A staggered time integrator for the linear acoustic wave equation using the Jacobi-Anger expansion

Abstract

In this study, we introduce a staggered time integrator with the Fourier pseudospectral method to solve the first-order linear wave equation, which is accelerated by using the Jacobi-Anger expansion. The proposed method can reduce the computational cost by approximately half compared to the scheme whose temporal order of accuracy is extended by the Lax-Wendroff method under the equivalent modeling conditions, such as time step length, grid interval and maximum wave propagation speed. This is because the Jacobi-Anger expansion can effectively approximate the sinusoidal function, which in our case is the sine function in the wavenumber domain. Based on the wavenumber domain analysis of the proposed method, a strategy to optimally design the simulation parameters to maintain a preset level of accuracy is also introduced. According to the strategy, as the time step length increases, not only the computational cost of the simulation is reduced, but also the accuracy of the numerical solution is improved. Numerical simulations are also performed by using both homogeneous and heterogeneous models to validate the introduced strategy, which supports the practicality of the proposed method.