Guaranteed bounds on homogenized periodic media by FFT‐based Galerkin method. Issue 1 (December 2014) - Vondřejc, Jaroslav; Zeman, Jan; Marek, Ivo
Abstract An FFT‐based method, introduced by Moulinec and Suquet [1] in 1994, is an effective alternative to conventional Finite Element Method (FEM) for numerical homogenization of periodic media. Here, we summarize the recent variational reformulation and discretizations by Vondřejc et al. [2–6], which are based on conforming Galerkin approximations with trigonometric polynomials as basis functions. This insight, naturally leading to guaranteed bounds on homogenized matrix, opens a wide area of further investigations, which are also briefly discussed here. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)