1,685 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
ELSI: A Unified Software Interface for Kohn-Sham Electronic Structure Solvers
Solving the electronic structure from a generalized or standard eigenproblem
is often the bottleneck in large scale calculations based on Kohn-Sham
density-functional theory. This problem must be addressed by essentially all
current electronic structure codes, based on similar matrix expressions, and by
high-performance computation. We here present a unified software interface,
ELSI, to access different strategies that address the Kohn-Sham eigenvalue
problem. Currently supported algorithms include the dense generalized
eigensolver library ELPA, the orbital minimization method implemented in
libOMM, and the pole expansion and selected inversion (PEXSI) approach with
lower computational complexity for semilocal density functionals. The ELSI
interface aims to simplify the implementation and optimal use of the different
strategies, by offering (a) a unified software framework designed for the
electronic structure solvers in Kohn-Sham density-functional theory; (b)
reasonable default parameters for a chosen solver; (c) automatic conversion
between input and internal working matrix formats, and in the future (d)
recommendation of the optimal solver depending on the specific problem.
Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800
basis functions) on distributed memory supercomputing architectures.Comment: 55 pages, 14 figures, 2 table
Parallelizing the QUDA Library for Multi-GPU Calculations in Lattice Quantum Chromodynamics
Graphics Processing Units (GPUs) are having a transformational effect on
numerical lattice quantum chromodynamics (LQCD) calculations of importance in
nuclear and particle physics. The QUDA library provides a package of mixed
precision sparse matrix linear solvers for LQCD applications, supporting single
GPUs based on NVIDIA's Compute Unified Device Architecture (CUDA). This
library, interfaced to the QDP++/Chroma framework for LQCD calculations, is
currently in production use on the "9g" cluster at the Jefferson Laboratory,
enabling unprecedented price/performance for a range of problems in LQCD.
Nevertheless, memory constraints on current GPU devices limit the problem sizes
that can be tackled. In this contribution we describe the parallelization of
the QUDA library onto multiple GPUs using MPI, including strategies for the
overlapping of communication and computation. We report on both weak and strong
scaling for up to 32 GPUs interconnected by InfiniBand, on which we sustain in
excess of 4 Tflops.Comment: 11 pages, 7 figures, to appear in the Proceedings of Supercomputing
2010 (submitted April 12, 2010
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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'
Minimizing synchronizations in sparse iterative solvers for distributed supercomputers
Eliminating synchronizations is one of the important techniques related to minimizing communications for modern high performance computing. This paper discusses principles of reducing communications due to global synchronizations in sparse iterative solvers on distributed supercomputers. We demonstrates how to minimizing global synchronizations by rescheduling a typical Krylov subspace method. The benefit of minimizing synchronizations is shown in theoretical analysis and is verified by numerical experiments using up to 900 processors. The experiments also show the communication complexity for some structured sparse matrix vector multiplications and global communications in the underlying supercomputers are in the order P1/2.5 and P4/5 respectively, where P is the number of processors and the experiments were carried on a Dawning 5000A
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