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KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
2009 (English)In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 8, no 1, 46-68 p.Article in journal (Refereed) Published
Abstract [en]

A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate equation. A stochastic simulation algorithm is used to obtain an exact realization of the process at the mesoscopic scale (in parallel). The underlying stochastic description is a jump process driven by the Poisson measure. A convergence result in this arguably difficult setting is established, suggesting that a homogenization of the solution is advantageous. We devise a simple but highly general such technique. Three numerical experiments on models representative to the field of computational systems biology illustrate the method. For nonstiff problems, it is shown that the method is able to quickly converge even when stochastic effects are present. For stiff problems, we are instead able to obtain fast convergence to a homogenized solution. Overall, the method builds an attractive bridge between, on the one hand, macroscopic deterministic scales and, on the other hand, mesoscopic stochastic ones. This construction is clearly possible to apply also to stochastic models within other fields.

Place, publisher, year, edition, pages
2009. Vol. 8, no 1, 46-68 p.
Keyword [en]
parareal, reaction rate equation, jump process, homogenization, next reaction method, stochastic reaction-diffusion
National Category
URN: urn:nbn:se:kth:diva-32210DOI: 10.1137/080733723ISI: 000271722900003ScopusID: 2-s2.0-70350274338OAI: diva2:409865
QC 20110411Available from: 2011-04-11 Created: 2011-04-11 Last updated: 2011-04-11Bibliographically approved

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Engblom, Stefan
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Numerical Analysis, NA
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