We study the impact of asynchronism on parallel iterative algorithms in the particular context of local clusters of workstations including GPUs. The application test is a classical PDE problem of advection-diffusion-reaction in 3D. We propose an asynchronous version of a previously developed PDE solver using GPUs for the inner computations. The algorithm is tested with two kinds of clusters, a homogeneous one and a heterogeneous one (with different CPUs and GPUs).