On the performance of a simple parallel implementation of the ILU-PCG for the Poisson equation on irregular domains

We report on the performance of a parallel algorithm for solving the Poisson equation on irregular domains. We use the spatial discretization of Gibou et al. (2002) [6] for the Poisson equation with Dirichlet boundary conditions, while we use a finite volume discretization for imposing Neumann boundary conditions (Ng et al., 2009; Purvis and Burkhalter, 1979) [8] and [10]. The parallelization algorithm is based on the Cuthill–McKee ordering. Its implementation is straightforward, especially in the case of shared memory machines, and produces significant speedup; about three times on a standard quad core desktop computer and about seven times on a octa core shared memory cluster. The implementation code is posted on the authors’ web pages for reference.