@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.}
}