The authors propose an efficient implementation of the numerical tensor-train (TT) based algorithm for solving the multicomponent coagulation equation. The key challenge is that the errors of the low-rank decomposition and discretization scheme can lead to unnatural negative elements in the constructed approximation.
To address this, the authors introduce a rank-one correction in the TT-format proportional to the minimal negative element. This minimal negative element can be found efficiently via global optimization methods implemented within the tensor train format. The authors incorporate this nonnegative correction into the time-integration scheme for the multicomponent coagulation equation, as well as for post-processing of the stationary solution for the problem with particle sources.
The authors demonstrate the effectiveness of their approach through numerical experiments for two- to four-dimensional problems with different coagulation kernels. The nonnegative corrections have a modest additional computational cost without loss of accuracy compared to the initial TT-based method.
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by Sergey A. Ma... о arxiv.org 04-18-2024
https://arxiv.org/pdf/2404.10898.pdfГлибші Запити