Publisher DOI: 10.1016/j.apnum.2016.02.009
Title: Algorithms for the Haar wavelet based fast evaluation of aggregation integrals in population balance equations
Language: English
Authors: Le Borne, Sabine  
Shahmuradyan, Lusine 
Keywords: Aggregation; Fast wavelet transformation; Locally refined nested grids; Population balance equation
Issue Date: 1-Oct-2016
Source: Applied Numerical Mathematics (108): 1-20 (2016-10-01)
Abstract (english): 
In several production processes, the distribution of particles dispersed in an environmental phase may be mathematically described by the solution of population balance equations. We are concerned with the development of efficient numerical techniques for the aggregation process: It invokes an integral term that is usually numerically expensive to evaluate and often dominates the total simulation cost. We describe an approach on locally refined nested grids to evaluate both the source and the sink terms in almost linear complexity (instead of quadratic complexity resulting from a direct approach). The key is to switch from a nodal to a wavelet basis representation of the density function. We illustrate the numerical performance of this approach, both in comparison to a discretization of piecewise constant functions on a uniform grid as well as to the fixed pivot method on a geometric grid.
ISSN: 0168-9274
Journal: Applied numerical mathematics 
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 Forschungsgesellschaft
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