Isogeometric spectral approximation for elliptic differential operators

© 2018 Elsevier B.V. We study the spectral approximation of a second-order elliptic differential eigenvalue problem that arises from structural vibration problems using isogeometric analysis. In this paper, we generalize recent work in this direction. We present optimally-blended quadrature rules fo...

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Main Authors: Deng, Quanling, Puzyrev, Vladimir, Calo, Victor
Format: Journal Article
Published: Elsevier Ltd 2018
Online Access:http://hdl.handle.net/20.500.11937/68869
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author Deng, Quanling
Puzyrev, Vladimir
Calo, Victor
author_facet Deng, Quanling
Puzyrev, Vladimir
Calo, Victor
author_sort Deng, Quanling
building Curtin Institutional Repository
collection Online Access
description © 2018 Elsevier B.V. We study the spectral approximation of a second-order elliptic differential eigenvalue problem that arises from structural vibration problems using isogeometric analysis. In this paper, we generalize recent work in this direction. We present optimally-blended quadrature rules for the isogeometric spectral approximation of a diffusion-reaction operator with both Dirichlet and Neumann boundary conditions. The blended rules improve the accuracy of the isogeometric approximation. In particular, the optimal blending rules minimize the dispersion error and lead to two extra orders of super-convergence in the eigenvalue error. Various numerical examples (including the Schrödinger operator for quantum mechanics) in one and three spatial dimensions demonstrate the performance of the blended rules.
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institution Curtin University Malaysia
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last_indexed 2025-11-14T10:39:11Z
publishDate 2018
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spelling curtin-20.500.11937-688692018-06-29T12:36:11Z Isogeometric spectral approximation for elliptic differential operators Deng, Quanling Puzyrev, Vladimir Calo, Victor © 2018 Elsevier B.V. We study the spectral approximation of a second-order elliptic differential eigenvalue problem that arises from structural vibration problems using isogeometric analysis. In this paper, we generalize recent work in this direction. We present optimally-blended quadrature rules for the isogeometric spectral approximation of a diffusion-reaction operator with both Dirichlet and Neumann boundary conditions. The blended rules improve the accuracy of the isogeometric approximation. In particular, the optimal blending rules minimize the dispersion error and lead to two extra orders of super-convergence in the eigenvalue error. Various numerical examples (including the Schrödinger operator for quantum mechanics) in one and three spatial dimensions demonstrate the performance of the blended rules. 2018 Journal Article http://hdl.handle.net/20.500.11937/68869 10.1016/j.jocs.2018.05.009 Elsevier Ltd restricted
spellingShingle Deng, Quanling
Puzyrev, Vladimir
Calo, Victor
Isogeometric spectral approximation for elliptic differential operators
title Isogeometric spectral approximation for elliptic differential operators
title_full Isogeometric spectral approximation for elliptic differential operators
title_fullStr Isogeometric spectral approximation for elliptic differential operators
title_full_unstemmed Isogeometric spectral approximation for elliptic differential operators
title_short Isogeometric spectral approximation for elliptic differential operators
title_sort isogeometric spectral approximation for elliptic differential operators
url http://hdl.handle.net/20.500.11937/68869