Releasing the Time Step Upper Bound of CFL Stability Condition for the Acoustic Wave Simulation With Model-Order Reduction

Abstract

The maximum time step size for the explicit finite-difference scheme complies with the Courant–Friedrichs–Lewy (CFL) stability condition, which essentially restricts the optimization and tuning of the communication-intensive massive seismic wave simulation in a parallel manner. This study brings forward the model-order reduction (MOR) method to simulate acoustic wave propagation. It briefly takes advantage of the update matrix’s eigenvalues and the expansion coefficients of the variables for the time in the semi-discrete scheme of the wave equation, reducing the computational complexity and enhancing its computing efficiency. Moreover, we introduced the eigenvalue abandonment and eigenvalue perturbation methods to stabilize the unstable oscillations when the time step size breaks the CFL stability upper bound. We then introduced the time-dispersion transform method to eliminate the time-dispersion error caused by the large time step and secure the high accuracy. Numerical experiments exhibit that the MOR method, in conjunction with eigenvalue abandonment (and the eigenvalue perturbation) and the time-dispersion transform method, can capture highly accurate waveforms even when the time step size exceeds the CFL stability condition. The eigenvalue perturbation method is suitable for strongly heterogenous media and can maintain the numerical accuracy and stability even when the time step size is toward the upper bound of the Nyquist sampling.