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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'
Taking advantage of hybrid systems for sparse direct solvers via task-based runtimes
The ongoing hardware evolution exhibits an escalation in the number, as well
as in the heterogeneity, of computing resources. The pressure to maintain
reasonable levels of performance and portability forces application developers
to leave the traditional programming paradigms and explore alternative
solutions. PaStiX is a parallel sparse direct solver, based on a dynamic
scheduler for modern hierarchical manycore architectures. In this paper, we
study the benefits and limits of replacing the highly specialized internal
scheduler of the PaStiX solver with two generic runtime systems: PaRSEC and
StarPU. The tasks graph of the factorization step is made available to the two
runtimes, providing them the opportunity to process and optimize its traversal
in order to maximize the algorithm efficiency for the targeted hardware
platform. A comparative study of the performance of the PaStiX solver on top of
its native internal scheduler, PaRSEC, and StarPU frameworks, on different
execution environments, is performed. The analysis highlights that these
generic task-based runtimes achieve comparable results to the
application-optimized embedded scheduler on homogeneous platforms. Furthermore,
they are able to significantly speed up the solver on heterogeneous
environments by taking advantage of the accelerators while hiding the
complexity of their efficient manipulation from the programmer.Comment: Heterogeneity in Computing Workshop (2014
On the acceleration of wavefront applications using distributed many-core architectures
In this paper we investigate the use of distributed graphics processing unit (GPU)-based architectures to accelerate pipelined wavefront applications—a ubiquitous class of parallel algorithms used for the solution of a number of scientific and engineering applications. Specifically, we employ a recently developed port of the LU solver (from the NAS Parallel Benchmark suite) to investigate the performance of these algorithms on high-performance computing solutions from NVIDIA (Tesla C1060 and C2050) as well as on traditional clusters (AMD/InfiniBand and IBM BlueGene/P). Benchmark results are presented for problem classes A to C and a recently developed performance model is used to provide projections for problem classes D and E, the latter of which represents a billion-cell problem. Our results demonstrate that while the theoretical performance of GPU solutions will far exceed those of many traditional technologies, the sustained application performance is currently comparable for scientific wavefront applications. Finally, a breakdown of the GPU solution is conducted, exposing PCIe overheads and decomposition constraints. A new k-blocking strategy is proposed to improve the future performance of this class of algorithm on GPU-based architectures
Self-adaptive Multiprecision Preconditioners on Multicore and Manycore Architectures
Abstract. Based on the premise that preconditioners needed for scien-tific computing are not only required to be robust in the numerical sense, but also scalable for up to thousands of light-weight cores, we argue that this two-fold goal is achieved for the recently developed self-adaptive multi-elimination preconditioner. For this purpose, we revise the under-lying idea and analyze the performance of implementations realized in the PARALUTION and MAGMA open-source software libraries on GPU architectures (using either CUDA or OpenCL), Intel’s Many Integrated Core Architecture, and Intel’s Sandy Bridge processor. The comparison with other well-established preconditioners like multi-coloured Gauss-Seidel, ILU(0) and multi-colored ILU(0), shows that the twofold goal of a numerically stable cross-platform performant algorithm is achieved.
Algorithm Architecture Co-design for Dense and Sparse Matrix Computations
abstract: With the end of Dennard scaling and Moore's law, architects have moved towards
heterogeneous designs consisting of specialized cores to achieve higher performance
and energy efficiency for a target application domain. Applications of linear algebra
are ubiquitous in the field of scientific computing, machine learning, statistics,
etc. with matrix computations being fundamental to these linear algebra based solutions.
Design of multiple dense (or sparse) matrix computation routines on the
same platform is quite challenging. Added to the complexity is the fact that dense
and sparse matrix computations have large differences in their storage and access
patterns and are difficult to optimize on the same architecture. This thesis addresses
this challenge and introduces a reconfigurable accelerator that supports both dense
and sparse matrix computations efficiently.
The reconfigurable architecture has been optimized to execute the following linear
algebra routines: GEMV (Dense General Matrix Vector Multiplication), GEMM
(Dense General Matrix Matrix Multiplication), TRSM (Triangular Matrix Solver),
LU Decomposition, Matrix Inverse, SpMV (Sparse Matrix Vector Multiplication),
SpMM (Sparse Matrix Matrix Multiplication). It is a multicore architecture where
each core consists of a 2D array of processing elements (PE).
The 2D array of PEs is of size 4x4 and is scheduled to perform 4x4 sized matrix
updates efficiently. A sequence of such updates is used to solve a larger problem inside
a core. A novel partitioned block compressed sparse data structure (PBCSC/PBCSR)
is used to perform sparse kernel updates. Scalable partitioning and mapping schemes
are presented that map input matrices of any given size to the multicore architecture.
Design trade-offs related to the PE array dimension, size of local memory inside a core
and the bandwidth between on-chip memories and the cores have been presented. An
optimal core configuration is developed from this analysis. Synthesis results using a 7nm PDK show that the proposed accelerator can achieve a performance of upto
32 GOPS using a single core.Dissertation/ThesisMasters Thesis Computer Engineering 201
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