Dispersion-minimizing quadrature rules for C1 quadratic isogeometric analysis
We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation. The rules are optimal in the sense that they only require two quadrature points per element to minimize the dispersion error [1],...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/56638 |
| _version_ | 1848759902251515904 |
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| author | Deng, Q. Barton, M. Puzyrev, Vladimir Calo, Victor |
| author_facet | Deng, Q. Barton, M. Puzyrev, Vladimir Calo, Victor |
| author_sort | Deng, Q. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation. The rules are optimal in the sense that they only require two quadrature points per element to minimize the dispersion error [1], and they are equivalent to the optimized blending rules we recently described. Our approach further simplifies the numerical integration: instead of blending two three-point standard quadrature rules, we construct directly a single two-point quadrature rule that reduces the dispersion error to the same order for uniform meshes with periodic boundary conditions. Also, we present a 2.5-point rule for both uniform and non-uniform meshes with arbitrary boundary conditions. Consequently, we reduce the computational cost by using the proposed quadrature rules. Various numerical examples demonstrate the performance of these quadrature rules. |
| first_indexed | 2025-11-14T10:07:15Z |
| format | Journal Article |
| id | curtin-20.500.11937-56638 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:07:15Z |
| publishDate | 2017 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-566382019-10-04T02:54:56Z Dispersion-minimizing quadrature rules for C1 quadratic isogeometric analysis Deng, Q. Barton, M. Puzyrev, Vladimir Calo, Victor We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation. The rules are optimal in the sense that they only require two quadrature points per element to minimize the dispersion error [1], and they are equivalent to the optimized blending rules we recently described. Our approach further simplifies the numerical integration: instead of blending two three-point standard quadrature rules, we construct directly a single two-point quadrature rule that reduces the dispersion error to the same order for uniform meshes with periodic boundary conditions. Also, we present a 2.5-point rule for both uniform and non-uniform meshes with arbitrary boundary conditions. Consequently, we reduce the computational cost by using the proposed quadrature rules. Various numerical examples demonstrate the performance of these quadrature rules. 2017 Journal Article http://hdl.handle.net/20.500.11937/56638 10.1016/j.cma.2017.09.025 fulltext |
| spellingShingle | Deng, Q. Barton, M. Puzyrev, Vladimir Calo, Victor Dispersion-minimizing quadrature rules for C1 quadratic isogeometric analysis |
| title | Dispersion-minimizing quadrature rules for C1 quadratic isogeometric analysis |
| title_full | Dispersion-minimizing quadrature rules for C1 quadratic isogeometric analysis |
| title_fullStr | Dispersion-minimizing quadrature rules for C1 quadratic isogeometric analysis |
| title_full_unstemmed | Dispersion-minimizing quadrature rules for C1 quadratic isogeometric analysis |
| title_short | Dispersion-minimizing quadrature rules for C1 quadratic isogeometric analysis |
| title_sort | dispersion-minimizing quadrature rules for c1 quadratic isogeometric analysis |
| url | http://hdl.handle.net/20.500.11937/56638 |