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

Richen Li, Qingbiao Wu & Shengfeng Zhu

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.

  • AMS Subject Headings

35K20, 65M12, 65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-30-396, author = {Li , RichenWu , Qingbiao and Zhu , Shengfeng}, 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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