Multidimensional Hierarchical Interpolation Method on Sparse Grids for the Absorption Problem
The numerical integration of multidimensional functions using some variables of the sparse grid method for the absorption problem is presented in this paper. The multivariate quadrature expressions are constructed by combining tensor of suited one dimensional formula. We develop a multidimensional a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IEEE
2019-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8917993/ |
| _version_ | 1811274078642765824 |
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| author | Xuesong Chen Heng Mai Lili Zhang |
| author_facet | Xuesong Chen Heng Mai Lili Zhang |
| author_sort | Xuesong Chen |
| collection | DOAJ |
| description | The numerical integration of multidimensional functions using some variables of the sparse grid method for the absorption problem is presented in this paper. The multivariate quadrature expressions are constructed by combining tensor of suited one dimensional formula. We develop a multidimensional adaptive quadrature algorithm for the implementation of sparse grid based on a hierarchical basis. Furthermore, we obtain a new error bound at each sparse grid point. The numerical examples are shown to demonstrate the efficiency of our algorithm for the absorption problem and confirm the theoretical estimates. |
| first_indexed | 2024-04-12T23:12:27Z |
| format | Article |
| id | doaj.art-277c3904a48644fe9ea3a51e52c0e702 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-12T23:12:27Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-277c3904a48644fe9ea3a51e52c0e7022022-12-22T03:12:46ZengIEEEIEEE Access2169-35362019-01-01717247017247610.1109/ACCESS.2019.29568098917993Multidimensional Hierarchical Interpolation Method on Sparse Grids for the Absorption ProblemXuesong Chen0https://orcid.org/0000-0001-9530-0644Heng Mai1https://orcid.org/0000-0002-0986-5532Lili Zhang2https://orcid.org/0000-0002-6844-4201School of Applied Mathematics, Guangdong University of Technology, Guangzhou, ChinaSchool of Applied Mathematics, Guangdong University of Technology, Guangzhou, ChinaSchool of Applied Mathematics, Guangdong University of Technology, Guangzhou, ChinaThe numerical integration of multidimensional functions using some variables of the sparse grid method for the absorption problem is presented in this paper. The multivariate quadrature expressions are constructed by combining tensor of suited one dimensional formula. We develop a multidimensional adaptive quadrature algorithm for the implementation of sparse grid based on a hierarchical basis. Furthermore, we obtain a new error bound at each sparse grid point. The numerical examples are shown to demonstrate the efficiency of our algorithm for the absorption problem and confirm the theoretical estimates.https://ieeexplore.ieee.org/document/8917993/Multidimensional systemsinterpolationgrid computingerror analysisconvergence of numerical methods |
| spellingShingle | Xuesong Chen Heng Mai Lili Zhang Multidimensional Hierarchical Interpolation Method on Sparse Grids for the Absorption Problem IEEE Access Multidimensional systems interpolation grid computing error analysis convergence of numerical methods |
| title | Multidimensional Hierarchical Interpolation Method on Sparse Grids for the Absorption Problem |
| title_full | Multidimensional Hierarchical Interpolation Method on Sparse Grids for the Absorption Problem |
| title_fullStr | Multidimensional Hierarchical Interpolation Method on Sparse Grids for the Absorption Problem |
| title_full_unstemmed | Multidimensional Hierarchical Interpolation Method on Sparse Grids for the Absorption Problem |
| title_short | Multidimensional Hierarchical Interpolation Method on Sparse Grids for the Absorption Problem |
| title_sort | multidimensional hierarchical interpolation method on sparse grids for the absorption problem |
| topic | Multidimensional systems interpolation grid computing error analysis convergence of numerical methods |
| url | https://ieeexplore.ieee.org/document/8917993/ |
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