2,944 research outputs found
GHOST: Building blocks for high performance sparse linear algebra on heterogeneous systems
While many of the architectural details of future exascale-class high
performance computer systems are still a matter of intense research, there
appears to be a general consensus that they will be strongly heterogeneous,
featuring "standard" as well as "accelerated" resources. Today, such resources
are available as multicore processors, graphics processing units (GPUs), and
other accelerators such as the Intel Xeon Phi. Any software infrastructure that
claims usefulness for such environments must be able to meet their inherent
challenges: massive multi-level parallelism, topology, asynchronicity, and
abstraction. The "General, Hybrid, and Optimized Sparse Toolkit" (GHOST) is a
collection of building blocks that targets algorithms dealing with sparse
matrix representations on current and future large-scale systems. It implements
the "MPI+X" paradigm, has a pure C interface, and provides hybrid-parallel
numerical kernels, intelligent resource management, and truly heterogeneous
parallelism for multicore CPUs, Nvidia GPUs, and the Intel Xeon Phi. We
describe the details of its design with respect to the challenges posed by
modern heterogeneous supercomputers and recent algorithmic developments.
Implementation details which are indispensable for achieving high efficiency
are pointed out and their necessity is justified by performance measurements or
predictions based on performance models. The library code and several
applications are available as open source. We also provide instructions on how
to make use of GHOST in existing software packages, together with a case study
which demonstrates the applicability and performance of GHOST as a component
within a larger software stack.Comment: 32 pages, 11 figure
QR Factorization of Tall and Skinny Matrices in a Grid Computing Environment
Previous studies have reported that common dense linear algebra operations do
not achieve speed up by using multiple geographical sites of a computational
grid. Because such operations are the building blocks of most scientific
applications, conventional supercomputers are still strongly predominant in
high-performance computing and the use of grids for speeding up large-scale
scientific problems is limited to applications exhibiting parallelism at a
higher level. We have identified two performance bottlenecks in the distributed
memory algorithms implemented in ScaLAPACK, a state-of-the-art dense linear
algebra library. First, because ScaLAPACK assumes a homogeneous communication
network, the implementations of ScaLAPACK algorithms lack locality in their
communication pattern. Second, the number of messages sent in the ScaLAPACK
algorithms is significantly greater than other algorithms that trade flops for
communication. In this paper, we present a new approach for computing a QR
factorization -- one of the main dense linear algebra kernels -- of tall and
skinny matrices in a grid computing environment that overcomes these two
bottlenecks. Our contribution is to articulate a recently proposed algorithm
(Communication Avoiding QR) with a topology-aware middleware (QCG-OMPI) in
order to confine intensive communications (ScaLAPACK calls) within the
different geographical sites. An experimental study conducted on the Grid'5000
platform shows that the resulting performance increases linearly with the
number of geographical sites on large-scale problems (and is in particular
consistently higher than ScaLAPACK's).Comment: Accepted at IPDPS10. (IEEE International Parallel & Distributed
Processing Symposium 2010 in Atlanta, GA, USA.
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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'
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