Joseph Paux (LSPM, Univ. Sorbonne Paris Nord)

Fast Fourier Transform (FFT)-based methods,  introduced by Moulinec and Suquet (1998), are an efficient class of numerical methods to solve conductivity and elasticity problems in periodic media. In this seminar, we present recent extensions of this method to non-periodic boundary conditions, which are required to, among others, non-periodic media, defect modeling and wave propagation. The proposed approach consists in using an approximation space spanned by sine and/or cosine series (instead of the classical Fourier series), associated with a known term describing the boundary condition. Constructions of the method, considering either the Gallerkin framework or the finite difference approach, associated difficulties and basic applications are presented and discussed.