Numerical solution of the acoustic wave equation by the rapid expansion method (REM) - A one step time evolution algorithm

We revisit a numerical solution for the time evolution of the acoustic wave equation where the wave field can be advanced in time in one large step, the rapid expansion method, or REM. This method has the advantage of being numerically stable even for large time steps and when combined with a pseudo spectral Fourier method for the spatial derivatives results in a highly accurate solution for the propagating wave fields. We show that the number of terms in the integration that produces the time snap shots can be significantly reduced making the method computationally attractive for high resolution simulations.