Transient wave propagations with the Noh-Bathe scheme and the spectral element method

Abstract

The spectral elements of the Lobatto family provide desirable characteristics of convergence and accuracy using a diagonal mass matrix in dynamic analysis. These characteristics might be expected to render the spectral element method with the use of an explicit time integration scheme effective for the transient analysis of wave propagations. In this paper we study the use of the central difference method and the recently proposed Noh-Bathe method for explicit time integration in the use of the spectral finite element method. The Noh-Bathe scheme is a second-order accurate procedure with small solution errors in the required frequency range while suppressing spurious high frequencies. We calculate appropriate CFL numbers for the time integrations and give an analysis of the dispersion errors for different orders of spectral elements. Finally, we demonstrate the capabilities of the Noh-Bathe scheme compared to the central difference method through the solution of several numerical examples of wave propagations.