Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients

TL;DR

This paper introduces a conjugate gradient acceleration technique for FFT-based numerical homogenization of periodic media, significantly improving convergence rates especially for high-contrast problems with minimal additional computational cost.

Contribution

The authors develop a novel conjugate gradient-based method to speed up an existing FFT solver for homogenization, enhancing efficiency for complex media.

Findings

Convergence rate increases significantly for high-contrast coefficients.

Algorithm remains robust with respect to internal parameters.

Low overhead per iteration improves computational efficiency.

Abstract

In this short note, we present a new technique to accelerate the convergence of a FFT-based solver for numerical homogenization of complex periodic media proposed by Moulinec and Suquet in 1994. The approach proceeds from discretization of the governing integral equation by the trigonometric collocation method due to Vainikko (2000), to give a linear system which can be efficiently solved by conjugate gradient methods. Computational experiments confirm robustness of the algorithm with respect to its internal parameters and demonstrate significant increase of the convergence rate for problems with high-contrast coefficients at a low overhead per iteration.