Mathematics – Numerical Analysis
Scientific paper
2012-04-03
Mathematics
Numerical Analysis
30 pages, 1 figure, cleaned up the first version
Scientific paper
Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. Such processes spend much of their time about the minima of an underlying potential, occasionally transitioning into different basins of attraction. The essential idea of parallel replica dynamics is that the exit time distribution from a given well for a single process can be approximated by the minimum of the exit time distributions of N independent identical processes, each run for only 1/N-th the amount of time. While promising, this leads to a series of numerical analysis questions about the convergence of the exit distributions. Following up on the recent work in Le Bris et al., we prove a refined result on the error in the decorrelation stage of the algorithm and calculate how this error cascades into the parallel step. Furthermore, we study a dephasing mechanism, and prove that it will successfully complete.
Luskin Mitchell
Simpson Gideon
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