On error controlled numerical model reduction in FE2-analysis of transient heat flow
Journal article, 2019

Numerical model reduction is exploited for solving the two-scale problem that arises from the computational homogenization of a model problem of transient heat flow. Since the problem is linear, an orthogonal basis is obtained via the method of spectral decomposition. A key feature is the construction of a symmetrized version of the space-time variational format, by which it is possible to estimate the error from the model reduction in (i) energy norm and in (ii) a given quantity of interest. In previous work by the authors, this strategy has been applied to the solution of an individual representative volume element problem, whereas the error transport to the macroscale problem in the finite element squared (FE2) approach was ignored. In this paper, such transport of error is included in the error estimate. It is remarkable that it is (still) possible to obtain guaranteed bounds on the error, as compared to the fully resolved discrete finite element problem, while using only the reduced basis and with minor extra computational effort. The performance of the error estimates is demonstrated via numerical results, whereby the subscale is modeled in three dimensions, whereas the macroscale problem is either one or two dimensional.

error control

model reduction

computational homogenization

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

International Journal for Numerical Methods in Engineering

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

Vol. 119 1 38-73

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

Probability Theory and Statistics

Control Engineering

DOI

10.1002/nme.6041

More information

Latest update

7/15/2019