Abstract
This paper proposes a novel method to accurately and efficiently reduce a microstructural mechanical model using a wavelet based discretisation. The model enriches a standard reduced order modelling (ROM) approach with a wavelet representation. Although the ROM approach reduces the dimensionality of the system of equations, the computational complexity of the integration of the weak form remains problematic. Using a sparse wavelet representation of the required integrands, the computational cost of the assembly of the system of equations is reduced significantly. This wavelet-reduced order model (W-ROM) is applied to the mechanical equilibrium of a microstructural volume as used in a computational homogenisation framework. The reduction technique however is not limited to micro-scale models and can also be applied to macroscopic problems to reduce the computational costs of the integration. For the sake of clarity, the W-ROM will be demonstrated using a one-dimensional example, providing full insight in the underlying steps taken.
| Original language | English |
|---|---|
| Pages (from-to) | 535-554 |
| Number of pages | 20 |
| Journal | Computational Mechanics |
| Volume | 63 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 15 Mar 2019 |
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Keywords
- Computational homogenisation
- Micro-mechanics
- Model reduction
- Multi-scale analysis
- Numerical integration
- Wavelets
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Wavelet based reduced order models for microstructural analyses. / van Tuijl, Rody A.; Harnish, Cale; Matouš, Karel; Remmers, Joris J.C.; Geers, Marc G.D. (Corresponding author).
In: Computational Mechanics, Vol. 63, No. 3, 15.03.2019, p. 535-554.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - Wavelet based reduced order models for microstructural analyses
AU - van Tuijl, Rody A.
AU - Harnish, Cale
AU - Matouš, Karel
AU - Remmers, Joris J.C.
AU - Geers, Marc G.D.
PY - 2019/3/15
Y1 - 2019/3/15
N2 - This paper proposes a novel method to accurately and efficiently reduce a microstructural mechanical model using a wavelet based discretisation. The model enriches a standard reduced order modelling (ROM) approach with a wavelet representation. Although the ROM approach reduces the dimensionality of the system of equations, the computational complexity of the integration of the weak form remains problematic. Using a sparse wavelet representation of the required integrands, the computational cost of the assembly of the system of equations is reduced significantly. This wavelet-reduced order model (W-ROM) is applied to the mechanical equilibrium of a microstructural volume as used in a computational homogenisation framework. The reduction technique however is not limited to micro-scale models and can also be applied to macroscopic problems to reduce the computational costs of the integration. For the sake of clarity, the W-ROM will be demonstrated using a one-dimensional example, providing full insight in the underlying steps taken.
AB - This paper proposes a novel method to accurately and efficiently reduce a microstructural mechanical model using a wavelet based discretisation. The model enriches a standard reduced order modelling (ROM) approach with a wavelet representation. Although the ROM approach reduces the dimensionality of the system of equations, the computational complexity of the integration of the weak form remains problematic. Using a sparse wavelet representation of the required integrands, the computational cost of the assembly of the system of equations is reduced significantly. This wavelet-reduced order model (W-ROM) is applied to the mechanical equilibrium of a microstructural volume as used in a computational homogenisation framework. The reduction technique however is not limited to micro-scale models and can also be applied to macroscopic problems to reduce the computational costs of the integration. For the sake of clarity, the W-ROM will be demonstrated using a one-dimensional example, providing full insight in the underlying steps taken.
KW - Computational homogenisation
KW - Micro-mechanics
KW - Model reduction
KW - Multi-scale analysis
KW - Numerical integration
KW - Wavelets
UR - http://www.scopus.com/inward/record.url?scp=85050911290&partnerID=8YFLogxK
U2 - 10.1007/s00466-018-1608-3
DO - 10.1007/s00466-018-1608-3
M3 - Article
AN - SCOPUS:85050911290
VL - 63
SP - 535
EP - 554
JO - Computational Mechanics
JF - Computational Mechanics
SN - 0178-7675
IS - 3
ER -