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

Authors:
Jan Zeman;Jaroslav Vondřejc;Jan Novák;Ivo Marek
Affiliations:
Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 166 29 Prague 6, Czech Republic;Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 166 29 Prague 6, Czech Republic;Centre for Integrated Design of Advanced Structures, Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 166 29 Prague 6, Czech Republic;Department of Mathematics, Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 166 29 Prague 6, Czech Republic
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

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 [1]. The approach proceeds from discretization of the governing integral equation by the trigonometric collocation method due to Vainikko [2], 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.