A Trade-off Analysis of the Parallel Hybrid SPIKE Preconditioner in a Unique Multi-core Computer

  • Leonardo Muniz de Lima
  • Lucia CatabrigaEmail author
  • Maria Cristina Rangel
  • Maria Claudia Silva Boeres
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10405)


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.


Parallel hybrid SPIKE preconditioner Combinatorial strategies Nonstationary iterative method 



This work has been supported in part by CNPq, CAPES, and FAPES.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Leonardo Muniz de Lima
    • 1
  • Lucia Catabriga
    • 1
    • 2
    Email author
  • Maria Cristina Rangel
    • 2
  • Maria Claudia Silva Boeres
    • 2
  1. 1.High Performance Computing LabFederal University of Espírito SantoVitóriaBrazil
  2. 2.Optimization LabFederal University of Espírito SantoVitóriaBrazil

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