A highly efficient time-space-domain optimized method with Lax-Wendroff type time discretization for the scalar wave equation

Abstract

In this paper, we propose an efficient time-space-domain optimized (OptTS) finite difference scheme to model 2D and 3D scalar wave propagation. It adopts piecewise constant interpolation coefficients for several consecutive Courant number ranges, which avoids the extra time costs caused by loading the coefficients consecutively according to different wave velocities in heterogeneous media. The new scheme is capable of suppressing numerical dispersion errors using a large time interval because we introduce a Lax-Wendroff type time discretization, which utilizes the wave-field information of O(M1M2) neighboring grid points in each step, with merely O(M1+M2) computation, where M1 and M2 are the stencil radii to generate the 2nd-order and 4th-order spatial derivatives. The improved computational efficiency and accuracy of OptTS are validated by substantial experiments using both theoretical analysis and numerical modeling. They show that in heterogeneous models, the maximal Courant numbers reach 1.0 and 0.85 in 2D and 3D cases respectively without severe temporal error, and the scheme is computationally nearly three times faster than its high-order counterpart, providing a powerful tool for large-scale modeling and high-resolution imaging.