Hierarchical Parallel Matrix Multiplication on Large-Scale Distributed Memory Platforms

Matrix multiplication is a very important computation kernel both in its own right as a building block of many scientific applications and as a popular representative for other scientific applications. Cannon algorithm which dates back to 1969 was the first efficient algorithm for parallel matrix multiplication providing theoretically optimal communication cost. However this algorithm requires a square number of processors. In the mid 1990s, the SUMMA algorithm was introduced. SUMMA overcomes the shortcomings of Cannon algorithm as it can be used on a non-square number of processors as well. Since then the number of processors in HPC platforms has increased by two orders of magnitude making the contribution of communication in the overall execution time more significant. Therefore, the state of the art parallel matrix multiplication algorithms should be revisited to reduce the communication cost further. This paper introduces a new parallel matrix multiplication algorithm, Hierarchical SUMMA (HSUMMA), which is a redesign of SUMMA. Our algorithm reduces the communication cost of SUMMA by introducing a two-level virtual hierarchy into the two-dimensional arrangement of processors. Experiments on an IBM BlueGene-P demonstrate the reduction of communication cost up to 2.08 times on 2048 cores and up to 5.89 times on 16384 cores.Comment: 9 page

Preparing sparse solvers for exascale computing.

Sparse solvers provide essential functionality for a wide variety of scientific applications. Highly parallel sparse solvers are essential for continuing advances in high-fidelity, multi-physics and multi-scale simulations, especially as we target exascale platforms. This paper describes the challenges, strategies and progress of the US Department of Energy Exascale Computing project towards providing sparse solvers for exascale computing platforms. We address the demands of systems with thousands of high-performance node devices where exposing concurrency, hiding latency and creating alternative algorithms become essential. The efforts described here are works in progress, highlighting current success and upcoming challenges. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'

A hierarchic task-based programming model for distributed heterogeneous computing

Distributed computing platforms are evolving to heterogeneous ecosystems with Clusters, Grids and Clouds introducing in its computing nodes, processors with different core architectures, accelerators (i.e. GPUs, FPGAs), as well as different memories and storage devices in order to achieve better performance with lower energy consumption. As a consequence of this heterogeneity, programming applications for these distributed heterogeneous platforms becomes a complex task. Additionally to the complexity of developing an application for distributed platforms, developers must also deal now with the complexity of the different computing devices inside the node. In this article, we present a programming model that aims to facilitate the development and execution of applications in current and future distributed heterogeneous parallel architectures. This programming model is based on the hierarchical composition of the COMP Superscalar and Omp Superscalar programming models that allow developers to implement infrastructure-agnostic applications. The underlying runtime enables applications to adapt to the infrastructure without the need of maintaining different versions of the code. Our programming model proposal has been evaluated on real platforms, in terms of heterogeneous resource usage, performance and adaptation.This work has been supported by the European Commission through the Horizon 2020 Research and Innovation program under contract 687584 (TANGO project) by the Spanish Government under contract TIN2015-65316 and grant SEV-2015-0493 (Severo Ochoa Program) and by Generalitat de Catalunya under contracts 2014-SGR-1051 and 2014-SGR-1272.Peer ReviewedPostprint (author's final draft

Achieving Efficient Strong Scaling with PETSc using Hybrid MPI/OpenMP Optimisation

The increasing number of processing elements and decreas- ing memory to core ratio in modern high-performance platforms makes efficient strong scaling a key requirement for numerical algorithms. In order to achieve efficient scalability on massively parallel systems scientific software must evolve across the entire stack to exploit the multiple levels of parallelism exposed in modern architectures. In this paper we demonstrate the use of hybrid MPI/OpenMP parallelisation to optimise parallel sparse matrix-vector multiplication in PETSc, a widely used scientific library for the scalable solution of partial differential equations. Using large matrices generated by Fluidity, an open source CFD application code which uses PETSc as its linear solver engine, we evaluate the effect of explicit communication overlap using task-based parallelism and show how to further improve performance by explicitly load balancing threads within MPI processes. We demonstrate a significant speedup over the pure-MPI mode and efficient strong scaling of sparse matrix-vector multiplication on Fujitsu PRIMEHPC FX10 and Cray XE6 systems