Stochastic diffusion processes on Cartesian meshes

Diffusion of molecules is simulated stochastically by letting them jump between voxels in a Cartesian mesh. The jump coefficients are first derived using finite difference, finite element, and finite volume approximations of the Laplacian on the mesh. An alternative is to let the first exit time for...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2016-03, Vol.294, p.1-11
Main Authors: Meinecke, Lina, Lötstedt, Per
Format: Article
Language:English
Subjects:
Approximation
Cartesian
Cartesian mesh
Computer simulation
Diffusion
Finite element method
Mathematical analysis
Mathematical models
Probability theory
Stochastic simulation
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Summary:Diffusion of molecules is simulated stochastically by letting them jump between voxels in a Cartesian mesh. The jump coefficients are first derived using finite difference, finite element, and finite volume approximations of the Laplacian on the mesh. An alternative is to let the first exit time for a molecule in random walk in a voxel define the jump coefficient. Such coefficients have the advantage of always being non-negative. These four different ways of obtaining the diffusion propensities are compared theoretically and in numerical experiments. A finite difference and a finite volume approximation generate the most accurate coefficients.
ISSN:0377-0427
1879-1778
1879-1778
DOI:10.1016/j.cam.2015.07.035