An Efficient Parallel Adaptive GMG Solver for Large-Scale Stokes Problems

We study the performance and scalability of the adaptive geometric multigrid method with the recently developed restricted additive Vanka (RAV) smoother for the finite element solution of large-scale Stokes problems on distributed-memory clusters. A comparison of the RAV smoother and the classical multiplicative and additive Vanka smoothers is presented. We present three cache policies for the smoother operators that provide a balance between cached and on-the-fly computation and discuss their memory footprint and computational cost. It is shown that the restricted additive smoother with the most efficient cache policy has the smallest memory footprint and is computationally cheaper in comparison with the other smoothers and can, therefore, be used for large-scale problems even when the available main memory is constrained. We discuss the parallelization aspects of the smoother operators and show that the RAV operator can be replicated exactly in parallel with a very small communication overhead. We present strong and weak scaling of the GMG solver for 2D and 3D examples with up to roughly 540 million degrees of freedom on up to 2048 MPI processes. The GMG solver with the restricted additive smoother is shown to achieve rapid convergence rates and scale well in both the strong and weak scaling studies, making it an attractive choice for the solution of large-scale Stokes problems on HPC systems.