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Published in:
2012 | OriginalPaper | Chapter
Analysis of a Fast Fourier Transform Based Method for Modeling of Heterogeneous Materials
Authors : Jaroslav Vondřejc, Jan Zeman, Ivo Marek
Published in: Large-Scale Scientific Computing
Publisher: Springer Berlin Heidelberg
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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.