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

4 Citations (Scopus)
38 Downloads (Pure)

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 languageEnglish
Pages (from-to)535-554
Number of pages20
JournalComputational Mechanics
Volume63
Issue number3
DOIs
Publication statusPublished - 15 Mar 2019

Keywords

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

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