Mathematics – Numerical Analysis
Scientific paper
2008-08-28
Multiscale Model. Simul. 8(1):46--68 (2009)
Mathematics
Numerical Analysis
30 pages, 7 figures, extended abstract to appear in proceedings of ICNAAM 2008
Scientific paper
10.1137/080733723
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 equations. 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 non-stiff 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.
No associations
LandOfFree
Parallel in Time Simulation of Multiscale Stochastic Chemical Kinetics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Parallel in Time Simulation of Multiscale Stochastic Chemical Kinetics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Parallel in Time Simulation of Multiscale Stochastic Chemical Kinetics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-327146