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

Authors:
Frédéric Gibou;Chohong Min
Affiliations:
Computer Science and Mechanical Engineering Departments, University of California, Santa Barbara, CA 93106, United States;Mathematics Department, Ewha Womans University, Seoul 120-750, Republic of Korea
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

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) [8,10]. 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.