Adaptive finite element method assisted by stochastic simulation of chemical systems
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 refinemen...
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| Format: | Journal article |
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2011
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| _version_ | 1826272687098429440 |
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| author | Cotter, S Vejchodsky, T Erban, R |
| author_facet | Cotter, S Vejchodsky, T Erban, R |
| author_sort | Cotter, S |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T22:16:31Z |
| format | Journal article |
| id | oxford-uuid:538f0d7a-7059-4395-b9a7-62a9d6bc2384 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T22:16:31Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:538f0d7a-7059-4395-b9a7-62a9d6bc23842022-03-26T16:32:28ZAdaptive finite element method assisted by stochastic simulation of chemical systemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:538f0d7a-7059-4395-b9a7-62a9d6bc2384Mathematical Institute - ePrints2011Cotter, SVejchodsky, TErban, RStochastic 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. |
| spellingShingle | Cotter, S Vejchodsky, T Erban, R Adaptive finite element method assisted by stochastic simulation of chemical systems |
| title | Adaptive finite element method assisted by stochastic simulation of chemical systems |
| title_full | Adaptive finite element method assisted by stochastic simulation of chemical systems |
| title_fullStr | Adaptive finite element method assisted by stochastic simulation of chemical systems |
| title_full_unstemmed | Adaptive finite element method assisted by stochastic simulation of chemical systems |
| title_short | Adaptive finite element method assisted by stochastic simulation of chemical systems |
| title_sort | adaptive finite element method assisted by stochastic simulation of chemical systems |
| work_keys_str_mv | AT cotters adaptivefiniteelementmethodassistedbystochasticsimulationofchemicalsystems AT vejchodskyt adaptivefiniteelementmethodassistedbystochasticsimulationofchemicalsystems AT erbanr adaptivefiniteelementmethodassistedbystochasticsimulationofchemicalsystems |