Hybrid discrete/continuum algorithms for stochastic reaction networks

Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; Najm, Habib N.

doi:10.1016/j.jcp.2014.10.026

Hybrid discrete/continuum algorithms for stochastic reaction networks

Journal Article · Wed Oct 22 00:00:00 EDT 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2014.10.026· OSTI ID:1121280

Safta, Cosmin ^[1]; Sargsyan, Khachik ^[1]; ^[1]; ^[1]

Sandia National Lab. (SNL-CA), Livermore, CA (United States)

Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components to avoid negative probability values. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. As a result, the performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1121280

Alternate ID(s):: OSTI ID: 22382165
OSTI ID: 1246992

Report Number(s):: SAND--2013-10187J; 485627

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 281; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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