The slice absorption method (SAM) is a numerical parallel solution reported by Rumpf et al. for analyzing large-scale devices with a complex structure. We use this method to simulate diffraction of the lamellar crossed gratings, and we use the wave matrix for the Fourier modal method (FMM) for SAM formulation. For this formulation, gratings with arbitrary profiles can be viewed as a stack of lamellar gratings via a staircase approximation, which is different from the difference approximation in the original SAM. In addition, an improved cascading-doubling algorithm is implemented, and not only for long uniform regions or repeated units. This algorithm provides a concurrent result with the FMM and promises an efficient application in scatterometry for multilevel gratings.