  A novel a priori Monte Carlo (APMC) algorithm is proposed to accurately
simulate the molecules absorbed at spherical receiver(s) with low computational
complexity in diffusion-based molecular communication (MC) systems. It is
demonstrated that the APMC algorithm achieves high simulation efficiency since
by using this algorithm, the fraction of molecules absorbed for a relatively
large time step length precisely matches the analytical result. Therefore, the
APMC algorithm overcomes the shortcoming of the existing refined Monte Carlo
(RMC) algorithm which enables accurate simulation for a relatively small time
step length only. Moreover, for the RMC algorithm, an expression is proposed to
quickly predict the simulation accuracy as a function of the time step length
and system parameters, which facilitates the choice of simulation time step for
a given system. Furthermore, a rejection threshold is proposed for both the RMC
and APMC algorithms to significantly save computational complexity while
causing an extremely small loss in accuracy.
