FILTERS FOR IMPROVEMENT OF MULTISCALE DATA FROM ATOMISTIC SIMULATIONS

DJ Gardnert and DR Reynolds, MULTISCALE MODELING & SIMULATION, 15, 1-28 (2017).

DOI: 10.1137/15M1053785

d Multiscale computational models strive to produce accurate and efficient numerical simulations of systems involving interactions across multiple spatial and temporal scales that typically differ by several orders of magnitude. Some such models utilize a hybrid continuum- atomistic approach combining continuum approximations with first- principles-based atomistic models to capture multiscale behavior. Following the heterogeneous multiscale method framework for developing multiscale computational models, unknown continuum scale data can be computed from an atomistic model. Concurrently coupling the two models requires performing numerous atomistic simulations which can dominate the computational cost of the method. When the resulting continuum data is noisy due to sampling error, stochasticity in the model, or randomness in the initial conditions, filtering can result in significant accuracy gains in the computed multiscale data without increasing the size or duration of the atomistic simulations. In this work, we demonstrate the effectiveness of spectral filtering for increasing the accuracy of noisy multiscale data obtained from atomistic simulations. Moreover, we present a robust and automatic method for closely approximating the optimum level of filtering in the case of additive white noise. The improved accuracy of this filtered simulation data leads to a dramatic computational savings by allowing for shorter and smaller atomistic simulations to achieve the same desired multiscale simulation precision.

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