FFT-based homogenization in Python is a numerical software for evaluating guaranteed upper-lower bounds on homogenized properties. The algorithms implemented here are based on the following papers.
- The code now contains tutorials including self-contained implementation of the method based on exact integration.
The basic manual can be found at
or downloaded at
Tutorials can be found in a folder '/tutorial'.
The code is based on the following papers, where you can find more theoretical information.
- J. Zeman, T. W. J. de Geus, J. Vondřejc, R. H. J. Peerlings, and M. G. D. Geers: A finite element perspective on non-linear FFT-based micromechanical simulations. 2016. arXiv:1601.05970
- N. Mishra, J. Vondřejc, J. Zeman: A comparative study on low-memory iterative solvers for FFT-based homogenization of periodic media. Journal of Computational Physics, 321, pp. 151-168, 2016. arXiv:1508.02045
- J. Vondřejc: Improved guaranteed computable bounds on homogenized properties of periodic media by Fourier-Galerkin method with exact integration. International Journal for Numerical Methods in Engineering, 2016. arXiv:1412.2033
- J. Vondřejc, J. Zeman, I. Marek: Guaranteed upper-lower bounds on homogenized properties by FFT-based Galerkin method. Computer Methods in Applied Mechanics and Engineering, 297, pp. 258–291, 2015. arXiv:1404.3614
- J. Vondřejc, J. Zeman, I. Marek: An FFT-based Galerkin method for homogenization of periodic media. Computers and Mathematics with Applications, 68, pp. 156-173, 2014. arXiv:1311.0089
- J. Zeman, J. Vondřejc, J. Novák and I. Marek: Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients. Journal of Computational Physics, 229 (21), pp. 8065-8071, 2010. arXiv:1004.1122