Commun. Comput. Phys., 13 (2013), pp. 958-984.

Efficient Sampling in Event-Driven Algorithms for Reaction-Diffusion Processes

Mohammad Hossein Bani-Hashemian 1, Stefan Hellander 1, Per Lotstedt 1*

1 Division of Scientific Computing, Department of Information Technology, Uppsala University, P. O. Box 337, SE-75105 Uppsala, Sweden.

Received 27 October 2011; Accepted (in revised version) 23 March 2012
Available online 21 September 2012


In event-driven algorithms for simulation of diffusing, colliding, and reacting particles, new positions and events are sampled from the cumulative distribution function (CDF) of a probability distribution. The distribution is sampled frequently and it is important for the efficiency of the algorithm that the sampling is fast. The CDF is known analytically or computed numerically. Analytical formulas are sometimes rather complicated making them difficult to evaluate. The CDF may be stored in a table for interpolation or computed directly when it is needed. Different alternatives are compared for chemically reacting molecules moving by Brownian diffusion in two and three dimensions. The best strategy depends on the dimension of the problem, the length of the time interval, the density of the particles, and the number of different reactions.

AMS subject classifications: 65C05, 65C35, 82C80
PACS: 02.50.Ey, 02.70.Uu, 83.10.Rs, 87.10.Rt
Key words: Event-driven algorithm, chemical reactions, diffusion, efficient sampling.

*Corresponding author.
Email: (M. H. Bani-Hashemian), (S. Hellander), (P. Lotstedt)

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