Nonnegative Tensor-Train Low-Rank Approximations of the Smoluchowski Coagulation Equation

We present a finite difference approximation of the nonnegative solutions of the two dimensional Smoluchowski equation by a nonnegative low-order tensor factorization. Two different implementations are compared. The first one is based on a full tensor representation of the numerical solution and the coagulation kernel. The second one is based on a tensor-train decomposition of solution and kernel. The convergence of the numerical solution to the analytical one is investigated for the Smoluchowski problem with the constant kernel and the influence of the nonnegative decomposition on the solution accuracy is investigated.