In this paper, the problem of face verification across illumination is addressed. In order to cope with different lighting conditions, a preprocessing step is applied to the face image so as to make it independent on the illumination conditions. The illuminant invariant representation of the image is obtained by first applying an anisotropic diffusion process to the original image. Hence, it implies the numerical resolution of an elliptic partial differential equation on a large grid: the image. So, a comparison is performed on two methods to resolve such diffusion problems, namely the Gauss-Seidel relaxation and the Multigrid V-cycle. The preprocessing algorithm with its different resolution schemes is applied prior to the task of face verification. Experiments conducted on the challenging BANCA database showed a significant improvement in terms of face verification error rate, while staying computationally efficient.