Publisher DOI: 10.1016/j.compchemeng.2014.12.011
Title: Fast evaluation of univariate aggregation integrals on equidistant grids
Language: English
Authors: Le Borne, Sabine  
Shahmuradyan, Lusine 
Sundmacher, Kai 
Keywords: Aggregation; Convolution; FFT; Population balance equation; Separable kernel approximation
Issue Date: 4-Mar-2015
Source: Computers and Chemical Engineering (74): 115-127 (2015-03-04)
Abstract (english): 
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.
ISSN: 0098-1354
Journal: Computers & chemical engineering 
Institute: Mathematik E-10 
Document Type: Article
Project: SPP 1679: Dynamische Simulation vernetzter Feststoffprozesse 
SPP 1679: Teilprojekt "Numerische Lösungsverfahren für gekoppelte Populationsbilanzsysteme zur dynamischen Simulation multivariater Feststoffprozesse am Beispiel der formselektiven Kristallisation" 
More Funding information: Deutsche Forschungsgemeinschaft (DFG)
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