2014.72: Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems
2014.72: Simon Cotter, Tomas Vejchodsky and Radek Erban (2013) Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems. SIAM Journal on Scientific Computing, 35 (1).
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Stochastic models of chemical systems are often analyzed 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 nonnegligible 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 stationary probability density. Numerical examples demonstrate that the presented method is competitive with existing a posteriori methods.
|Subjects:||MSC 2000 > 65 Numerical analysis|
|Deposited By:||Dr Simon L Cotter|
|Deposited On:||18 December 2014|