Isogeometric Analysis with Proper Orthogonal Decomposition for Elastodynamics

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.