Thermal Conductivity Calculation with the Molecular Dynamics Direct Method II: Improving the Computational Efficiency
PC Howell, JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE, 8, 2144-2154 (2011).
The molecular dynamics non-equilibrium direct method is a well- established way of predicting thermal conductivity K, but in good thermal conductors such as crystalline semi-conductors it can yield unacceptably large statistical uncertainties in the extrapolation to a bulk system, K infinity.We show how to extract more information from the simulation data in order to reliably calculate tight confidence intervals for K infinity. We prove that the measurement error in K for a single simulation of size L-i and duration D-i is proportional to (DiLi3)(-1/2), so that using very large simulations reduces the error more efficiently than using very long durations, as we confirm explicitly with molecular dynamics data. By considering the error propagation we derive an algorithm to determine the optimal set of Li, Di) which minimizes the probable measurement error in K infinity for given total computational effort. Overall, these improvements reduce by an order of magnitude the computational effort required to calculate K infinity with a given statistical uncertainty.
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