Tensor trains and moment conservation for multivariate aggregation in population balance modeling

Publikationstyp
Journal Article
Date Issued
2020-03-13
Sprache
English
Author(s)
Ahrens, Robin  
Le Borne, Sabine  orcid-logo
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/7839
Journal
Applied numerical mathematics  
Volume
153
Issue
July
Start Page
473
End Page
491
Citation
Applied Numerical Mathematics (153): 473-491 (2020)
Publisher DOI
10.1016/j.apnum.2020.03.002
Scopus ID
2-s2.0-85081656716
Publisher
Elsevier
© 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.
Subjects
FFT
Moment conservation
Multivariate convolution
Population balance equation
Tensor trains
DDC Class
510: Mathematik