title: Stochastic diffusion processes on Cartesian meshes.
abstract: 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.
authors.affiliation: Division of Scientific Computing, Department of Information Technology Uppsala University, P. O. Box 337, SE-75105 Uppsala, Sweden.
authors.forename: Lina
authors.initials: L
authors.lastname: Meinecke
authors.affiliation: Division of Scientific Computing, Department of Information Technology Uppsala University, P. O. Box 337, SE-75105 Uppsala, Sweden.
authors.forename: Per
authors.initials: P
authors.lastname: Lötstedt
keywords: 65C05; 65C35; 92C05; Cartesian mesh; diffusion; stochastic simulation