Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems

Details Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems

2011-11-09

arxiv.org/abs/1111.2265v1

Mathematics

Numerical Analysis

19 pages, 14 figures

Scientific paper

Stochastic models of chemical systems are often analysed by solving the corresponding Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with non-negligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the probability density.

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