Abstract
In this paper we apply the parallel hybrid SPIKE algorithm as a preconditioner for a nonstationary iterative method to solve large sparse linear systems. In order to obtain a good preconditioner, we employ several strategies solving combinatorial problems such as matching, reordering, partitioning, and quadratic knapsack. Our SPIKE implementation combines MPI and OpenMP paradigms in a unique multi-core computer. The computational experiments show the influence of each strategy evaluating the number of iterations and CPU time of the iterative solver in a set of large systems from miscellaneous application areas. The experiments suggest that the SPIKE preconditioner is very advantageous when a suitable set of parameters is chosen. The choice of the number of MPI ranks and OpenMP threads is not an easy task, because the SPIKE algorithm can increase the number of iterations when the number of MPI ranks grows. Moreover, the increase in the number of threads does not ensure a better performance.
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This work has been supported in part by CNPq, CAPES, and FAPES.
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All codes are developed in C language and compiled with Intel version 2015 Update 3 optimized with Library Math Kernel Library MKL version 11.2 Update 3 and MPI version 5.0 Update 3, available at https://github.com/leomunizlima/ SPIKE. The SPIKE preconditioner steps involving calculations using direct methods that are solved by pardiso500-INTEL1301-X86-64 library of PARDISO software. The matrix operations as reordering, scaling and matching are performed using the HSL Mathematical Software Library.
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de Lima, L.M., Catabriga, L., Rangel, M.C., Boeres, M.C.S. (2017). A Trade-off Analysis of the Parallel Hybrid SPIKE Preconditioner in a Unique Multi-core Computer. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2017. ICCSA 2017. Lecture Notes in Computer Science(), vol 10405. Springer, Cham. https://doi.org/10.1007/978-3-319-62395-5_29
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DOI: https://doi.org/10.1007/978-3-319-62395-5_29
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