期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 31, 期 3, 页码 1774-1797出版社
SIAM PUBLICATIONS
DOI: 10.1137/080721388
关键词
master equation; diffusion; reaction rate equations; hybrid method; finite element method; unstructured mesh
资金
- Swedish Foundation for Strategic Research
- Swedish National Graduate School in Mathematics and Computing
We model stochastic chemical systems with diffusion by a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic level, the master equation for a well stirred chemical system is combined with a discretized Brownian motion in space to obtain the reaction-diffusion master equation. The space is covered in our method by an unstructured mesh, and the diffusion coefficients on the mesoscale are obtained from a finite element discretization of the Laplace operator on the macroscale. The resulting method is a flexible hybrid algorithm in that the diffusion can be handled either on the meso- or on the macroscale level. The accuracy and the efficiency of the method are illustrated in three numerical examples inspired by molecular biology.
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