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http://hdl.handle.net/10397/106382
Title: | Error analysis in stochastic solutions of population balance equations | Authors: | Zhou, K Jiang, X Chan, TL |
Issue Date: | Apr-2020 | Source: | Applied mathematical modelling, Apr. 2020, v. 80, p. 531-552 | Abstract: | Stochastic simulation of population balance equations (PBEs) is robust and flexible; however, it exhibits intrinsic stochastic errors which decreases at a very slow rate when increasing the computational resolution. Generally, these stochastic methods can be classified into two groups: (i) the classical Gillespie method and (ii) weighted flow algorithm. An analytical relationship is derived for the first time to connect the variances in these two groups. It also provides a detailed analysis of the resampling process, which has not been given appropriate attention previously. It is found that resampling has a profound effect on the numerical precision. Moreover, by comparing the time evolutions between systematic errors (i.e., errors in the mean value) and stochastic errors (i.e., variances), it is found that the former grows considerably faster than the latter; thus, systematic errors eventually dominate. The present findings facilitate the choice of the most suitable stochastic method for a specific PBE a priori in order to balance numerical precision and efficiency. | Keywords: | Aerosol dynamics Population balance equations Smoluchowski equation Stochastic methods Stochastic variance Weighted flow algorithm |
Publisher: | Elsevier Inc. | Journal: | Applied mathematical modelling | EISSN: | 0307-904X | DOI: | 10.1016/j.apm.2019.11.045 | Rights: | © 2019 Elsevier Inc. All rights reserved. © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/. The following publication Zhou, K., Jiang, X., & Chan, T. L. (2020). Error analysis in stochastic solutions of population balance equations. Applied Mathematical Modelling, 80, 531-552 is available at https://doi.org/10.1016/j.apm.2019.11.045. |
Appears in Collections: | Journal/Magazine Article |
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Jiang_Error_Analysis_Stochastic.pdf | Pre-Published version | 1.43 MB | Adobe PDF | View/Open |
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