Isogeometric Analysis with Proper Orthogonal Decomposition for Elastodynamics (Communications in Computational Physics, 2021)
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 fortransient 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 effectivenessof our method.
Keywords: Isogeometric analysis; proper orthogonal decomposition; reduced order modelling; elastic wave; generalized-$α$ method.