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The proposed numerical method, "FLAME-slab," solves electromagnetic wavescattering problems for aperiodic slab structures by exploiting short-rangeregularities in these structures. The computational procedure involves specialdifference schemes with high accuracy even on coarse grids. These schemes arebased on Trefftz approximations, utilizing functions that locally satisfy thegoverning differential equations, as is done in the Flexible LocalApproximation Method (FLAME). Radiation boundary conditions are implemented viaFourier expansions in the air surrounding the slab. When applied to ensemblesof slab structures with identical short-range features, such as amorphous orquasicrystalline lattices, the method is significantly more efficient, both inruntime and in memory consumption, than traditional approaches. This efficiencyis due to the fact that the Trefftz functions need to be computed only once forthe whole ensemble.

The FLAME-slab method for electromagnetic wave scattering in aperiodic slabs