1,597 research outputs found
Algorithmic patterns for -matrices on many-core processors
In this work, we consider the reformulation of hierarchical ()
matrix algorithms for many-core processors with a model implementation on
graphics processing units (GPUs). matrices approximate specific
dense matrices, e.g., from discretized integral equations or kernel ridge
regression, leading to log-linear time complexity in dense matrix-vector
products. The parallelization of matrix operations on many-core
processors is difficult due to the complex nature of the underlying algorithms.
While previous algorithmic advances for many-core hardware focused on
accelerating existing matrix CPU implementations by many-core
processors, we here aim at totally relying on that processor type. As main
contribution, we introduce the necessary parallel algorithmic patterns allowing
to map the full matrix construction and the fast matrix-vector
product to many-core hardware. Here, crucial ingredients are space filling
curves, parallel tree traversal and batching of linear algebra operations. The
resulting model GPU implementation hmglib is the, to the best of the authors
knowledge, first entirely GPU-based Open Source matrix library of
this kind. We conclude this work by an in-depth performance analysis and a
comparative performance study against a standard matrix library,
highlighting profound speedups of our many-core parallel approach
Performance Evaluation of Sparse Matrix Multiplication Kernels on Intel Xeon Phi
Intel Xeon Phi is a recently released high-performance coprocessor which
features 61 cores each supporting 4 hardware threads with 512-bit wide SIMD
registers achieving a peak theoretical performance of 1Tflop/s in double
precision. Many scientific applications involve operations on large sparse
matrices such as linear solvers, eigensolver, and graph mining algorithms. The
core of most of these applications involves the multiplication of a large,
sparse matrix with a dense vector (SpMV). In this paper, we investigate the
performance of the Xeon Phi coprocessor for SpMV. We first provide a
comprehensive introduction to this new architecture and analyze its peak
performance with a number of micro benchmarks. Although the design of a Xeon
Phi core is not much different than those of the cores in modern processors,
its large number of cores and hyperthreading capability allow many application
to saturate the available memory bandwidth, which is not the case for many
cutting-edge processors. Yet, our performance studies show that it is the
memory latency not the bandwidth which creates a bottleneck for SpMV on this
architecture. Finally, our experiments show that Xeon Phi's sparse kernel
performance is very promising and even better than that of cutting-edge general
purpose processors and GPUs
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
Solution of Few-Body Coulomb Problems with Latent Matrices on Multicore Processors
We re-formulate a classical numerical method for the solution of systems of linear equations to tackle problems with latent data, that is, linear systems of dimension that is a priori unknown. This type of systems appears in the solution of few-body Coulomb problems for Atomic Simulation Physics, in the form of multidimensional partial differential equations (PDEs) that require the numerical solution of a sequence of recurrent dense linear systems of growing scale. The large dimension of these systems, with up to several hundred thousands of unknowns, is tackled in our approach via a task-parallel implementation of the solver, using the OmpSs framework.Fil: Biedma, Luis Ariel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Colavecchia, Flavio Dario. Comisión Nacional de Energía Atómica. Gerencia del Area Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Balseiro). División Colisiones Atómicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Quintana Ortí, Enrique. Universitat Jaume I; EspañaInternational Conference on Computational Science, ICCS 2017ZurichSuizaETH ZürichUniversiteit Van AmsterdamUniversity of TennesseeNanyang Technological Universit
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