A Krylov-based proper orthogonal decomposition method for elastodynamics problems with isogeometric analysis

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.