We describe a GPU- and multicore-oriented implementation technique for a key
component of finite element based simulation toolkits for partial differential
equations on unstructured grids: Geometric Multigrid solvers. We use efficient
sparse matrix-vector multiplications throughout the solver pipeline: within
the coarse-grid solver, smoothers and even grid transfers. Our implementation
can handle several low- and high-order finite element spaces in 2D and 3D, and
for representative benchmark problems, we achieve close to an order of
magnitude speedup on a single GPU over a multithreaded CPU code. In addition we
present preliminary results for experiments with strong smoothers for
unstructured problems on the GPU, aiming at augmenting numerical and
computational efficiency simultaneously.