Jaroslav Vondřejc
ČVUT v Praze, Fakulta stavební

FFT-based finite element method of homogenization
We present a mathematical theory to FFT-based homogenization introduced as a numerical algorithm by Moulinec and Suquet in 1994. This approach is based on the Lippmann-Schwinger type integral equation exploiting the Green function for some reference homogeneous conductivity being a parameter of the method. We show that this equation is equivalent to weak formulation in the sense that the solutions of both formulations are identical. Moreover, we describe a discretization using Galerkin approximation and numerical integration using trigonometric polynomials as basis functions. Convergence of discrete solutions to the solution of weak formulation is presented. A solution of the resulting non-symmetric linear system by conjugate gradients is discussed.