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  • 1.
    Myllykoski, Mirko
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    A Task-Based Algorithm for Reordering the Eigenvalues of a Matrix in Real Schur Form2018In: Parallel Processing and Applied Mathematics: PPAM 2017 / [ed] Roman Wyrzykowski, Jack Dongarra, Ewa Deelman, Konrad Karczewski, Springer, 2018, p. 207-216Conference paper (Refereed)
    Abstract [en]

    A task-based parallel algorithm for reordering the eigenvalues of a matrix in real Schur form is presented.The algorithm is realized on top of the StarPU runtime system.Only the aspects which are relevant for shared memory machines are discussed here, but the implementation can be configured to run on distributed memory machines as well.Various techniques to reduce the overhead and the core idle time are discussed.Computational experiments indicate that the new algorithm is between 1.5 and 6.6 times faster than a state of the art MPI-based implementation found in ScaLAPACK.With medium to large matrices, strong scaling efficiencies above 60\% up to 28 CPU cores are reported.The overhead and the core idle time are shown to be negligible with the exception of the smallest matrices and highest core counts.

  • 2.
    Myllykoski, Mirko
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science. Department of Mathematical Information Technology, University of Jyväskylä.
    Rossi, Tuomo
    Department of Mathematical Information Technology, University of Jyväskylä.
    Toivanen, Jari
    Department of Mathematical Information Technology, University of Jyväskylä; Department of Aeronautics & Astronautics, Stanford University.
    On solving separable block tridiagonal linear systems using a GPU implementation of radix-4 PSCR method2018In: Journal of Parallel and Distributed Computing, ISSN 0743-7315, E-ISSN 1096-0848, Vol. 115, p. 56-66Article in journal (Refereed)
    Abstract [en]

    Partial solution variant of the cyclic reduction (PSCR) method is a direct solver that can be applied to certain types of separable block tridiagonal linear systems. Such linear systems arise, e.g., from the Poisson and the Helmholtz equations discretized with bilinear finite-elements. Furthermore, the separability of the linear system entails that the discretization domain has to be rectangular and the discretization mesh orthogonal. A generalized graphics processing unit (GPU) implementation of the PSCR method is presented. The numerical results indicate up to 24-fold speedups when compared to an equivalent CPU implementation that utilizes a single CPU core. Attained floating point performance is analyzed using roofline performance analysis model and the resulting models show that the attained floating point performance is mainly limited by the off-chip memory bandwidth and the effectiveness of a tridiagonal solver used to solve arising tridiagonal subproblems. The performance is accelerated using off-line autotuning techniques.

    The full text will be freely available from 2020-06-01 15:36
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