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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v6.i4.80
pages 371-392

Adaptive Bridging of Scales in Continuum Modeling Based on Error Control

Fredrik Larsson
Department of Applied Mechanics, Chalmers University of Technology, S-412 96 Gothenburg
Kenneth Runesson
Department of Structural Mechanics Chalmers, University of Technology S-41296 Goteborg, Sweden

ABSTRACT

The common approach of spatial homogenization for resolving strong material heterogeneity is based on complete scale separation. The other extreme approach is to completely resolve the fine scale(s) in the macroscale computation. In this paper, we propose a novel algorithm for scaletransition such that the two extremes presented above are bridged in a "seamless" fashion. An important ingredient is a generalized macrohomogeneity condition. As part of the algorithm, the approach to the subscale modeling is chosen adaptively based on the relation of the macroscale mesh diameter to the typical length scale of the subscale structure. Moreover, the macroscale mesh adaptivity is driven by an estimation of discretization errors, which is an absolutely essential feature. Numerical examples, although quite simple, illustrate the principle and the effectivity of the adaptive procedure.


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