Wavelet based reduced order models for microstructural analyses

Rody A. van Tuijl, Cale Harnish, Karel Matouš, Joris J.C. Remmers, Marc G.D. Geers (Corresponding author)

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)

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.

LanguageEnglish
Pages535-554
JournalComputational Mechanics
Volume63
Issue number3
DOIs
StatePublished - 2019

Fingerprint

Reduced Order Model
Wavelets
Reduced-order Modeling
System of equations
Computational Cost
Integrand
Homogenization
Dimensionality
Costs
Computational complexity
Computational Complexity
Discretization
Model

Keywords

  • Computational homogenisation
  • Micro-mechanics
  • Model reduction
  • Multi-scale analysis
  • Numerical integration
  • Wavelets

Cite this

van Tuijl, Rody A. ; Harnish, Cale ; Matouš, Karel ; Remmers, Joris J.C. ; Geers, Marc G.D./ Wavelet based reduced order models for microstructural analyses. In: Computational Mechanics. 2019 ; Vol. 63, No. 3. pp. 535-554
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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, 2019, p. 535-554.

Research output: Contribution to journalArticleAcademicpeer-review

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