ABOUT WAVELET-BASED MULTIGRID NUMERICAL METHOD OF STRUCTURAL ANALYSIS WITH THE USE OF DISCRETE HAAR BASIS
he distinctive paper is devoted to so-called multigrid (particularly two-grid) method of structural analysis based on discrete Haar basis (one-dimensional, two-dimensional and three-dimensional problems are under consideration). Approximations of the mesh functions in discrete Haar bases of zero and...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Publishing House ASV
2018-09-01
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| Series: | International Journal for Computational Civil and Structural Engineering |
| Subjects: | |
| Online Access: | http://ijccse.iasv.ru/article/view/158 |
| _version_ | 1819203708548808704 |
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| author | Marina L. Mozgaleva Pavel A. Akimov Taymuraz B. Kaytukov |
| author_facet | Marina L. Mozgaleva Pavel A. Akimov Taymuraz B. Kaytukov |
| author_sort | Marina L. Mozgaleva |
| collection | DOAJ |
| description | he distinctive paper is devoted to so-called multigrid (particularly two-grid) method of structural analysis based on discrete Haar basis (one-dimensional, two-dimensional and three-dimensional problems are under consideration). Approximations of the mesh functions in discrete Haar bases of zero and first levels are described (the mesh function is represented as the sum in which 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 vector functions of the original grid to the space of their approximation on the first-level grid and its complement (the refinement component) to the initial state. Basic scheme of the two-grid method is presented. This method allows solution of boundary problems of structural mechanics with the use of matrix operators of significantly smaller dimension. It should be noted that discrete analogue of the initial operator equation 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. |
| first_indexed | 2024-12-23T04:24:13Z |
| format | Article |
| id | doaj.art-fb842accca684bc495c2369c97e7628f |
| institution | Directory Open Access Journal |
| issn | 2587-9618 2588-0195 |
| language | English |
| last_indexed | 2024-12-23T04:24:13Z |
| publishDate | 2018-09-01 |
| publisher | Publishing House ASV |
| record_format | Article |
| series | International Journal for Computational Civil and Structural Engineering |
| spelling | doaj.art-fb842accca684bc495c2369c97e7628f2022-12-21T18:00:11ZengPublishing House ASVInternational Journal for Computational Civil and Structural Engineering2587-96182588-01952018-09-0114310.22337/2587-9618-2018-14-3-83-102ABOUT WAVELET-BASED MULTIGRID NUMERICAL METHOD OF STRUCTURAL ANALYSIS WITH THE USE OF DISCRETE HAAR BASISMarina L. Mozgaleva0Pavel A. Akimov1Taymuraz B. Kaytukov2National Research Moscow State University of Civil Engineering, Moscow, RUSSIARussian Academy of Architecture and Construction Sciences, Moscow, RUSSIARussian Academy of Architecture and Construction Sciences, Moscow, RUSSIAhe distinctive paper is devoted to so-called multigrid (particularly two-grid) method of structural analysis based on discrete Haar basis (one-dimensional, two-dimensional and three-dimensional problems are under consideration). Approximations of the mesh functions in discrete Haar bases of zero and first levels are described (the mesh function is represented as the sum in which 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 vector functions of the original grid to the space of their approximation on the first-level grid and its complement (the refinement component) to the initial state. Basic scheme of the two-grid method is presented. This method allows solution of boundary problems of structural mechanics with the use of matrix operators of significantly smaller dimension. It should be noted that discrete analogue of the initial operator equation 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.http://ijccse.iasv.ru/article/view/158structural analysis, wavelet analysis, numerical methods, multigrid methods, two-grid method, discrete Haar basis, reduction, local structural analysis, approximation, boundary problem |
| spellingShingle | Marina L. Mozgaleva Pavel A. Akimov Taymuraz B. Kaytukov ABOUT WAVELET-BASED MULTIGRID NUMERICAL METHOD OF STRUCTURAL ANALYSIS WITH THE USE OF DISCRETE HAAR BASIS International Journal for Computational Civil and Structural Engineering structural analysis, wavelet analysis, numerical methods, multigrid methods, two-grid method, discrete Haar basis, reduction, local structural analysis, approximation, boundary problem |
| title | ABOUT WAVELET-BASED MULTIGRID NUMERICAL METHOD OF STRUCTURAL ANALYSIS WITH THE USE OF DISCRETE HAAR BASIS |
| title_full | ABOUT WAVELET-BASED MULTIGRID NUMERICAL METHOD OF STRUCTURAL ANALYSIS WITH THE USE OF DISCRETE HAAR BASIS |
| title_fullStr | ABOUT WAVELET-BASED MULTIGRID NUMERICAL METHOD OF STRUCTURAL ANALYSIS WITH THE USE OF DISCRETE HAAR BASIS |
| title_full_unstemmed | ABOUT WAVELET-BASED MULTIGRID NUMERICAL METHOD OF STRUCTURAL ANALYSIS WITH THE USE OF DISCRETE HAAR BASIS |
| title_short | ABOUT WAVELET-BASED MULTIGRID NUMERICAL METHOD OF STRUCTURAL ANALYSIS WITH THE USE OF DISCRETE HAAR BASIS |
| title_sort | about wavelet based multigrid numerical method of structural analysis with the use of discrete haar basis |
| topic | structural analysis, wavelet analysis, numerical methods, multigrid methods, two-grid method, discrete Haar basis, reduction, local structural analysis, approximation, boundary problem |
| url | http://ijccse.iasv.ru/article/view/158 |
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