# A finite element perspective on nonlinear FFT‐based micromechanical simulations

@article{Zeman2016AFE, title={A finite element perspective on nonlinear FFT‐based micromechanical simulations}, author={Jan Zeman and T. W. J. Geus and Jaroslav Vondrejc and Ron H. J. Peerlings and Marc G. D. Geers}, journal={International Journal for Numerical Methods in Engineering}, year={2016}, volume={111}, pages={903 - 926} }

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 fixed‐point solutions of the Lippmann–Schwinger type integral equation. Their computational efficiency results from handling the kernel of this equation by the fast Fourier transform (FFT). However, the kernel is derived from an auxiliary homogeneous linear problem, which renders the extension of FFT…

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