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Reconstruction of low-rank aggregation kernels in univariate population balance equations

Citation Link: https://doi.org/10.15480/882.3547
Publikationstyp
Journal Article
Publikationsdatum
2021-05-02
Sprache
English
Author
Ahrens, Robin 
Le Borne, Sabine orcid-logo
Institut
Mathematik E-10 
DOI
10.15480/882.3547
TORE-URI
http://hdl.handle.net/11420/9572
Lizenz
https://creativecommons.org/licenses/by/4.0/
Enthalten in
Advances in computational mathematics 
Volume
47
Issue
3
Article Number
39
Citation
Advances in Computational Mathematics 47 (3): 39 (2021-06-01)
Publisher DOI
10.1007/s10444-021-09871-w
Scopus ID
2-s2.0-85105236031
Publisher
Springer Science + Business Media B.V
The dynamics of particle processes can be described by population balance equations which are governed by phenomena including growth, nucleation, breakage and aggregation. Estimating the kinetics of the aggregation phenomena from measured density data constitutes an ill-conditioned inverse problem. In this work, we focus on the aggregation problem and present an approach to estimate the aggregation kernel in discrete, low rank form from given (measured or simulated) data. The low-rank assumption for the kernel allows the application of fast techniques for the evaluation of the aggregation integral (O(nlogn) instead of O(n ) where n denotes the number of unknowns in the discretization) and reduces the dimension of the optimization problem, allowing for efficient and accurate kernel reconstructions. We provide and compare two approaches which we will illustrate in numerical tests. 2
Schlagworte
Aggregation kernel
Inverse method
Low rank approximation
Population balance equation
DDC Class
510: Mathematik
Projekt(e)
SPP 1679: Teilprojekt "Numerische Lösungsverfahren für gekoppelte Populationsbilanzsysteme zur dynamischen Simulation multivariater Feststoffprozesse am Beispiel der formselektiven Kristallisation" 
Projekt DEAL 
Funding Organisations
Deutsche Forschungsgemeinschaft (DFG) 
TUHH
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