Combining spectral and POD modes to improve error estimation of numerical model reduction for porous media
Journal article, 2022

Numerical model reduction (NMR) is used to solve the microscale problem that arises from computational homogenization of a model problem of porous media with displacement and pressure as unknown fields. The reduction technique and an associated error estimator for the NMR error have been presented in prior work, where both spectral decomposition (SD) and proper orthogonal decomposition (POD) were used to construct the reduced basis. It was shown that the POD basis performs better w.r.t. minimizing the residual, but the SD basis has some advantageous properties for the estimator. Since it is the estimated error that will govern the error control, the most efficient procedure is the one that results in the lowest error bound. The main contribution of this paper is further development of the previous work with a proposed combined basis constructed using both SD and POD modes together with an adaptive mode selection strategy. The performance of the combined basis is compared to (i) the pure SD basis and (ii) the pure POD basis via numerical examples. The examples show that it is possible to find a combination of SD/POD modes which is improved, i.e. it yields a smaller estimate, compared to the cases of pure SD or pure POD.

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

Ralf Jänicke

Chalmers, Industrial and Materials Science, Material and Computational Mechanics

Computational Mechanics

0178-7675 (ISSN) 1432-0924 (eISSN)

Vol. 69 3 767-786

Numerical model reduction for computational homogenization of polycrystals

Swedish Research Council (VR) (2019-05080), 2020-01-01 -- 2023-12-31.

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

Swedish Research Council (VR) (2015-05422), 2016-01-01 -- 2019-12-31.

Subject Categories

Computational Mathematics

Control Engineering

Signal Processing

DOI

10.1007/s00466-021-02113-2

More information

Latest update

4/5/2022 5