SC16 Salt Lake City, UT

80. symPACK: a Solver for Sparse Symmetric Matrices

Authors: Mathias Jacquelin (Lawrence Berkeley National Laboratory)Yili Zheng (Google)Esmond Ng (Lawrence Berkeley National Laboratory)Katherine Yelick (Lawrence Berkeley National Laboratory)

Abstract: Systems of linear equations arise at the heart of many scientific applications. Most of these systems are sparse. Direct methods are sometimes needed to ensure accurate solutions (e.g. in shift-invert Lanczos). Performance and resource usage of sparse matrix factorizations are critical to time-to-solution and maximum solvable problem size. In many applications, matrices are symmetric. Exploiting the symmetry reduces both the amount of work and storage cost. On large-scale distributed memory platforms, communication cost can become critical. In addition, network topologies have become more complex. Modern platforms thus exhibit a higher level of performance variability, which makes scheduling of computations an intricate task. We investigate the novel use of an asynchronous task paradigm coupled with dynamic scheduling, in implementing sparse Cholesky factorization. Our solver symPACK, shows good strong scaling. It relies on efficient communication primitives provided by the UPC++ library. Performance evaluation shows that symPACK outperforms state-of-the-art packages, validating our approach.

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