Technical Report 47, c4e-Preprint Series, Cambridge
Weighted particle methods for the Smoluchowski coagulation equation
ref: Technical Report 47, c4e-Preprint Series, Cambridge
The Smoluchowski coagulation with additional linear terms is formulated on an explicitly weighted space. The use of such a space extends the ideas behind the mass flow algorithm [A. Eibeck and W. Wagner, Ann. Appl. Prob. (2001) 11:1137-1165] and allows the derivation of a range of new stochastic particle algorithms. Two such algorithms, which seem particularly natural, are implemented and successfully validated. The weighted algorithms are then compared to each other and to a version direct simulation algorithm, which uses particle doubling as a variance reduction technique. One weighted algorithm is found to consistently outperform the other by a significant amount. Applications for which the better weighted algorithm outperforms direct simulation are demonstrated, along with situations where the converse is true.
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