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.

中文翻译：

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具有高阶有限差分和伪谱方案的小尺度介质变化

使用伪谱法和高阶有限差分等粗网格方法实现接口的精度被认为是低的。我们的重点是界面位置的变化和明显小于网格步长的夹杂物。使用这些交错网格高阶方法的经典实现。Heaviside 阶跃函数的带限版本用于操纵材料参数网格。接口可以以比步长小一个数量级的精度实现。小的中等夹杂物（衍射器）的面积可以比典型的单元尺寸小三个数量级，并且仍能以良好的精度建模。如果将用于实现接口或实现小规模包含的方法视为过滤器，