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

Abstract

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.