Modern-day supercomputers are equipped with sophisticated graphics processing units (GPUs) along with high-performance CPUs. Adapting existing algorithms specifically to GPU has resulted in under-utilization of CPU computing power. In this respect, we parallelize Jacobi and successive-over relaxation (SOR), which are used as smoother in multigrid method to maximize the combined utilization of both CPUs and GPUs. We study the performance of multigrid method in terms of total execution time by employing different hybrid parallel approaches, viz. accelerating the smoothing operation using only GPU across all multigrid levels, alternately switching between GPU and CPU based on the multigrid level and our proposed novel approach of using combination of GPU and CPU across all multigrid levels. Our experiments demonstrate a significant speedup using the hybrid parallel approaches, across different problem sizes and finite element types, as compared to the MPI only approach. However, the scalability challenge persists for the hybrid parallel multigrid smoothers.
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