We describe our FE-gMG solver, a geometric multigrid approach for problems relying on unstructured grids. We augment our GPUand multicore-oriented implementation technique based on cascades of sparse matrix-vector multiply by applying strong smoothers. In particular, we employ Sparse Approximated Inverse (SPAI) and Stabilised Approximated Inverse (SAINV) techniques. We focus on presenting the numerical efficiency of our smoothers in combination with low- and high-order finite element spaces as well as the hardware efficiency of the FE-gMG. For a representative benchmark problem, we achieve a speedup of an average of 5 on a single GPU over a multithreaded CPU code. In addition, our strong smoothers offer a speedup of 1:5 to 2:5 depending on the element space, compared to simple Jacobi smoothing.