Fast evaluation of univariate aggregation integrals on equidistant grids

Publikationstyp
Journal Article
Date Issued
2015-03-04
Sprache
English
Author(s)
Le Borne, Sabine  orcid-logo
Shahmuradyan, Lusine  
Sundmacher, Kai  
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/4965
Journal
Computers & chemical engineering  
Volume
74
Start Page
115
End Page
127
Citation
Computers and Chemical Engineering (74): 115-127 (2015-03-04)
Publisher DOI
10.1016/j.compchemeng.2014.12.011
Scopus ID
2-s2.0-84936943295
A variety of production processes in chemistry and biotechnology are concerned with particles dispersed in an environmental phase. The particle distribution is mathematically described by the solution of population balance equations of integro-differential type. We are concerned with the aggregation process: it invokes an integral term that is usually numerically expensive to evaluate and often dominates the total simulation cost. We will expose the algorithmic details of an efficient approach based on a separable approximation of the aggregation kernel and a subsequent fast Fourier transformation. This approach reduces the originally quadratic complexity to an almost optimal complexity O(nlogn) in the dimension of the approximation space. We include numerical tests illustrating its application to representative aggregation kernels from the literature. While originally developed in the context of a discretization with piecewise constant functions, we illustrate how these ideas can be applied in the setting of the popular sectional methods.
Subjects
Aggregation
Convolution
FFT
Population balance equation
Separable kernel approximation
DDC Class
510: Mathematik