Effective Geometry Monte Carlo: A Fast and Reliable Simulation Framework for Molecular Communication

Angular information of messenger molecules absorbed by a receiver plays a significant role in the molecular communication literature. In this paper, we address systematic biases and random errors in the angular information stemming from finite step sizes encountered in traditional simulation frameworks. We show that the effective geometry Monte Carlo (EG-MC) simulation algorithm, which modifies the geometry of the receiver, is a fast and reliable simulation method to overcome these systematic biases. We motivate our approach for a 3-D unbounded diffusion channel consisting of an absorbing receiver and a point transmitter. We show that, with minimal computational cost, the angular distribution of the absorbed particles by the receiver can be precisely obtained using EG-MC algorithm. Afterwards, we demonstrate the accuracy of our simulations and compare them to traditional methods. Then, we comment on the range of applicability of our results. Finally, we consider two simple cases with constant flow and show that the EG-MC algorithm gives consistent results even when the drift is dominant over diffusion. We conclude with further remarks on the computational efficiency and reliability of the EG-MC method.