Improving the convergence behavior of hierarchical atomistic-to-continuum multiscale models using stochastic approximation

Patrick Wurm*, Manfred Hannes Ulz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)565–566
JournalProceedings in Applied Mathematics and Mechanics
Issue number1
Publication statusPublished - 2016

Fields of Expertise

  • Advanced Materials Science

Cite this