Abstract
This paper describes parallelization techniques for a multigrid solver for finite difference analysis of three-dimensional Poisson equations. We first apply our block red-black ordering for parallelization of a Gauss-Seidel (GS) smoother, whose sequentiality is often problematic in parallelization of multigrid methods. Furthermore, we introduce a new multiplicative Schwarz smoother, in which multiple GS iterations are performed in each of red-black ordered blocks. Numerical tests are conducted on a cluster of multi-processor nodes comprising four quad-core AMD Opteron processors to examine the effectiveness of these parallel smoothers. The multi-process test using 216 processes in flat-MPI model shows that the block red-black GS smoother and its multiplicative Schwarz variant achieve 1.3 and 1.8 times better performance than the conventional red-black GS smoother, respectively.
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Kawai, M., Iwashita, T., Nakashima, H., Marques, O. (2013). Parallel Smoother Based on Block Red-Black Ordering for Multigrid Poisson Solver. In: Daydé, M., Marques, O., Nakajima, K. (eds) High Performance Computing for Computational Science - VECPAR 2012. VECPAR 2012. Lecture Notes in Computer Science, vol 7851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38718-0_29
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DOI: https://doi.org/10.1007/978-3-642-38718-0_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38717-3
Online ISBN: 978-3-642-38718-0
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