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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'
A Review of Lightweight Thread Approaches for High Performance Computing
High-level, directive-based solutions are becoming the programming models (PMs) of the multi/many-core architectures. Several solutions relying on operating system (OS) threads perfectly work with a moderate number of cores. However, exascale systems will spawn hundreds of thousands of threads in order to exploit their massive parallel architectures and thus conventional OS threads are too heavy for that purpose. Several lightweight thread (LWT) libraries have recently appeared offering lighter mechanisms to tackle massive concurrency. In order to examine the suitability of LWTs in high-level runtimes, we develop a set of microbenchmarks consisting of commonly-found patterns in current parallel codes. Moreover, we study the semantics offered by some LWT libraries in order to expose the similarities between different LWT application programming interfaces. This study reveals that a reduced set of LWT functions can be sufficient to cover the common parallel code patterns andthat those LWT libraries perform better than OS threads-based solutions in cases where task and nested parallelism are becoming more popular with new architectures.The researchers from the Universitat Jaume I de Castelló were supported by project TIN2014-53495-R of the MINECO, the Generalitat Valenciana fellowship programme Vali+d 2015, and FEDER. This work was partially supported by the U.S. Dept. of Energy, Office of Science, Office of Advanced
Scientific Computing Research (SC-21), under contract DEAC02-06CH11357. We gratefully acknowledge the computing resources provided and operated by the Joint Laboratory for System Evaluation (JLSE) at Argonne National Laboratory.Peer ReviewedPostprint (author's final draft
Enhancing Energy Production with Exascale HPC Methods
High Performance Computing (HPC) resources have become the key actor for achieving more ambitious challenges in many disciplines. In this step beyond, an explosion on the available parallelism and the use of special purpose
processors are crucial. With such a goal, the HPC4E project applies new exascale HPC techniques to energy industry simulations, customizing them if necessary, and going beyond the state-of-the-art in the required HPC exascale
simulations for different energy sources. In this paper, a general overview of these methods is presented as well as some specific preliminary results.The research leading to these results has received funding from the European Union's Horizon 2020 Programme (2014-2020) under the HPC4E Project (www.hpc4e.eu), grant agreement n° 689772, the Spanish Ministry of
Economy and Competitiveness under the CODEC2 project (TIN2015-63562-R), and
from the Brazilian Ministry of Science, Technology and Innovation through Rede
Nacional de Pesquisa (RNP). Computer time on Endeavour cluster is provided by the
Intel Corporation, which enabled us to obtain the presented experimental results in
uncertainty quantification in seismic imagingPostprint (author's final draft
Optimal Point Placement for Mesh Smoothing
We study the problem of moving a vertex in an unstructured mesh of
triangular, quadrilateral, or tetrahedral elements to optimize the shapes of
adjacent elements. We show that many such problems can be solved in linear time
using generalized linear programming. We also give efficient algorithms for
some mesh smoothing problems that do not fit into the generalized linear
programming paradigm.Comment: 12 pages, 3 figures. A preliminary version of this paper was
presented at the 8th ACM/SIAM Symp. on Discrete Algorithms (SODA '97). This
is the final version, and will appear in a special issue of J. Algorithms for
papers from SODA '9
Task-based Augmented Contour Trees with Fibonacci Heaps
This paper presents a new algorithm for the fast, shared memory, multi-core
computation of augmented contour trees on triangulations. In contrast to most
existing parallel algorithms our technique computes augmented trees, enabling
the full extent of contour tree based applications including data segmentation.
Our approach completely revisits the traditional, sequential contour tree
algorithm to re-formulate all the steps of the computation as a set of
independent local tasks. This includes a new computation procedure based on
Fibonacci heaps for the join and split trees, two intermediate data structures
used to compute the contour tree, whose constructions are efficiently carried
out concurrently thanks to the dynamic scheduling of task parallelism. We also
introduce a new parallel algorithm for the combination of these two trees into
the output global contour tree. Overall, this results in superior time
performance in practice, both in sequential and in parallel thanks to the
OpenMP task runtime. We report performance numbers that compare our approach to
reference sequential and multi-threaded implementations for the computation of
augmented merge and contour trees. These experiments demonstrate the run-time
efficiency of our approach and its scalability on common workstations. We
demonstrate the utility of our approach in data segmentation applications
Computing Heavy Elements
Reliable calculations of the structure of heavy elements are crucial to
address fundamental science questions such as the origin of the elements in the
universe. Applications relevant for energy production, medicine, or national
security also rely on theoretical predictions of basic properties of atomic
nuclei. Heavy elements are best described within the nuclear density functional
theory (DFT) and its various extensions. While relatively mature, DFT has never
been implemented in its full power, as it relies on a very large number (~
10^9-10^12) of expensive calculations (~ day). The advent of leadership-class
computers, as well as dedicated large-scale collaborative efforts such as the
SciDAC 2 UNEDF project, have dramatically changed the field. This article gives
an overview of the various computational challenges related to the nuclear DFT,
as well as some of the recent achievements.Comment: Proceeding of the Invited Talk given at the SciDAC 2011 conference,
Jul. 10-15, 2011, Denver, C
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
Sparse approximate inverse preconditioners on high performance GPU platforms
Simulation with models based on partial differential equations often requires the solution of (sequences of) large and sparse algebraic linear systems. In multidimensional domains, preconditioned Krylov iterative solvers are often appropriate for these duties. Therefore, the search for efficient preconditioners for Krylov subspace methods is a crucial theme. Recent developments, especially in computing hardware, have renewed the interest in approximate inverse preconditioners in factorized form, because their application during the solution process can be more efficient. We present here some experiences focused on the approximate inverse preconditioners proposed by Benzi and Tůma from 1996 and the sparsification and inversion proposed by van Duin in 1999. Computational costs, reorderings and implementation issues are considered both on conventional and innovative computing architectures like Graphics Programming Units (GPUs)
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