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

TL;DR

The FLAME-slab method offers an efficient numerical approach for electromagnetic wave scattering in aperiodic slabs by leveraging local regularities and Trefftz approximations, reducing computational costs for complex structures.

Contribution

It introduces a novel FLAME-slab technique that exploits short-range regularities and Trefftz functions for efficient electromagnetic scattering simulations in aperiodic slabs.

Findings

Significantly reduces runtime and memory compared to traditional methods.

Achieves high accuracy with coarse computational grids.

Efficiently handles ensembles of similar aperiodic structures.

Abstract

The proposed numerical method, "FLAME-slab," solves electromagnetic wave scattering problems for aperiodic slab structures by exploiting short-range regularities in these structures. The computational procedure involves special difference schemes with high accuracy even on coarse grids. These schemes are based on Trefftz approximations, utilizing functions that locally satisfy the governing differential equations, as is done in the Flexible Local Approximation Method (FLAME). Radiation boundary conditions are implemented via Fourier expansions in the air surrounding the slab. When applied to ensembles of slab structures with identical short-range features, such as amorphous or quasicrystalline lattices, the method is significantly more efficient, both in runtime and in memory consumption, than traditional approaches. This efficiency is due to the fact that the Trefftz functions need to be computed only once for the whole ensemble.