The two-regime method (TRM) has been recently developed for optimizing stochastic reaction-diffusion simulations [M. Flegg, J. Chapman, and R. Erban, J. Roy. Soc. Interface, 9 (2012), pp. 859-868]. It is a multiscale (hybrid) algorithm which uses stochastic reaction-diffusion models with different levels of detail in different parts of the computational domain. The coupling condition on the interface between different modeling regimes of the TRM was previously derived for onedimensional models. In this paper, the TRM is generalized to higher dimensional reaction-diffusion systems. Coupling Brownian dynamics models with compartment-based models on regular (square) two-dimensional lattices is studied in detail. In this case, the interface between different modeling regimes contains either flat parts or right-angle corners. Both cases are studied in the paper. For flat interfaces, it is shown that the one-dimensional theory can be used along the line perpendicular to the TRM interface. In the direction tangential to the interface, two choices of the TRM parameters are presented. Their applicability depends on the compartment size and the time step used in the molecular-based regime. The two-dimensional generalization of the TRM is also discussed in the case of corners. © 2014 Society for Industrial and Applied Mathematics.
|Original language||English (US)|
|Number of pages||1|
|Journal||SIAM Journal on Scientific Computing|
|State||Published - Jan 2014|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This work was supported by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement No. 239870 and in part by Award No. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST).The fourth author's work was also supported by a Royal Society University Research Fellowship; by a Nicholas Kurti Junior Fellowship from Brasenose College, University of Oxford; and by the Philip Leverhulme Prize from the Leverhulme Trust.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.