Publisher DOI: 10.1016/j.apnum.2020.03.002
Title: Tensor trains and moment conservation for multivariate aggregation in population balance modeling
Language: English
Authors: Ahrens, Robin 
Le Borne, Sabine  
Keywords: FFT; Moment conservation; Multivariate convolution; Population balance equation; Tensor trains
Issue Date: 13-Mar-2020
Publisher: Elsevier
Source: Applied Numerical Mathematics (153): 473-491 (2020)
Abstract (english): 
© 2020 IMACS We consider the numerical solution of the multivariate aggregation population balance equation on a uniform tensor grid. This class of equations is numerically challenging to solve - the computational complexity of “straightforward” algorithms grows exponentially with respect to the number of internal coordinates describing particle properties. Here, we develop algorithms which reduce the storage and computational complexity to almost linear order, O(dn) and O(dnlog⁡(n)), respectively, where d denotes the number of internal coordinates and n the number of pivots per internal coordinate. In particular, we develop fast algorithms in tensor train format to evaluate the multidimensional aggregation integral exploiting fast Fourier transformation for the underlying convolution. A further significant result lies in the conservation of the first 2d moments for our proposed method. Numerical tests confirm the favorable theoretical results concerning computational complexity and conservation of moments.
ISSN: 0168-9274
Journal: Applied numerical mathematics 
Institute: Mathematik E-10 
Document Type: Article
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