Volume 30, Issue 2
Isogeometric Analysis with Proper Orthogonal Decomposition for Elastodynamics

Commun. Comput. Phys., 30 (2021), pp. 396-422.

Published online: 2021-05

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• Abstract

We consider reduced order modelling of elastodynamics with proper orthogonal decomposition and isogeometric analysis, a recent novel and promising discretization method for partial differential equations. The generalized-$α$ method for transient problems is used for additional flexibility in controlling high frequency dissipation. We propose a fully discrete scheme for the elastic wave equation with isogeometric analysis for spatial discretization, generalized-$α$ method for time discretization, and proper orthogonal decomposition for model order reduction. Numerical convergence and dispersion are shown in detail to show the feasibility of the method. A variety of numerical examples in both 2D and 3D are provided to show the effectiveness of our method.

• Keywords

Isogeometric analysis, proper orthogonal decomposition, reduced order modelling, elastic wave, generalized-$α$ method.

35K20, 65M12, 65M15, 65M60

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@Article{CiCP-30-396, author = {Richen and Li and and 16160 and and Richen Li and Qingbiao and Wu and and 16161 and and Qingbiao Wu and Shengfeng and Zhu and and 16162 and and Shengfeng Zhu}, title = {Isogeometric Analysis with Proper Orthogonal Decomposition for Elastodynamics}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {2}, pages = {396--422}, abstract = {

We consider reduced order modelling of elastodynamics with proper orthogonal decomposition and isogeometric analysis, a recent novel and promising discretization method for partial differential equations. The generalized-$α$ method for transient problems is used for additional flexibility in controlling high frequency dissipation. We propose a fully discrete scheme for the elastic wave equation with isogeometric analysis for spatial discretization, generalized-$α$ method for time discretization, and proper orthogonal decomposition for model order reduction. Numerical convergence and dispersion are shown in detail to show the feasibility of the method. A variety of numerical examples in both 2D and 3D are provided to show the effectiveness of our method.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0018}, url = {http://global-sci.org/intro/article_detail/cicp/19119.html} }
TY - JOUR T1 - Isogeometric Analysis with Proper Orthogonal Decomposition for Elastodynamics AU - Li , Richen AU - Wu , Qingbiao AU - Zhu , Shengfeng JO - Communications in Computational Physics VL - 2 SP - 396 EP - 422 PY - 2021 DA - 2021/05 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2020-0018 UR - https://global-sci.org/intro/article_detail/cicp/19119.html KW - Isogeometric analysis, proper orthogonal decomposition, reduced order modelling, elastic wave, generalized-$α$ method. AB -

We consider reduced order modelling of elastodynamics with proper orthogonal decomposition and isogeometric analysis, a recent novel and promising discretization method for partial differential equations. The generalized-$α$ method for transient problems is used for additional flexibility in controlling high frequency dissipation. We propose a fully discrete scheme for the elastic wave equation with isogeometric analysis for spatial discretization, generalized-$α$ method for time discretization, and proper orthogonal decomposition for model order reduction. Numerical convergence and dispersion are shown in detail to show the feasibility of the method. A variety of numerical examples in both 2D and 3D are provided to show the effectiveness of our method.

Richen Li, Qingbiao Wu & Shengfeng Zhu. (2021). Isogeometric Analysis with Proper Orthogonal Decomposition for Elastodynamics. Communications in Computational Physics. 30 (2). 396-422. doi:10.4208/cicp.OA-2020-0018
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