dorsal/arxiv
View SchemaSpatially Distributed Stochastic Systems: equation-free and equation-assisted preconditioned computation
| Authors | Liang Qiao, Radek Erban, C. T. Kelley, Ioannis G. Kevrekidis |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0606006 |
| URL | https://arxiv.org/abs/q-bio/0606006 |
| DOI | 10.1063/1.2372492 |
Abstract
Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer scale, atomistic models, and using suitable averaging, is often a challenging task; approximate PDEs are typically obtained through mathematical closure procedures (e.g. mean-field approximations). In this paper, we show how such approximate macroscopic PDEs can be exploited in constructing preconditioners to accelerate stochastic simulations for spatially distributed particle-based process models. We illustrate how such preconditioning can improve the convergence of equation-free coarse-grained methods based on coarse timesteppers. Our model problem is a stochastic reaction-diffusion model capable of exhibiting Turing instabilities.
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"abstract": "Spatially distributed problems are often approximately modelled in terms of\npartial differential equations (PDEs) for appropriate coarse-grained quantities\n(e.g. concentrations). The derivation of accurate such PDEs starting from finer\nscale, atomistic models, and using suitable averaging, is often a challenging\ntask; approximate PDEs are typically obtained through mathematical closure\nprocedures (e.g. mean-field approximations). In this paper, we show how such\napproximate macroscopic PDEs can be exploited in constructing preconditioners\nto accelerate stochastic simulations for spatially distributed particle-based\nprocess models. We illustrate how such preconditioning can improve the\nconvergence of equation-free coarse-grained methods based on coarse\ntimesteppers. Our model problem is a stochastic reaction-diffusion model\ncapable of exhibiting Turing instabilities.",
"arxiv_id": "q-bio/0606006",
"authors": [
"Liang Qiao",
"Radek Erban",
"C. T. Kelley",
"Ioannis G. Kevrekidis"
],
"categories": [
"q-bio.QM",
"physics.comp-ph",
"quant-ph"
],
"doi": "10.1063/1.2372492",
"title": "Spatially Distributed Stochastic Systems: equation-free and equation-assisted preconditioned computation",
"url": "https://arxiv.org/abs/q-bio/0606006"
},
"schema_id": "dorsal/arxiv",
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