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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'
Abstractions of Stochastic Hybrid Systems
In this paper we define a stochastic bisimulation concept for a very general class of stochastic hybrid systems, which subsumes most classes of stochastic hybrid systems. The definition of this bisimulation builds on the concept of zigzag morphism defined for strong Markov processes.
The main result is that this stochastic bisimulation is indeed an equivalence relation. The secondary result is that this bisimulation relation for the stochastic hybrid system models used in this paper implies the same
kind of bisimulation for their continuous parts and respectively for their jumping structures
Discrete Simulation of Behavioural Hybrid Process Calculus
Hybrid systems combine continuous-time and discrete behaviours. Simulation is one of the tools to obtain insight in dynamical systems behaviour. Simulation results provide information on performance of system and are helpful in detecting potential weaknesses and errors. Moreover, the results are handy in choosing adequate control strategies and parameters. In our contribution we report a work in progress, a technique for simulation of Behavioural Hybrid Process Calculus, an extension of process algebra that is suitable for the modelling and analysis of hybrid systems
GHOST: Building blocks for high performance sparse linear algebra on heterogeneous systems
While many of the architectural details of future exascale-class high
performance computer systems are still a matter of intense research, there
appears to be a general consensus that they will be strongly heterogeneous,
featuring "standard" as well as "accelerated" resources. Today, such resources
are available as multicore processors, graphics processing units (GPUs), and
other accelerators such as the Intel Xeon Phi. Any software infrastructure that
claims usefulness for such environments must be able to meet their inherent
challenges: massive multi-level parallelism, topology, asynchronicity, and
abstraction. The "General, Hybrid, and Optimized Sparse Toolkit" (GHOST) is a
collection of building blocks that targets algorithms dealing with sparse
matrix representations on current and future large-scale systems. It implements
the "MPI+X" paradigm, has a pure C interface, and provides hybrid-parallel
numerical kernels, intelligent resource management, and truly heterogeneous
parallelism for multicore CPUs, Nvidia GPUs, and the Intel Xeon Phi. We
describe the details of its design with respect to the challenges posed by
modern heterogeneous supercomputers and recent algorithmic developments.
Implementation details which are indispensable for achieving high efficiency
are pointed out and their necessity is justified by performance measurements or
predictions based on performance models. The library code and several
applications are available as open source. We also provide instructions on how
to make use of GHOST in existing software packages, together with a case study
which demonstrates the applicability and performance of GHOST as a component
within a larger software stack.Comment: 32 pages, 11 figure
Towards Efficient Path Query on Social Network with Hybrid RDF Management
The scalability and exibility of Resource Description Framework(RDF) model
make it ideally suited for representing online social networks(OSN). One basic
operation in OSN is to find chains of relations,such as k-Hop friends. Property
path query in SPARQL can express this type of operation, but its implementation
suffers from performance problem considering the ever growing data size and
complexity of OSN.In this paper, we present a main memory/disk based hybrid RDF
data management framework for efficient property path query. In this hybrid
framework, we realize an efficient in-memory algebra operator for property path
query using graph traversal, and estimate the cost of this operator to
cooperate with existing cost-based optimization. Experiments on benchmark and
real dataset demonstrated that our approach can achieve a good tradeoff between
data load expense and online query performance
Towards a General Theory of Stochastic Hybrid Systems
In this paper we set up a mathematical structure,
called Markov string, to obtaining a very general class of models for stochastic hybrid systems. Markov Strings are, in fact, a class of Markov processes, obtained by a
mixing mechanism of stochastic processes, introduced
by Meyer. We prove that Markov strings are strong Markov processes with the cadlag property. We then show how a very general class of stochastic hybrid processes can be embedded
in the framework of Markov strings. This class, which
is referred to as the General Stochastic Hybrid Systems (GSHS), includes as special cases all the classes of stochastic hybrid processes, proposed in the literature
Practical Sparse Matrices in C++ with Hybrid Storage and Template-Based Expression Optimisation
Despite the importance of sparse matrices in numerous fields of science,
software implementations remain difficult to use for non-expert users,
generally requiring the understanding of underlying details of the chosen
sparse matrix storage format. In addition, to achieve good performance, several
formats may need to be used in one program, requiring explicit selection and
conversion between the formats. This can be both tedious and error-prone,
especially for non-expert users. Motivated by these issues, we present a
user-friendly and open-source sparse matrix class for the C++ language, with a
high-level application programming interface deliberately similar to the widely
used MATLAB language. This facilitates prototyping directly in C++ and aids the
conversion of research code into production environments. The class internally
uses two main approaches to achieve efficient execution: (i) a hybrid storage
framework, which automatically and seamlessly switches between three underlying
storage formats (compressed sparse column, Red-Black tree, coordinate list)
depending on which format is best suited and/or available for specific
operations, and (ii) a template-based meta-programming framework to
automatically detect and optimise execution of common expression patterns.
Empirical evaluations on large sparse matrices with various densities of
non-zero elements demonstrate the advantages of the hybrid storage framework
and the expression optimisation mechanism.Comment: extended and revised version of an earlier conference paper
arXiv:1805.0338
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