Small-scale medium variations with high-order finite-difference and pseudospectral schemes

Abstract

The accuracy of implementing interfaces with coarse-grid methods such as the pseudospectral method and high-order finite differences has been considered to be low. Our focus is on variations in interface locations and on inclusions that are significantly smaller than the grid step sizes. Classic implementations of these staggered-grid high-order methods are used. Band-limited versions of the Heaviside step function are used to manipulate the material-parameter grids. Interfaces can be implemented with accuracy that is one order of magnitude smaller than the step size. Small medium inclusions, diffractors, can, be three orders of magnitude smaller in area than the typical cell size and still be modeled with good accuracy. If the method used to implement an interface or to implement a small-scale inclusion is viewed as a filter, then this filter must be accurate up to the spatial Nyquist wavenumber of the simulation grid.