Improvements of a Fast Parallel Poisson Solver on Irregular Domains

We discuss the scalable parallel solution of the Poisson equation on irregularly shaped domains discretized by finite differences. The symmetric positive definite system is solved by the preconditioned conjugate gradient algorithm with smoothed aggregation (SA) based algebraic multigrid (AMG) preconditioning. We investigate variants of the implementation of SA-AMG that lead to considerable improvements in the execution times. The improvements are due to a better data partitioning and the iterative solution of the coarsest level system in AMG. We demonstrate good scalability of the solver on a distributed memory parallel computer with up to 2048 processors.