Towards solving lippmann-schwinger integral equation in 2D with polylogarithmic complexity with quantized tensor train decomposition

Having low-parametric structure in a computational problem may provide significant benefits, such as effective data compression for large arrays or speeding up the computations. In this paper we solve 2D VIE-type Lippmann-Schwinger Equation for time-harmonic scattering problem. We show that application of modern low-rank Quantized Tensor Train (QTT) format and associated algorithms may provide a solution pipeline with polylogarithmic overall complexity O(log p N), where N — total number of elements in the grid and p ≥ 4.