Using Skeletons to Implement a Parallel Multigrid Method with Overlapping Adaptive Grids

Algorithmic skeletons are polymorphic higher-order functions that represent common parallelization patterns. They can be used as the building blocks of parallel applications by integrating them into a sequential language. In this paper we present a skeleton-based approach to manage overlapping of distributed grids, which occur in parallel adaptive multigrid algorithms. Overlapping is necessary to assure the convergence rate of a sequential multigrid solver in a parallel implementation. If we use overlapping we have to cope with distributed grid objects, for example grid nodes or elements. We present two overlapping strategies and discuss the differences of necessary modifications on parts of the sequential multigrid solver. For these modifications we use skeletons that are designed to hide necessary communication that comes along with distributed objects.