Reduced‐order FFT‐based homogenisation by tensor approximation

Abstract

AbstractWe enhanced the efficiency of Fast Fourier transform (FFT) based Galerkin methods on numerical homogenisation problems by exploiting low‐rank tensor approximations in canonical, Tucker, and tensor train formats. This leads to a significant reduction in computational complexity and memory requirement. The advantages of the approach are demonstrated in a numerical example of a model homogenisation problem with stochastic heterogeneous material coefficients.