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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'
Adaptive control in rollforward recovery for extreme scale multigrid
With the increasing number of compute components, failures in future
exa-scale computer systems are expected to become more frequent. This motivates
the study of novel resilience techniques. Here, we extend a recently proposed
algorithm-based recovery method for multigrid iterations by introducing an
adaptive control. After a fault, the healthy part of the system continues the
iterative solution process, while the solution in the faulty domain is
re-constructed by an asynchronous on-line recovery. The computations in both
the faulty and healthy subdomains must be coordinated in a sensitive way, in
particular, both under and over-solving must be avoided. Both of these waste
computational resources and will therefore increase the overall
time-to-solution. To control the local recovery and guarantee an optimal
re-coupling, we introduce a stopping criterion based on a mathematical error
estimator. It involves hierarchical weighted sums of residuals within the
context of uniformly refined meshes and is well-suited in the context of
parallel high-performance computing. The re-coupling process is steered by
local contributions of the error estimator. We propose and compare two criteria
which differ in their weights. Failure scenarios when solving up to
unknowns on more than 245\,766 parallel processes will be
reported on a state-of-the-art peta-scale supercomputer demonstrating the
robustness of the method
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
A bibliography on parallel and vector numerical algorithms
This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also
Research and Education in Computational Science and Engineering
Over the past two decades the field of computational science and engineering
(CSE) has penetrated both basic and applied research in academia, industry, and
laboratories to advance discovery, optimize systems, support decision-makers,
and educate the scientific and engineering workforce. Informed by centuries of
theory and experiment, CSE performs computational experiments to answer
questions that neither theory nor experiment alone is equipped to answer. CSE
provides scientists and engineers of all persuasions with algorithmic
inventions and software systems that transcend disciplines and scales. Carried
on a wave of digital technology, CSE brings the power of parallelism to bear on
troves of data. Mathematics-based advanced computing has become a prevalent
means of discovery and innovation in essentially all areas of science,
engineering, technology, and society; and the CSE community is at the core of
this transformation. However, a combination of disruptive
developments---including the architectural complexity of extreme-scale
computing, the data revolution that engulfs the planet, and the specialization
required to follow the applications to new frontiers---is redefining the scope
and reach of the CSE endeavor. This report describes the rapid expansion of CSE
and the challenges to sustaining its bold advances. The report also presents
strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie
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