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Publisher DOI: 10.1007/s10444-021-09871-w
Title: Reconstruction of low-rank aggregation kernels in univariate population balance equations
Language: English
Authors: Ahrens, Robin 
Le Borne, Sabine  
Keywords: Aggregation kernel; Inverse method; Low rank approximation; Population balance equation
Issue Date: 2-May-2021
Publisher: Springer Science + Business Media B.V
Source: Advances in Computational Mathematics 47 (3): 39 (2021-06-01)
Abstract (english): 
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
DOI: 10.15480/882.3547
ISSN: 1019-7168
Journal: Advances in computational mathematics 
Institute: Mathematik E-10 
Document Type: Article
Project: SPP 1679: Teilprojekt "Numerische Lösungsverfahren für gekoppelte Populationsbilanzsysteme zur dynamischen Simulation multivariater Feststoffprozesse am Beispiel der formselektiven Kristallisation" 
Projekt DEAL 
Funded by: Deutsche Forschungsgemeinschaft (DFG) 
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
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