Parallelization, processor communication and error analysis in lattice kinetic Monte Carlo

Arampatzis, Giorgos; Katsoulakis, Markos A.; Plecháč, Petr

doi:10.48550/arxiv.1208.1049

Cited by 1 publication

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“…For the existing approximate and hybrid methods for the RDME, splitting the physics (reaction and diffusion) is necessary. For parallel implementations, another possibility is to split the computational grid into blocks, as proposed by [14], where the error introduced by operator splitting at block boundaries was analyzed. Our analysis here is different since it applies to the case of splitting the reaction and diffusion operators.…”

Section: Introductionmentioning

confidence: 99%

Local error estimates for adaptive simulation of the reaction–diffusion master equation via operator splitting

Hellander

Lawson

Drawert

et al. 2014

Journal of Computational Physics

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The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps are adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the Diffusive Finite-State Projection (DFSP) method, to incorporate temporal adaptivity.

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Section: Introductionmentioning

confidence: 99%