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Hybrid Solver for Quasi Block Diagonal Linear Systems

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Book cover Parallel Processing and Applied Mathematics (PPAM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12043))

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Abstract

We present a solver for a class of sparse linear systems that we call quasi block diagonal. The solver combines multi-processors and multi-threaded parallelisms using MPI and OpenMP to implement preconditioned Jacobi. Specific formats for sparse matrices are exploited in order to reduce memory storage requirements. Our experiments show that communication costs are negligible, so as that speed-up and efficiency with respect to the sequential implementation are very high. Our hybrid implementation is tested on a cluster and compared to Intel MKL PARDISO linear solver.

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Notes

  1. 1.

    More details on Intel MKL cluster_sparse_solver available options can be found on page: https://software.intel.com/en-us/mkl-developer-reference-c-cluster-sparse-solver-iparm-parameter.

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Acknowledgements

This work has been partially supported by MIUR grant Excellence Departments 2018–2022, assigned to the Computer Science Department of Sapienza University of Rome. The experimental part has been run on the Galileo cluster, located at Cineca, Bologna, Italy, thanks to Class C ISCRA Project n. HP10CCM8RG.

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Authors and Affiliations

  1. Department of Computer Science, Sapienza University of Rome, Rome, Italy

    Viviana Arrigoni & Annalisa Massini

Authors
  1. Viviana Arrigoni
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  2. Annalisa Massini
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Corresponding authors

Correspondence to Viviana Arrigoni or Annalisa Massini .

Editor information

Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Southern California, Marina del Rey, CA, USA

    Ewa Deelman

  3. University of Tennessee, Knoxville, TN, USA

    Jack Dongarra

  4. Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

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Arrigoni, V., Massini, A. (2020). Hybrid Solver for Quasi Block Diagonal Linear Systems. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2019. Lecture Notes in Computer Science(), vol 12043. Springer, Cham. https://doi.org/10.1007/978-3-030-43229-4_12

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  • DOI: https://doi.org/10.1007/978-3-030-43229-4_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-43228-7

  • Online ISBN: 978-3-030-43229-4

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