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 |
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Pages (from-to) | 535-554 |
Number of pages | 20 |
Journal | Computational Mechanics |
Volume | 63 |
Issue number | 3 |
DOIs | |
Publication status | Published - 15 Mar 2019 |
Keywords
- Computational homogenisation
- Micro-mechanics
- Model reduction
- Multi-scale analysis
- Numerical integration
- Wavelets