A Quantized Tensor Train Method for High-Frequency Scattering Problems Involving Heterogeneous Dielectric Layers

We present a new numerical scheme to solve efficiently scattering problems involving an elongated and flat heterogeneous dielectric material assumed to be invariant along a direction of space. The technique consists of compressing the integral operators of an integro-differential formulation with a so-called quantized tensor train (QTT) algorithm whose use is rather original in this context. We show that it allows to compute and store operators with a notably small memory footprint while having at the same time a fast matrix-vector product (MVP) leading to a competitive method compared with the more classical
$\mathcal {H}$
-matrix approach.