10,025 research outputs found
An efficient multi-core implementation of a novel HSS-structured multifrontal solver using randomized sampling
We present a sparse linear system solver that is based on a multifrontal
variant of Gaussian elimination, and exploits low-rank approximation of the
resulting dense frontal matrices. We use hierarchically semiseparable (HSS)
matrices, which have low-rank off-diagonal blocks, to approximate the frontal
matrices. For HSS matrix construction, a randomized sampling algorithm is used
together with interpolative decompositions. The combination of the randomized
compression with a fast ULV HSS factorization leads to a solver with lower
computational complexity than the standard multifrontal method for many
applications, resulting in speedups up to 7 fold for problems in our test
suite. The implementation targets many-core systems by using task parallelism
with dynamic runtime scheduling. Numerical experiments show performance
improvements over state-of-the-art sparse direct solvers. The implementation
achieves high performance and good scalability on a range of modern shared
memory parallel systems, including the Intel Xeon Phi (MIC). The code is part
of a software package called STRUMPACK -- STRUctured Matrices PACKage, which
also has a distributed memory component for dense rank-structured matrices
A recursive-faulting model of distributed damage in confined brittle materials
We develop a model of distributed damage in brittle materials deforming in triaxial compression based on the explicit construction of special microstructures obtained by recursive faulting. The model aims to predict the effective or macroscopic behavior of the material from its elastic and fracture properties; and to predict the microstructures underlying the microscopic behavior. The model accounts for the elasticity of the matrix, fault nucleation and the cohesive and frictional behavior of the faults. We analyze the resulting quasistatic boundary value problem and determine the relaxation of the potential energy, which describes the macroscopic material behavior averaged over all possible fine-scale structures. Finally, we present numerical calculations of the dynamic multi-axial compression experiments on sintered aluminum nitride of Chen and Ravichandran [1994. Dynamic compressive behavior of ceramics under lateral confinement. J. Phys. IV 4, 177–182; 1996a. Static and dynamic compressive behavior of aluminum nitride under moderate confinement. J. Am. Soc. Ceramics 79(3), 579–584; 1996b. An experimental technique for imposing dynamic multiaxial compression with mechanical confinement. Exp. Mech. 36(2), 155–158; 2000. Failure mode transition in ceramics under dynamic multiaxial compression. Int. J. Fracture 101, 141–159]. The model correctly predicts the general trends regarding the observed damage patterns; and the brittle-to-ductile transition resulting under increasing confinement
Semi-optimal Practicable Algorithmic Cooling
Algorithmic Cooling (AC) of spins applies entropy manipulation algorithms in
open spin-systems in order to cool spins far beyond Shannon's entropy bound. AC
of nuclear spins was demonstrated experimentally, and may contribute to nuclear
magnetic resonance (NMR) spectroscopy. Several cooling algorithms were
suggested in recent years, including practicable algorithmic cooling (PAC) and
exhaustive AC. Practicable algorithms have simple implementations, yet their
level of cooling is far from optimal; Exhaustive algorithms, on the other hand,
cool much better, and some even reach (asymptotically) an optimal level of
cooling, but they are not practicable. We introduce here semi-optimal
practicable AC (SOPAC), wherein few cycles (typically 2-6) are performed at
each recursive level. Two classes of SOPAC algorithms are proposed and
analyzed. Both attain cooling levels significantly better than PAC, and are
much more efficient than the exhaustive algorithms. The new algorithms are
shown to bridge the gap between PAC and exhaustive AC. In addition, we
calculated the number of spins required by SOPAC in order to purify qubits for
quantum computation. As few as 12 and 7 spins are required (in an ideal
scenario) to yield a mildly pure spin (60% polarized) from initial
polarizations of 1% and 10%, respectively. In the latter case, about five more
spins are sufficient to produce a highly pure spin (99.99% polarized), which
could be relevant for fault-tolerant quantum computing.Comment: 13 pages, 5 figure
Real-time filtering and detection of dynamics for compression of HDTV
The preprocessing of video sequences for data compressing is discussed. The end goal associated with this is a compression system for HDTV capable of transmitting perceptually lossless sequences at under one bit per pixel. Two subtopics were emphasized to prepare the video signal for more efficient coding: (1) nonlinear filtering to remove noise and shape the signal spectrum to take advantage of insensitivities of human viewers; and (2) segmentation of each frame into temporally dynamic/static regions for conditional frame replenishment. The latter technique operates best under the assumption that the sequence can be modelled as a superposition of active foreground and static background. The considerations were restricted to monochrome data, since it was expected to use the standard luminance/chrominance decomposition, which concentrates most of the bandwidth requirements in the luminance. Similar methods may be applied to the two chrominance signals
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