The Mathematical Institute, University of Oxford, Eprints Archive

Adaptive finite element method assisted by stochastic simulation of chemical systems

Cotter, S. L. and Vejchodsky, T. and Erban, R. (2011) Adaptive finite element method assisted by stochastic simulation of chemical systems. SIAM Journal on Scientific Computing . (Submitted)

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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.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1467
Deposited By:Peter Hudston
Deposited On:22 Feb 2012 07:53
Last Modified:22 Feb 2012 07:53

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