Analysis of a Fast Fourier Transform Based Method for Modeling of Heterogeneous Materials
arXiv:1107.4830 · doi:10.1007/978-3-642-29843-1_58
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, 1994). 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.
8 pages, 2 figures