Tensor decompositions for solving the equations of mathematical models of aggregation with multiple collisions of particles

Efficient methods for the numerical solving of a Cauchy problem for systems of Smoluchowski-type kinetic equations of aggregation with multiple collisions of particles are proposed. The developed methods are based on the tensor representations of kinetic coefficient arrays. The canonical, Tucker, and tensor train (TT) decompositions are compared. The computational complexity of these tensor representations is estimated for a second-order Runge-Kutta. The efficiency of the proposed methods for the systems with collisions of up to five particles is shown in a series of numerical experiments for the canonical and TT-decompositions.