A Krylov-based proper orthogonal decomposition method for elastodynamics problems with isogeometric analysis. (1st December 2021)

• Record Type: Journal Article
• Authors: Liu, Xiaofei; Wang, Hu; Yu, Xiaolong; Wang, Chengjing
• Is Part Of: Engineering analysis with boundary elements. Volume 133(2021)
• Page Start: 71
• Page End: 83
• Publication Date: 2021-12-01
• Subjects: Linear elastodynamics problems -- Isogeometric analysis -- Reduced-Order model -- Krylov subspace method -- Proper orthogonal decomposition; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2021.08.025
• Languages: English
• ISSNs: 0955-7997

Abstract

Highlights: A novel Krylov-based proper orthogonal decomposition (KPOD) extrapolation strategy is proposed for dynamic problem. Isogeometric analysis (IGA) is extended to exactly discrete geometric models and improve the accuracy of the solution. The combination of KPOD and IGA establishes a reduced-order model (ROM) which extremely decrease the computational cost. Abstract: In this study, the application of isogeometric analysis (IGA) is extended to the linear elastodynamics problems. In order to improve the efficiency of time-dependent problems with IGA, a novel effective Krylov-based proper orthogonal decomposition (KPOD) strategy is suggested to establish an efficient extrapolated algorithm by dimension reduction. In this method, a reduced-order model (ROM) is constructed to save the computational cost and the Krylov subspace method is used to achieve effective extrapolation through expanding the solution space formed by proper orthogonal decomposition (POD) basis with the addition of Krylov subspace. To validate the performance of the suggested method, two numerical examples are tested. Moreover, with the increasing of scale of the problem, much more computational cost should be saved. Specifically, the efficiency is increased by more than 20 times with 100, 000 degrees of freedom.