@TechReport{ it:2014-012,
author = {Per L{\"o}tstedt and Lina Meinecke},
title = {Simulation of Stochastic Diffusion via First Exit Times},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2014},
number = {2014-012},
month = apr,
abstract = {In molecular biology it is of interest to simulate
diffusion stochastically. In the mesoscopic model we
partition a biological cell into voxels in an unstructured
mesh. In each voxel the number of molecules is recorded at
each time step and molecules can jump between neighboring
voxels to model diffusion. The jump rates are computed by
discretizing the diffusion equation on the unstructured
mesh. If the mesh is of poor quality, due to a complicated
cell geometry, standard discretization methods can generate
negative jump coefficients, which no longer allows the
interpretation as the probability to leave the subvolume.
We propose a method based on the mean first exit time of a
molecule from a subvolume, which guarantees positive jump
coefficients. Two approaches to exit times, a global and a
local one, are presented and tested in simulations with
diffusion and chemical reactions on meshes of different
quality in two dimensions.}
}