Comparison of high-accuracy finite-difference methods for linear wave propagation

This paper analyzes a number of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such a electromagnetic, acoustic, and elastic waves. The spatial operators analyzed include compact schemes, noncompact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics. The time-marching methods include Runge Kutta methods, Adams-Bashforth methods, and the leapfrog method. In addition, the following fully-discrete finite-difference methods are studied: a one-step implicit scheme with a three-point spatial stencil, a one-step explicit scheme with a five-point spatial stencil, and a two-step explicit scheme with a five-point spatial stencil. For each method, the number of grid points per wavelength required for accurate simulation of wave propagation over large distances is presented. The results provide a clear understanding of the relative merits of the methods compared, especially the trade-offs associated with the use of optimized methods. A numerical example is given which shows that the bene ts of an optimized scheme can be small if the waveform has broad spectral content.