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.
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References
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Vondřejc, J., Zeman, J., Marek, I. (2012). Analysis of a Fast Fourier Transform Based Method for Modeling of Heterogeneous Materials. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_58
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DOI: https://doi.org/10.1007/978-3-642-29843-1_58
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