Improving Time Stability Constraints for the Spectral Finite Element Method in Acoustic Wave Propagation Numerical Simulations

Abstract

The numerical solution of the scalar wave equation, arising, for instance, in geophysics and seismic engineering, by means of the spectral finite element method (SFEM) based on the Gauss-Lobatto-Legendre quadrature has been receiving great popularity. The SFEM can be viewed as a higherorder finite element method (FEM) with some advantages such as mass-lumping and less dispersion errors. However, when common explicit time-stepping schemes are employed, the critical time step becomes too restrictive as the polynomial degree increases. In this context, an explicit time-stepping scheme based on numerical Green’s functions is presented to circumvent this drawback. The Green’s functions are explicitly computed taking into account the Runge-Kutta (RK) scheme and a time substep procedure. Unlike the standard Runge-Kutta scheme, the present methodology allows the use of large time steps without loss of accuracy. Numerical simulations of a heterogeneous seismic model in an unbounded medium are presented and analyzed in order to illustrate the effectiveness of the proposed formulation.