A posteriori error estimation for numerical model reduction in computational homogenization of porous media
Journal article, 2020

Numerical model reduction is adopted for solving the microscale problem that arizes 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 (i) spectral decomposition (SD) and (ii) proper orthogonal decomposition (POD). This strategy has been used in previous work—the main contribution of this article is the extension with an a posteriori estimator for assessing the error in (i) energy norm and in (ii) a given quantity of interest. The error estimator builds on previous work by the authors; the novelty presented in this article is the generalization of the estimator to a coupled problem, and, more importantly, to accommodate the estimator for a POD basis rather than the SD basis. Guaranteed, fully computable and low-cost bounds are derived and the performance of the error estimates is demonstrated via numerical results.

error control

computational homogenization

model reduction

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

Ralf Jänicke

Chalmers, Industrial and Materials Science, Material and Computational Mechanics

International Journal for Numerical Methods in Engineering

0029-5981 (ISSN) 1097-0207 (eISSN)

Vol. 121 23 5350-5380

Numerisk modellreduktion vid beräkningsbaserad homogenisering av deformation och strömning i porösa medier

Swedish Research Council (VR), 2016-01-01 -- 2019-12-31.

Subject Categories

Computational Mathematics

Control Engineering

Signal Processing

DOI

10.1002/nme.6504

More information

Latest update

11/5/2020