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Parallel Solution of Sparse Linear Systems

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High-Performance Scientific Computing

Abstract

Many simulations in science and engineering give rise to sparse linear systems of equations. It is a well known fact that the cost of the simulation process is almost always governed by the solution of the linear systems especially for large-scale problems. The emergence of extreme-scale parallel platforms, along with the increasing number of processing cores available on a single chip pose significant challenges for algorithm development. Machines with tens of thousands of multicore processors place tremendous constraints on the communication as well as memory access requirements of algorithms. The increase in number of cores in a processing unit without an increase in memory bandwidth aggravates an already significant memory bottleneck. Sparse linear algebra kernels are well-known for their poor processor utilization. This is a result of limited memory reuse, which renders data caching less effective. In view of emerging hardware trends, it is necessary to develop algorithms that strike a more meaningful balance between memory accesses, communication, and computation. Specifically, an algorithm that performs more floating point operations at the expense of reduced memory accesses and communication is likely to yield better performance. We present two alternative variations of DS factorization based methods for solution of sparse linear systems on parallel computing platforms. Performance comparisons to traditional LU factorization based parallel solvers are also discussed. We show that combining iterative methods with direct solvers and using DS factorization, one can achieve better scalability and shorter time to solution.

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Acknowledgements

I would like to thank Ahmed Sameh, Ananth Grama, Faisal Saied, Eric Cox, Kenji Takizawa, Madan Sathe, Mehmet Koyuturk, Olaf Schenk, and Tayfun Tezduyar for their help and many useful discussions.

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Authors and Affiliations

  1. Department of Computer Engineering, Middle East Technical University, 06531, Ankara, Turkey

    Murat Manguoglu

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  1. Murat Manguoglu
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Correspondence to Murat Manguoglu .

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Editors and Affiliations

  1. Dept. Electrical Eng. & Computer Science, University of Tennessee, Volunteer Boulevard 1122, Knoxville, 37996-3450, Tennessee, USA

    Michael W. Berry

  2. Department of Mathematics, Florida State University, Academic Way 1017, Tallahassee, 32306, Florida, USA

    Kyle A. Gallivan

  3. Dept. Computer Engineering & Informatics, University of Patras, Patras, 26500, Greece

    Efstratios Gallopoulos

  4. Department of Computer Science, Purdue University, 305 North University Street, West Lafayette, 47907-2107, Indiana, USA

    Ananth Grama

  5. IRISA, INRIA Rennes - Bretagne Atlantique, Campus de Beaulieu, Rennes, 35042, France

    Bernard Philippe

  6. Dept. of Computer Science & Engineering, University of Minnesota, Union Street SE 200, Minneapolis, 55455, Minnesota, USA

    Yousef Saad

  7. Department of Computer Science, Purdue University, N. University Street 305, West Lafayette, 47907-2107, Indiana, USA

    Faisal Saied

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Manguoglu, M. (2012). Parallel Solution of Sparse Linear Systems. In: Berry, M., et al. High-Performance Scientific Computing. Springer, London. https://doi.org/10.1007/978-1-4471-2437-5_8

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  • DOI: https://doi.org/10.1007/978-1-4471-2437-5_8

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-2436-8

  • Online ISBN: 978-1-4471-2437-5

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