Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients

By Jan Zeman, Jaroslav Vondrejc, Jan Novák, Ivo Marek. Journal of Computational Physics, 2010

297 citations recorded by the source corpus.

In this short note, we present a new technique to accelerate the convergence of a FFT-based solver for numerical homogenization of complex periodic media proposed by Moulinec and Suquet in 1994. The approach proceeds from discretization of the governing integral equation by the trigonometric collocation method due to Vainikko (2000), to give a linear system which can be efficiently solved by conjugate gradient methods. Computational experiments confirm robustness of the algorithm with respect to its internal parameters and demonstrate significant increase of the convergence rate for problems with high-contrast coefficients at a low overhead per iteration.

Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/e16fae5842374999d1fe1d9640f0a26ea27a84b0

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In Atomic and Molecular Physics, and Optics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Convergence of FFT‐based homogenization for strongly heterogeneous media (2015, unknown): “Zeman et al [30] noticed that (1.”
A virtual laboratory using high resolution crystal plasticity simulations to determine the initial yield surface for sheet metal forming operations (2016, methodology): “Improved convergence can also be obtained via the use of advanced solution methods compared to the original approach (Zeman et al., 2010; Brisard and Dormieux, 2010).”
FFT‐based homogenization for microstructures discretized by linear hexahedral elements (2017, methodology): “[26] would require 4 8 D 32 strains, the eight corresponding to the number of Gauss points and the four reflecting the number of vectors used in the Krylov update of the conjugate gradient method.”
Computational homogenization of elasticity on a staggered grid (2016, methodology): “Improved fixed point solvers entered the scene in [17–19], as well as Krylov subspace methods [20, 21].”
An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials (2012, methodology): “To improve the convergence of this basic scheme, accelerated schemes have been proposed by different authors (Eyre and Milton, 1999; Brisard and Dormieux, 2010; Zeman et al., 2010).”