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.
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