Analysis of a fast fourier transform based method for modeling of heterogeneous materials

Authors:
Jaroslav Vondřejc;Jan Zeman;Ivo Marek
Affiliations:
Faculty of Civil Engineering, Department of Mechanics, Czech Technical University in Prague, Czech Republic;Faculty of Civil Engineering, Department of Mechanics, Czech Technical University in Prague, Czech Republic;Faculty of Civil Engineering, Department of Mathematics, Czech Technical University in Prague, Czech Republic
Venue:
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Year:
2011

Citing 2
Cited 0

Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems
Short note: Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients

Journal of Computational Physics

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Abstract

The focus of this paper is on the analysis of the Conjugate Gradient method applied to a non-symmetric system of linear equations, arising from a Fast Fourier Transform-based homogenization method due to Moulinec and Suquet [1]. Convergence of the method is proven by exploiting a certain projection operator reflecting physics of the underlying problem. These results are supported by a numerical example, demonstrating significant improvement of the Conjugate Gradient-based scheme over the original Moulinec-Suquet algorithm.