Presentation Details
Numerical Model Reduction in Computational Homogenization of Transient Heat Flow
Wednesday, 11 Oct 2017; 17:00 - 17:20 in room 7.02
In Session:
MS16-2: Reduced Order Models for Multiscale and Multiphysics Problems (Show complete Mini Symposium)
Wednesday, 11 Oct 2017; 16:00 - 18:00 in room 7.02
Show complete Session
1st and presenting Author
Fredrik Ekre
Department of Industrial and Materials Science
Chalmers University of Technology
Gothenburg, Sweden
Department of Industrial and Materials Science
Chalmers University of Technology
Gothenburg, Sweden
2nd Author
Fredrik Larsson
Department of Industrial and Materials Science
Chalmers University of Technology
Gothenburg, Sweden
Department of Industrial and Materials Science
Chalmers University of Technology
Gothenburg, Sweden
3rd Author
Kenneth Runesson
Department of Industrial and Materials Science
Chalmers University of Technology
Gothenburg, Sweden
Department of Industrial and Materials Science
Chalmers University of Technology
Gothenburg, Sweden
Micro Abstract:
We present a two-scale finite element (FE$^2$) formulation for transient linear heat flow. For the sub-scale problem, we use spectral decomposition in order to to establish a reduced basis. We discuss a few methods to estimate the error introduced by the reduction, and in particular we aim for explicit bounds on the error in (i) energy norm and (ii) an arbitrary ``quantity of interest''. Numerical results confirm the validity of the computed error bounds.