Binary interaction algorithms for the simulation of flocking and swarming dynamics

Giacomo Albi, Lorenzo Pareschi
(04/03/2012 Multiscale Modeling and Simulation 11, (2013), 1-29.  arXiv:1203.0721)

Microscopic models of flocking and swarming takes in account large numbers of interacting individuals. Numerical resolution of large flocks implies huge computational costs. Typically for N interacting individuals we have a cost of O(N2). We tackle the problem numerically by considering approximated binary interaction dynamics described by kinetic equations and simulating such equations by suitable stochastic methods.
This approach permits to compute approximate solutions as functions of a small scaling parameter at a reduced complexity of O(N) operations. Several numerical results show the efficiency of the algorithms proposed.

Flocking behavior in birds (top) and mill dynamics in fishes (bottom)

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