Nonnegative tensor train for the multicomponent Smoluchowski equation
arXiv:2404.10898 · doi:10.1007/s40314-024-02993-z
Abstract
We propose an efficient implementation of the numerical tensor-train (TT) based algorithm solving the multicomponent coagulation equation preserving the nonnegativeness of solution. Unnatural negative elements in the constructed approximation arise due to the errors of the low-rank decomposition and discretization scheme. In this work, we propose to apply the rank-one corrections in the TT-format proportional to the minimal negative element. Such an element can be found via application of the global optimization methods that can be fully implemented within efficient operations in the tensor train format. We incorporate this trick into the time-integration scheme for the multicomponent coagulation equation and also use it for post-processing of the stationary solution for the problem with the source of particles.
arXiv comment12 pages, 4 figures, 4 tables
References in corpus (6)
- Scaling Theory and Exactly Solved Models In the Kinetics of Irreversible Aggregation
- Size distribution of particles in Saturn's rings from aggregation and fragmentation
- Dislocation contrast in cathodoluminescence and electron-beam induced current maps on GaN(0001)
- Low-rank nonnegative tensor approximation via alternating projections and sketching
- Probabilistic estimation of the rank 1 cross approximation accuracy
- Sketching for low-rank nonnegative matrix approximation: Numerical study