Publications

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This report summarizes the first year’s effort on the Enceladus project, under which Sandia was asked to evaluate the potential advantages of adiabatic quantum computing for analyzing large data sets in the near future, 5-to-10 years from now. We were not specifically evaluating the machine being sold by D-Wave Systems, Inc; we were asked to anticipate what future adiabatic quantum computers might be able to achieve. While realizing that the greatest potential anticipated from quantum computation is still far into the future, a special purpose quantum computing capability, Adiabatic Quantum Optimization (AQO), is under active development and is maturing relatively rapidly; indeed, D-Wave Systems Inc. already offers an AQO device based on superconducting flux qubits. The AQO architecture solves a particular class of problem, namely unconstrained quadratic Boolean optimization. Problems in this class include many interesting and important instances. Because of this, further investigation is warranted into the range of applicability of this class of problem for addressing challenges of analyzing big data sets and the effectiveness of AQO devices to perform specific analyses on big data. Further, it is of interest to also consider the potential effectiveness of anticipated special purpose adiabatic quantum computers (AQCs), in general, for accelerating the analysis of big data sets. The objective of the present investigation is an evaluation of the potential of AQC to benefit analysis of big data problems in the next five to ten years, with our main focus being on AQO because of its relative maturity. We are not specifically assessing the efficacy of the D-Wave computing systems, though we do hope to perform some experimental calculations on that device in the sequel to this project, at least to provide some data to compare with our theoretical estimates.

The subject of this work is the development of models for the numerical simulation of matter, momentum, and energy balance in heterogeneous materials. These are materials that consist of multiple phases or species or that are structured on some (perhaps many) scale(s). By computational mechanics we mean to refer generally to the standard type of modeling that is done at the level of macroscopic balance laws (mass, momentum, energy). We will refer to the flow or flux of these quantities in a generalized sense as transport. At issue here are the forms of the governing equations in these complex materials which are potentially strongly inhomogeneous below some correlation length scale and are yet homogeneous on larger length scales. The question then becomes one of how to model this behavior and what are the proper multi-scale equations to capture the transport mechanisms across scales. To address this we look to the area of generalized stochastic process that underlie the transport processes in homogeneous materials. The archetypal example being the relationship between a random walk or Brownian motion stochastic processes and the associated Fokker-Planck or diffusion equation. Here we are interested in how this classical setting changes when inhomogeneities or correlations in structure are introduced into the problem. Aspects of non-classical behavior need to be addressed, such as non-Fickian behavior of the mean-squared-displacement (MSD) and non-Gaussian behavior of the underlying probability distribution of jumps. We present an experimental technique and apparatus built to investigate some of these issues. We also discuss diffusive processes in inhomogeneous systems, and the role of the chemical potential in diffusion of hard spheres is considered. Also, the relevance to liquid metal solutions is considered. Finally we present an example of how inhomogeneities in material microstructure introduce fluctuations at the meso-scale for a thermal conduction problem. These fluctuations due to random microstructures also provide a means of characterizing the aleatory uncertainty in material properties at the mesoscale.

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We present a new extended finite element method with algebraic constraints (XFEM-AC) for recovering weakly discontinuous solutions across internal element interfaces. If necessary, cut elements are further partitioned by a local secondary cut into body-fitting subelements. Each resulting subelement contributes an enrichment of the parent element. The enriched solutions are then tied using algebraic constraints, which enforce C0 continuity across both cuts. These constraints impose equivalence of the enriched and body-fitted finite element solutions, and are the key differentiating feature of the XFEM-AC. In so doing, a stable mixed formulation is obtained without having to explicitly construct a compatible Lagrange multiplier space and prove a formal inf-sup condition. Likewise, convergence of the XFEM-AC solution follows from its equivalence to the interface-fitted finite element solution. This relationship is further exploited to improve the numerical solution of the resulting XFEM-AC linear system. Examples are shown demonstrating the new approach for both steady-state and transient diffusion problems. © 2013 Elsevier B.V.

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Accuracy of component based power measuring devices forms a necessary basis for research in the area of power-efficient and power-aware computing. The accuracy of these devices must be quantified within a reasonable tolerance. This study focuses on PowerInsight, an out- of-band embedded measuring device which takes readings of power rails on compute nodes within a HPC system in realtime. We quantify how well the device performs in comparison to a digital oscilloscope as well as PowerMon2. We show that the accuracy is within a 6% deviation on measurements under reasonable load.

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