Spectral-Element Method and comparison with the Method of Fundamental Solutions in 2D

The Spectral-Element Method (SEM) is a finite-element method that solves the wave equa-tion in the time domain based on high-degree polynomial interpolation on quadrangular elements in 2D and hexahedral elements in 3D [1, 2]. This method is well adapted to the simulation of seismic wave propagation in complex geological models. We show here how to implement plane wave sources with any incidence angle for this time-domain method. We also implement absorbing bounary conditions following the ideas of [3], which is crucial ensure that no significant spurious waves propagate back into the main domain. We validate the method and check its accuracy for the numerical modeling of seismic wave propagation, in particular in order to compute the response of a free surface with topography under the incidence of a plane wave with different angles by comparing the results obtained to the Method of Fundamental Solutions (MFS) [4], which is a new method to solve the wave equation in the frequency domain