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 multilevel 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.

Velocity–pressure coupling on GPUs

“…We restrict ourselves to the class of aggregation methods that splits the number of nodes on the fine grid into disjoint sets of nodes, the so-called aggregates that act as nodes on the coarse grid, see e.g. Darwish et al [4]. The mapping from the coarse grid to the fine grid is then achieved by simply assigning the coarse-grid value of the aggregate to all the fine-grid nodes belonging to this aggregate.…”

Parallel strategies for reduced number of processors applied for CFD simulations on workstations

“…This partitioning strategy is usually used for problems where data is static or the domain is unchanging but the computation within different parts of the domain is dynamic. In the majority of the research investigations on parallel CFD, this terminology of domain decomposition is referred to as grid partitioning ([20], [21], [22], [23], [24], [25]). Behind this term of grid partitioning lays a simple idea which came from a natural way of dealing with large-scale computational meshes.…”