Elimination of ringing artifacts by finite-element projection in FFT-based homogenization

@article{Leute2022EliminationOR,
  title={Elimination of ringing artifacts by finite-element projection in FFT-based homogenization},
  author={Richard J. Leute and Martin Ladeck'y and Ali Falsafi and Indre J{\"o}dicke and Ivana Pultarov'a and Jan Zeman and Till Junge and Lars Pastewka},
  journal={J. Comput. Phys.},
  year={2022},
  volume={453},
  pages={110931}
}

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References

SHOWING 1-10 OF 49 REFERENCES
Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems
TLDR
Compared to established Fourier-based methods, the number of convolutions is reduced by FANS, and many numerical examples focusing on convergence properties for both thermal and mechanical problems, including also plasticity, are presented.
A review of nonlinear FFT-based computational homogenization methods
TLDR
A condensed overview of results scattered throughout the literature is provided and guides the reader to the current state of the art in nonlinear computational homogenization methods using the fast Fourier transform.
FFT-based homogenization for microstructures discretized by linear hexahedral elements
TLDR
This work generalizes the FFT‐based homogenization method of Moulinec–Suquet to problems discretized by trilinear hexahedral elements on Cartesian grids and physically nonlinear elasticity problems.
An FFT-based Galerkin method for homogenization of periodic media
Computational homogenization of elasticity on a staggered grid
TLDR
This article proposes to discretize the problem of linear elastic homogenization by finite differences on a staggered grid and introduces fast and robust solvers and reduces the memory consumption of the Moulinec–Suquet algorithms by 50%.
Lippmann‐Schwinger solvers for the computational homogenization of materials with pores
  • M. Schneider
  • Mathematics
    International Journal for Numerical Methods in Engineering
  • 2020
We show that under suitable hypotheses on the nonporous material law and a geometric regularity condition on the pore space, Moulinec‐Suquet's basic solution scheme converges linearly. We also
Numerical artifacts of Fast Fourier Transform solvers for elastic problems of multi-phase materials: their causes and reduction methods
TLDR
An improved composite voxel method by using the level-set technique is proposed, which alleviates the implementation difficulty of the composite v oxel method.
A finite element perspective on nonlinear FFT‐based micromechanical simulations
Fourier solvers have become efficient tools to establish structure–property relations in heterogeneous materials. Introduced as an alternative to the finite element (FE) method, they are based on
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