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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'
Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures
A new solver featuring time-space adaptation and error control has been
recently introduced to tackle the numerical solution of stiff
reaction-diffusion systems. Based on operator splitting, finite volume adaptive
multiresolution and high order time integrators with specific stability
properties for each operator, this strategy yields high computational
efficiency for large multidimensional computations on standard architectures
such as powerful workstations. However, the data structure of the original
implementation, based on trees of pointers, provides limited opportunities for
efficiency enhancements, while posing serious challenges in terms of parallel
programming and load balancing. The present contribution proposes a new
implementation of the whole set of numerical methods including Radau5 and
ROCK4, relying on a fully different data structure together with the use of a
specific library, TBB, for shared-memory, task-based parallelism with
work-stealing. The performance of our implementation is assessed in a series of
test-cases of increasing difficulty in two and three dimensions on multi-core
and many-core architectures, demonstrating high scalability
A Multi-Kernel Multi-Code Polar Decoder Architecture
Polar codes have received increasing attention in the past decade, and have
been selected for the next generation of wireless communication standard. Most
research on polar codes has focused on codes constructed from a
polarization matrix, called binary kernel: codes constructed from binary
kernels have code lengths that are bound to powers of . A few recent works
have proposed construction methods based on multiple kernels of different
dimensions, not only binary ones, allowing code lengths different from powers
of . In this work, we design and implement the first multi-kernel successive
cancellation polar code decoder in literature. It can decode any code
constructed with binary and ternary kernels: the architecture, sized for a
maximum code length , is fully flexible in terms of code length, code
rate and kernel sequence. The decoder can achieve frequency of more than
GHz in nm CMOS technology, and a throughput of Mb/s. The area
occupation ranges between mm for and mm for
. Implementation results show an unprecedented degree of
flexibility: with , up to code lengths can be decoded with
the same hardware, along with any kernel sequence and code rate
Design and optimization of a portable LQCD Monte Carlo code using OpenACC
The present panorama of HPC architectures is extremely heterogeneous, ranging
from traditional multi-core CPU processors, supporting a wide class of
applications but delivering moderate computing performance, to many-core GPUs,
exploiting aggressive data-parallelism and delivering higher performances for
streaming computing applications. In this scenario, code portability (and
performance portability) become necessary for easy maintainability of
applications; this is very relevant in scientific computing where code changes
are very frequent, making it tedious and prone to error to keep different code
versions aligned. In this work we present the design and optimization of a
state-of-the-art production-level LQCD Monte Carlo application, using the
directive-based OpenACC programming model. OpenACC abstracts parallel
programming to a descriptive level, relieving programmers from specifying how
codes should be mapped onto the target architecture. We describe the
implementation of a code fully written in OpenACC, and show that we are able to
target several different architectures, including state-of-the-art traditional
CPUs and GPUs, with the same code. We also measure performance, evaluating the
computing efficiency of our OpenACC code on several architectures, comparing
with GPU-specific implementations and showing that a good level of
performance-portability can be reached.Comment: 26 pages, 2 png figures, preprint of an article submitted for
consideration in International Journal of Modern Physics
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