sciences, Associated Professor, Department of Computer Science and Applied Mathematics +7 (499) 183-59-94, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Akimov Pavel Alekseevich - Moscow State University of Civil Engineering (MSUCE) Doctor of Technical Sciences, Corresponding Member of the Russian Academy of Architecture and Construction Science, Professor, Department of Computer Science and Applied Mathematics +7 (499) 183-59-94, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 98 - 103

The Wavelet analysis, that replaces the conventional Fourier analysis, is an exciting new
problem-solving tool employed by mathematicians, scientists and engineers. Recent decades have
witnessed intensive research in the theory of wavelets and their applications. Wavelets are mathematical
functions that divide the data into different frequency components, and examine each
component with a resolution adjusted to its scale. Therefore, the solution to the boundary problem
of structural mechanics within multilevel wavelet-based methods has local and global components.
The researcher may assess the infl uence of various factors. High-quality design models and reasonable
design changes can be made.
The Haar wavelet, known since 1910, is the simplest possible wavelet. Corresponding
computational algorithms are quite fast and effective. The problem of computing the convolution
of functions in the Haar basis, considered in this paper, arises, in particular, within the waveletbased
discrete-continual boundary element method of structural analysis. The authors present
their concept of convolution of functions within the Haar basis (one-dimensional case), share
their useful ideas concerning Haar functions, and derive a relevant convolution formula of Haar
functions.

DOI: 10.22227/1997-0935.2012.8.98 - 103

References
  1. Zolotov A.B., Akimov P.A., Sidorov V.N., Mozgaleva M.L. Diskretnye i diskretno-kontinual’nye realizatsii metoda granichnykh integral’nykh uravneniy [Discrete and Discrete-continual Versions of the Boundary Integral Equation Method]. Moscow, MSUCE, 2011, 368 p.
  2. Zolotov A.B., Akimov P.A., Sidorov V.N., Mozgaleva M.L. Diskretno-kontinual’nye metody rascheta sooruzheniy [Discrete-continual Methods of Structural Analysis]. Moscow, Arhitektura-S Publ., 2010, 336 p.
  3. Zolotov A.B., Akimov P.A., Sidorov V.N., Mozgaleva M.L. Chislennye i analiticheskie metody rascheta stroitel’nykh konstruktsiy [Numerical and Analytical Methods of Structural Analysis]. Moscow, ASV Publ., 2009, 336 p.
  4. Zakharova T.V., Shestakov O.V. Veyvlet-analiz i ego prilozheniya [Wavelet-analysis and Its Applications]. Moscow, Infra-M Publ., 2012, 158 p.
  5. Kech V., Teodoresku P. Vvedenie v teoriyu obobshchennykh funktsiy s prilozheniyami v tekhnike [Introduction into the Theory of Generalized Functions and Their Engineering Applications]. Moscow, Mir Publ., 1978, 518 p.

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