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Algorithms for the Haar wavelet based fast evaluation of aggregation integrals in population balance equations
Publikationstyp
Journal Article
Publikationsdatum
2016-10-01
Sprache
English
Institut
TORE-URI
Enthalten in
Volume
108
Start Page
1
End Page
20
Citation
Applied Numerical Mathematics (108): 1-20 (2016-10-01)
Publisher DOI
Scopus ID
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.
Schlagworte
Aggregation
Fast wavelet transformation
Locally refined nested grids
Population balance equation
DDC Class
510: Mathematik
More Funding Information
Deutsche Forschungsgesellschaft