An FFT-based fast gradient method for elastic and inelastic unit cell homogenization problems

Building upon the previously established equivalence of the basic scheme of Moulinec-Suquet's FFT-based computational homogenization method with a gradient descent method, this work concerns the impact of the fast gradient method of Nesterov in the context of computational homogenization. Nesterov's method leads to a significant speed up compared to the basic scheme for linear problems with moderate contrast, and compares favorably to the (Newton-)conjugate gradient (CG) method for problems in digital rock physics and (small strain) elastoplasticity. We present an efficient implementation requiring twice the storage of the basic scheme, but only half of the storage of the CG method.