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Derivation of Higher-Order Terms in FFT-Based Numerical Homogenization

  • Felix DietrichEmail author
  • Dennis Merkert
  • Bernd Simeon
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)

Abstract

In this paper, we first introduce the reader to the Basic Scheme of Moulinec and Suquet in the setting of quasi-static linear elasticity, which takes advantage of the fast Fourier transform on homogenized microstructures to accelerate otherwise time-consuming computations. By means of an asymptotic expansion, a hierarchy of linear problems is then derived, whose solutions are looked at in detail. It is highlighted how these generalized homogenization problems depend on each other. We extend the Basic Scheme to fit this new problem class and give some numerical results for the first two problem orders.

Notes

Acknowledgements

The collaboration with H. Andrä, M. Kabel and M. Schneider, Fraunhofer ITWM Kaiserslautern, is gratefully acknowledged.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Technische Universität KaiserslauternKaiserslauternGermany

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