2,896 research outputs found
An Algebra of Synchronous Scheduling Interfaces
In this paper we propose an algebra of synchronous scheduling interfaces
which combines the expressiveness of Boolean algebra for logical and functional
behaviour with the min-max-plus arithmetic for quantifying the non-functional
aspects of synchronous interfaces. The interface theory arises from a
realisability interpretation of intuitionistic modal logic (also known as
Curry-Howard-Isomorphism or propositions-as-types principle). The resulting
algebra of interface types aims to provide a general setting for specifying
type-directed and compositional analyses of worst-case scheduling bounds. It
covers synchronous control flow under concurrent, multi-processing or
multi-threading execution and permits precise statements about exactness and
coverage of the analyses supporting a variety of abstractions. The paper
illustrates the expressiveness of the algebra by way of some examples taken
from network flow problems, shortest-path, task scheduling and worst-case
reaction times in synchronous programming.Comment: In Proceedings FIT 2010, arXiv:1101.426
Sparse Tensor Transpositions
We present a new algorithm for transposing sparse tensors called Quesadilla.
The algorithm converts the sparse tensor data structure to a list of
coordinates and sorts it with a fast multi-pass radix algorithm that exploits
knowledge of the requested transposition and the tensors input partial
coordinate ordering to provably minimize the number of parallel partial sorting
passes. We evaluate both a serial and a parallel implementation of Quesadilla
on a set of 19 tensors from the FROSTT collection, a set of tensors taken from
scientific and data analytic applications. We compare Quesadilla and a
generalization, Top-2-sadilla to several state of the art approaches, including
the tensor transposition routine used in the SPLATT tensor factorization
library. In serial tests, Quesadilla was the best strategy for 60% of all
tensor and transposition combinations and improved over SPLATT by at least 19%
in half of the combinations. In parallel tests, at least one of Quesadilla or
Top-2-sadilla was the best strategy for 52% of all tensor and transposition
combinations.Comment: This work will be the subject of a brief announcement at the 32nd ACM
Symposium on Parallelism in Algorithms and Architectures (SPAA '20
High accuracy binary black hole simulations with an extended wave zone
We present results from a new code for binary black hole evolutions using the
moving-puncture approach, implementing finite differences in generalised
coordinates, and allowing the spacetime to be covered with multiple
communicating non-singular coordinate patches. Here we consider a regular
Cartesian near zone, with adapted spherical grids covering the wave zone. The
efficiencies resulting from the use of adapted coordinates allow us to maintain
sufficient grid resolution to an artificial outer boundary location which is
causally disconnected from the measurement. For the well-studied test-case of
the inspiral of an equal-mass non-spinning binary (evolved for more than 8
orbits before merger), we determine the phase and amplitude to numerical
accuracies better than 0.010% and 0.090% during inspiral, respectively, and
0.003% and 0.153% during merger. The waveforms, including the resolved higher
harmonics, are convergent and can be consistently extrapolated to
throughout the simulation, including the merger and ringdown. Ringdown
frequencies for these modes (to ) match perturbative
calculations to within 0.01%, providing a strong confirmation that the remnant
settles to a Kerr black hole with irreducible mass and spin $S_f/M_f^2 = 0.686923 \pm 10\times10^{-6}
A massively parallel exponential integrator for advection-diffusion models
This work considers the Real Leja Points Method (ReLPM) for the exponential integration of large-scale sparse systems of ODEs, generated by Finite Element or Finite Difference discretizations of 3-D advection-diffusion models. We present an efficient parallel implementation of ReLPM for polynomial interpolation of the matrix exponential propagators. A scalability analysis of the most important computational kernel inside the code, the parallel sparse matrix\u2013vector product, has been performed, as well as an experimental study of the communication overhead. As a result of this study an optimized parallel sparse matrix\u2013vector product routine has been implemented. The resulting code shows good scaling behavior even when using more than one thousand processors. The numerical results presented on a number of very large test cases gives experimental evidence that ReLPM is a reliable and efficient tool for the simulation of complex hydrodynamic processes on parallel architectures
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