  In this work, we address the systematic biases and random errors stemming
from finite step sizes encountered in diffusion simulations. We introduce the
Effective Geometry Monte Carlo (EG-MC) simulation algorithm which modifies the
geometry of the receiver. We motivate our approach in a 1D toy model and then
apply our findings to a spherical absorbing receiver in a 3D unbounded
environment. We show that with minimal computational cost, the impulse response
of this receiver can be precisely simulated using EG-MC. Afterwards, we
demonstrate the accuracy of our simulations and give tight constraints on the
single free parameter in EG-MC. Finally, we comment on the range of
applicability of our results. While we present the EG-MC algorithm for the
specific case of molecular diffusion, we believe that analogous methods with
effective geometry manipulations can be utilized to approach a variety of
problems in other branches of physics such as condensed matter physics and
cosmological large scale structure simulations.
