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Filters for improvement of multiscale data from atomistic simulations. (English) Zbl 1372.35297

Most problems in science and engineering involve interactions between multiple spatial and temporal scales that may differ by several orders of magnitude. Despite this multi-scale behavior, the systems can still be simulated in many cases at a single scale, this allows for effective and efficient numerical simulation of large physical systems.
Among various approaches to achieve this purpose, one can try to combine continuum and atomistic approximations. In this case, the dominant computational cost of the model typically consists of the atomistic components. In this work, the authors demonstrate the effectiveness of spectral filtering for improving the quality of continuum scale data computed from atomistic simulations in a multi-scale model. The accuracy gains from filtering allow for running atomistic simulations with fewer particles for a shorter duration to reach the same desired level of accuracy as a more expensive atomistic simulations. This lowers the primary cost of the multi-scale method and leads to faster simulations for a desired overall accuracy.

MSC:

35Q70 PDEs in connection with mechanics of particles and systems of particles
35Q84 Fokker-Planck equations
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs

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