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 be invariant along direction of space. The technique consists compressing the integral operators integro-differential formulation with so-called quantized tensor train (QTT) algorithm whose use is rather original in this context. show that it allows compute store notably small memory footprint while having at same time fast matrix-vector product (MVP) leading competitive method compared more classical $\mathcal {H}$ -matrix approach.