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

Frédéric Gibou, Chohong Min

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7 Scopus citations


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.

Original languageEnglish
Pages (from-to)4531-4536
Number of pages6
JournalJournal of Computational Physics
Issue number14
StatePublished - 20 May 2012

Bibliographical note

Funding Information:
The authors thank Miles Detrixhe for helping in running those tests. The work of C. Min was supported by the Ewha Womans University Research Grant of 2010, the Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2010–0028298 ) and by the Korea Research Foundation Grant funded by the Korean Government ( KRF-2011–0013649 ). The research of F. Gibou was supported in part by ONR N00014–11-1–0027 , NSF CHE 1027817 , DOE DE-FG 02–08ER15991 , ICB W911NF-09-D-0001 and by the W.M. Keck Foundation. The authors acknowledge computational resources from the ‘Center for Scientific Computing at UCSB’ and NSF Grant CNS-0960316 .


  • Cuthill-Mckee ordering
  • Incomple LU factorization
  • Level set method
  • Lexicographical ordering
  • Parallel algorithm
  • Poisson equation
  • Preconditioned conjugate gradient


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