Wavelet-based two-grid numerical method of structural analysis with the use of discrete Haar basis

7th International Symposium Actual Problems of Computational Simulation in Civil Engineering

土木建筑工程;计算机科学

Mozgaleva, M.L.^1 ; Akimov, P.A.^2,3,4,5

Department of Applied Mathematics, National Research Moscow State University of Civil Engineering, 26, Yaroslavskoe Shosse, Moscow

129337, Russia^1

Russian Academy of Architecture and Construction Sciences, 24, ul. Bolshaya Dmitrovka, Moscow

107031, Russia^2

Research and Development Centre StaDyO, 18, 3ya Ulitsa Yamskogo Polya, Moscow

125040, Russia^3

Department of Applied Mathematics, Tomsk State University of Architecture and Building, 2, Solyanaya sq., Tomsk

634003, Russia^4

Department of Architecture and Civil Engineering, Peoples' Friendship University of Russia, 6, Miklukho-Maklaya str., Moscow

117198, Russia^5

关键词: Boundary problems;    Direct solution;    Initial state;    Operator equation;    Structural mechanics;    System of linear algebraic equations;    Three-dimensional problems;    Two grid method;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/456/1/012120/pdf
DOI  :  10.1088/1757-899X/456/1/012120

来源: IOP

【 摘 要 】

The distinctive paper is devoted to so-called two-grid method of structural analysis based on discrete Haarbasis (three-dimensional problems are under consideration). Approximations of the mesh functions in discrete Haar bases of zero andfirst levels are described (the mesh function is represented as the sum where one term is its approximation of the first level, and the second term is so-called complement (up to the initial state) on the grid of the first level). Special projectors are constructed for the spaces of the original grid vector functions to the space of their approximationon the first-level grid and its complement (the detailing component) to the initial state. Basic scheme of the two-grid method is presented. This method allows boundary problems solution of structural mechanics with the matrix operators' use of significantly smaller dimension. It should be noted that discrete analogue of the initial operator equation (defined on a given interval) is a system of linear algebraic equations which is constructed with the use of finite element method or finite difference method. Block Gauss method can be used for direct solution.