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arXiv · 1111.2265

Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems

Simon L. Cotter·Tomas Vejchodsky·Radek Erban
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Abstract

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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Simon L. Cotter, Tomas Vejchodsky, Radek Erban. 2011-11-09. Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems. https://arxiv.org/abs/1111.2265

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