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Improving the convergence behavior of hierarchical atomistic‐to‐continuum multiscale models using stochastic approximation
Author(s) -
Wurm Patrick,
Ulz Manfred H.
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610271
Subject(s) - microscale chemistry , convergence (economics) , statistical physics , computer science , mathematical optimization , mathematics , scale (ratio) , noise (video) , work (physics) , thermal , algorithm , artificial intelligence , physics , mathematics education , meteorology , quantum mechanics , economics , image (mathematics) , thermodynamics , economic growth
Abstract The aim of this work is to provide an improved information exchange in hierarchical atomistic‐to‐continuum models by applying stochastic approximation (SA) methods. A typical hierarchical two‐scale model is chosen and enhanced. Due to very high computational cost, the microscale of this model may not be sufficiently sampled in practical calculations; a problem, which was recently investigated in [1]. As a consequence, the microscale produces noise‐corrupted output due to thermal effects. The thermal noise creates a setting that shows remarkable resemblance to the Robbins‐Monro iteration scheme known from SA. This resemblance justifies the use of two averaging strategies known to improve the convergence behavior of SA schemes under certain, fairly general, conditions. No additional computational cost is introduced by this approach. The proposed strategies implemented in the multiscale model are tested on a numerical example. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)