Parallelization of an additive multigrid solver

Abstract

This article deals with the implementation and performance analysis of a parallel algebraic multigrid solver (pAMG) for a finite-volume, unstructured computational fluid dynamics (CFD) code. The parallelization of the solver is based on the domain decomposition approach using the single program, multiple data paradigm. The Message Passing Interface library (MPI) is used for communication of data. An ILU(0) iterative solver is used for smoothing the errors arising within each partition at the different grid levels, and a multi-level synchronization across the computational domain partitions is enforced in order to improve the performance of the parallelized multigrid solver. Two synchronization strategies are evaluated. In the first the synchronization is applied across the multigrid levels during the restriction step in addition to the base level, while in the second the synchronization is enforced during the restriction and prolongation steps. The effect of gathering the coefficients across partitions for the coarsest level is also investigated. Tests on grids up to 800,000 elements are conducted for a number of diffusion and advection problems on up to 20 processors. Results show that synchronization across partitions for multigrid levels plays an essential role in ensuring good scalability. Furthermore, for a large number of partitions, gathering coefficients across partitions is important to ensure a convergence history that is consistent with the sequential solver, thus yielding the same number of iterations for parallel and sequential runs, which is crucial for retaining high scalability. The shadow-to-core elements ratio is also shown to be a good indicator for scalability.