Analysis of a Fast Fourier Transform Based Method for Modeling of Heterogeneous Materials
For researchers in computational homogenization, this provides a theoretically grounded and faster solver for heterogeneous material modeling.
The paper analyzes the Conjugate Gradient method for a non-symmetric linear system from FFT-based homogenization, proving convergence via a projection operator and showing significant improvement over the original algorithm in a numerical example.
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.