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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'
DPP-PMRF: Rethinking Optimization for a Probabilistic Graphical Model Using Data-Parallel Primitives
We present a new parallel algorithm for probabilistic graphical model
optimization. The algorithm relies on data-parallel primitives (DPPs), which
provide portable performance over hardware architecture. We evaluate results on
CPUs and GPUs for an image segmentation problem. Compared to a serial baseline,
we observe runtime speedups of up to 13X (CPU) and 44X (GPU). We also compare
our performance to a reference, OpenMP-based algorithm, and find speedups of up
to 7X (CPU).Comment: LDAV 2018, October 201
Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication
Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many
high-performance graph algorithms as well as for some linear solvers, such as
algebraic multigrid. The scaling of existing parallel implementations of SpGEMM
is heavily bound by communication. Even though 3D (or 2.5D) algorithms have
been proposed and theoretically analyzed in the flat MPI model on Erdos-Renyi
matrices, those algorithms had not been implemented in practice and their
complexities had not been analyzed for the general case. In this work, we
present the first ever implementation of the 3D SpGEMM formulation that also
exploits multiple (intra-node and inter-node) levels of parallelism, achieving
significant speedups over the state-of-the-art publicly available codes at all
levels of concurrencies. We extensively evaluate our implementation and
identify bottlenecks that should be subject to further research
An efficient multi-core implementation of a novel HSS-structured multifrontal solver using randomized sampling
We present a sparse linear system solver that is based on a multifrontal
variant of Gaussian elimination, and exploits low-rank approximation of the
resulting dense frontal matrices. We use hierarchically semiseparable (HSS)
matrices, which have low-rank off-diagonal blocks, to approximate the frontal
matrices. For HSS matrix construction, a randomized sampling algorithm is used
together with interpolative decompositions. The combination of the randomized
compression with a fast ULV HSS factorization leads to a solver with lower
computational complexity than the standard multifrontal method for many
applications, resulting in speedups up to 7 fold for problems in our test
suite. The implementation targets many-core systems by using task parallelism
with dynamic runtime scheduling. Numerical experiments show performance
improvements over state-of-the-art sparse direct solvers. The implementation
achieves high performance and good scalability on a range of modern shared
memory parallel systems, including the Intel Xeon Phi (MIC). The code is part
of a software package called STRUMPACK -- STRUctured Matrices PACKage, which
also has a distributed memory component for dense rank-structured matrices
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