Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media

Sab et al. (2024) have recently proposed an FFT-based iterative algorithm, termed Adaptive Eyre–Milton (AEM), for solving the Lippmann–Schwinger equation in the context of periodic homogenization of infinitely double contrasted linear elastic composites (heterogeneous materials with linear constitutive laws that contain both pores and rigid inclusions). They have demonstrated the unconditional linear convergence of this scheme, regardless of initialization and the chosen reference material. However, numerical simulations have shown that the rate of convergence of AEM strongly depends on the chosen reference material. In this paper, we introduce a new version of the AEM scheme where the reference material is updated iteratively, resulting in a fast and versatile scheme, termed Accelerated Adaptive Eyre–Milton (A2EM). Numerical simulations with A2EM on linear elastic composites with both pores and infinitely rigid inclusions show that, regardless of the initial chosen reference material, this algorithm has the same rate of convergence as AEM with the best choice of reference material.