A stochastic spectral finite element method for wave propagation analyses with medium uncertainties

Abstract

• Wave propagation in a medium with stochastic properties is studied. • A stochastically enriched spectral finite element method (StSFEM) is applied. • StSFEM accelerates temporal integration schemes and decreases numerical dispersion. • It provides an efficient numerical solution for Fredholm equation of KL Expansion. • The StSFEM is developed to large-scale stochastic wave propagation phenomena. A stochastically enriched spectral finite element method (StSFEM) is developed to solve wave propagation problems in random media. This method simultaneously includes all features of spectral finite element and stochastic finite element methods, which leads to excellent accuracy and convergence by implementing Gauss–Lobatto–Legendre collocation points permitting to generate coarser meshes. In addition, the proposed StSFEM leads to diagonal mass matrices, which accelerates temporal integration schemes and provides desirable accuracy. Furthermore, it numerically solves the Fredholm integral equation arising from Karhunen–Loève Expansion with favorable accuracy and computing time. Here, the StSFEM is examined and developed to stochastic wave propagation phenomena through several numerical simulations. Results demonstrate successful performance of the StSFEM in the solved problems so that one can accomplish uncertainty quantification of time domain wave propagation within random continua by incorporating the StSFEM.