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.

翻译：我们提出了一种基于数值张量列（TT）的高效算法实现，用于求解多组分凝聚方程，并保持解的非负性。由低秩分解和离散化方案产生的误差会在构建的近似解中引入非自然的负元素。本文提出在TT格式中应用与最小负元素成比例的秩一修正。此类元素可通过全局优化方法寻得，且这些方法可完全基于张量列格式的高效运算实现。我们将该技巧融入多组分凝聚方程的时间积分方案，并将其用于含有粒子源的稳态解的后处理。