Generalization of the Pythagorean Eigenvalue Error Theorem and Its Application to Isogeometric Analysis
© 2018, Springer Nature Switzerland AG. This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagation and structural vibration problems. The dispersion error of the isogeometric elements is minimized by optimally blending two standard Gauss-type quadrature ru...
| Main Authors: | , , , |
|---|---|
| Format: | Book Chapter |
| Published: |
2018
|
| Online Access: | http://hdl.handle.net/20.500.11937/70784 |
| _version_ | 1848762300860727296 |
|---|---|
| author | Barton, M. Calo, Victor Deng, Quanling Puzyrev, Vladimir |
| author_facet | Barton, M. Calo, Victor Deng, Quanling Puzyrev, Vladimir |
| author_sort | Barton, M. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2018, Springer Nature Switzerland AG. This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagation and structural vibration problems. The dispersion error of the isogeometric elements is minimized by optimally blending two standard Gauss-type quadrature rules. These blending rules approximate the inner products and increase the convergence rate by two extra orders when compared to those with fully-integrated inner products. To quantify the approximation errors, we generalize the Pythagorean eigenvalue error theorem of Strang and Fix. To reduce the computational cost, we further propose a two-point rule for C1 quadratic isogeometric elements which produces equivalent inner products on uniform meshes and yet requires fewer quadrature points than the optimally-blended rules. |
| first_indexed | 2025-11-14T10:45:23Z |
| format | Book Chapter |
| id | curtin-20.500.11937-70784 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:45:23Z |
| publishDate | 2018 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-707842018-12-13T09:32:49Z Generalization of the Pythagorean Eigenvalue Error Theorem and Its Application to Isogeometric Analysis Barton, M. Calo, Victor Deng, Quanling Puzyrev, Vladimir © 2018, Springer Nature Switzerland AG. This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagation and structural vibration problems. The dispersion error of the isogeometric elements is minimized by optimally blending two standard Gauss-type quadrature rules. These blending rules approximate the inner products and increase the convergence rate by two extra orders when compared to those with fully-integrated inner products. To quantify the approximation errors, we generalize the Pythagorean eigenvalue error theorem of Strang and Fix. To reduce the computational cost, we further propose a two-point rule for C1 quadratic isogeometric elements which produces equivalent inner products on uniform meshes and yet requires fewer quadrature points than the optimally-blended rules. 2018 Book Chapter http://hdl.handle.net/20.500.11937/70784 10.1007/978-3-319-94676-4_6 restricted |
| spellingShingle | Barton, M. Calo, Victor Deng, Quanling Puzyrev, Vladimir Generalization of the Pythagorean Eigenvalue Error Theorem and Its Application to Isogeometric Analysis |
| title | Generalization of the Pythagorean Eigenvalue Error Theorem and Its Application to Isogeometric Analysis |
| title_full | Generalization of the Pythagorean Eigenvalue Error Theorem and Its Application to Isogeometric Analysis |
| title_fullStr | Generalization of the Pythagorean Eigenvalue Error Theorem and Its Application to Isogeometric Analysis |
| title_full_unstemmed | Generalization of the Pythagorean Eigenvalue Error Theorem and Its Application to Isogeometric Analysis |
| title_short | Generalization of the Pythagorean Eigenvalue Error Theorem and Its Application to Isogeometric Analysis |
| title_sort | generalization of the pythagorean eigenvalue error theorem and its application to isogeometric analysis |
| url | http://hdl.handle.net/20.500.11937/70784 |