A hybrid CPU/GPU approach for the parallel algebraic recursive multilevel solver pARMS

We illustrate how the distributed parallel Algebraic Recursive Multilevel Solver based on MPI can be adapted for heterogeneous CPU/GPU architectures. The tasks performed on the GPU are related to the preconditioning of each part of the distributed matrix (local preconditioning) which is handled in the distributed version by each MPI process. The solving step remains on the CPU. In our implementation, the local preconditioning can be based either on the randomization of the last Schur complement system in the multilevel recursive process, or on an Incomplete LU factorization from the MAGMA library. Numerical experiments show that a promising performance improvement can be obtained using either randomized multilevel recursive preconditioning or Incomplete LU preconditioning for large enough matrices. Each preconditioning method ensures a good performance for a given set of matrices.