Adaptive Finite Element Method Assisted by Stochastic Simulation of\n Chemical Systems

2011/11/09 by Simon L. Cotter, Cotter, Simon L., Tomáš Vejchodský +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Decision Sciences · #Advanced Multi-Objective Optimization Algorithms #FOS: Mathematics #Gene Regulatory Network Analysis #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.1111.2265

openalex publication_date 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Stochastic models of chemical systems are often analysed by solving the\ncorresponding Fokker-Planck equation which is a drift-diffusion partial\ndifferential equation for the probability distribution function. Efficient\nnumerical solution of the Fokker-Planck equation requires adaptive mesh\nrefinements. In this paper, we present a mesh refinement approach which makes\nuse of a stochastic simulation of the underlying chemical system. By observing\nthe stochastic trajectory for a relatively short amount of time, the areas of\nthe state space with non-negligible probability density are identified. By\nrefining the finite element mesh in these areas, and coarsening elsewhere, a\nsuitable mesh is constructed and used for the computation of the probability\ndensity.\n

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