Numerical Model Reduction with error estimation for computational homogenization of non-linear consolidation
Journal article, 2022

Numerical Model Reduction (NMR) is adopted for solving the non-linear microscale problem that arises from computational homogenization of a model problem of porous media with displacement and pressure as unknown fields. A reduced basis is obtained for the pressure field using Proper Orthogonal Decomposition and the pertinent displacement basis is obtained using Nonuniform Transformation Field Analysis. An explicit, fully computable, a posteriori error estimator is derived based on the linearized error equation for quantification of the NMR error in terms of a suitably chosen energy norm. The performance of the error estimates is demonstrated via a set of numerical examples with varying load amplitudes.

Model reduction

Computational homogenization

Error control

Author

Fredrik Ekre

Chalmers, Industrial and Materials Science, Material and Computational Mechanics

Fredrik Larsson

Chalmers, Industrial and Materials Science, Material and Computational Mechanics

Kenneth Runesson

Chalmers, Industrial and Materials Science, Material and Computational Mechanics

R. Janicke

Technische Universität Braunschweig

Computer Methods in Applied Mechanics and Engineering

0045-7825 (ISSN)

Vol. 389 114334

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Subject Categories

Applied Mechanics

Computational Mathematics

Control Engineering

DOI

10.1016/j.cma.2021.114334

More information

Latest update

3/25/2022