Stochastic diffusion processes on Cartesian meshes

• Lina Meinecke ^[1] ; Per Lötstedt ^[1]
  1. [1] Uppsala University

     Uppsala University

     Uppsala domkyrkoförs., Suecia

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 294, Nº 1 (1 March 2016), 2016, págs. 1-11
• Idioma: inglés
• DOI: 10.1016/j.cam.2015.07.035
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• Resumen

  • 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.