Publications

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Thermodynamic quantities, such as pressure and internal energy, and their derivatives, are used in many applications. Depending on application, a natural set of quantities related to one of four thermodynamic potentials are typically used. For example, hydro-codes use internal energy derived quantities and Equation of State work often uses Helmholtz free energy quantities. When performing work spanning over several fields, transformations between one set of quantities and another set of quantities are often needed. A short, but comprehensive, review of such transformations are given in this report.

We present a verification and validation analysis of a coordinate-transformation-based numerical solution method for the two-dimensional axisymmetric magnetic diffusion equation, implemented in the finite-element simulation code ALEGRA. The transformation, suggested by Melissen and Simkin, yields an equation set perfectly suited for linear finite elements and for problems with large jumps in material conductivity near the axis. The verification analysis examines transient magnetic diffusion in a rod or wire in a very low conductivity background by first deriving an approximate analytic solution using perturbation theory. This approach for generating a reference solution is shown to be not fully satisfactory. A specialized approach for manufacturing an exact solution is then used to demonstrate second-order convergence under spatial refinement and tem- poral refinement. For this new implementation, a significant improvement relative to previously available formulations is observed. Benefits in accuracy for computed current density and Joule heating are also demonstrated. The validation analysis examines the circuit-driven explosion of a copper wire using resistive magnetohydrodynamics modeling, in comparison to experimental tests. The new implementation matches the accuracy of the existing formulation, with both formulations capturing the experimental burst time and action to within approximately 2%.

We report on a new technique for obtaining off-Hugoniot pressure vs. density data for solid metals compressed to extreme pressure by a magnetically driven liner implosion on the Z-machine (Z) at Sandia National Laboratories. In our experiments, the liner comprises inner and outer metal tubes. The inner tube is composed of a sample material (e.g., Ta and Cu) whose compressed state is to be inferred. The outer tube is composed of Al and serves as the current carrying cathode. Another aluminum liner at much larger radius serves as the anode. A shaped current pulse quasi-isentropically compresses the sample as it implodes. The iterative method used to infer pressure vs. density requires two velocity measurements. Photonic Doppler velocimetry probes measure the implosion velocity of the free (inner) surface of the sample material and the explosion velocity of the anode free (outer) surface. These two velocities are used in conjunction with magnetohydrodynamic simulation and mathematical optimization to obtain the current driving the liner implosion, and to infer pressure and density in the sample through maximum compression. This new equation of state calibration technique is illustrated using a simulated experiment with a Cu sample. Monte Carlo uncertainty quantification of synthetic data establishes convergence criteria for experiments. Results are presented from experiments with Al/Ta, Al/Cu, and Al liners. Symmetric liner implosion with quasi-isentropic compression to peak pressure ∼1000 GPa is achieved in all cases. These experiments exhibit unexpectedly softer behavior above 200 GPa, which we conjecture is related to differences in the actual and modeled properties of aluminum.

Rebooting Computing (RC) is an effort in the IEEE to rethink future computers. RC started in 2012 by the co-chairs, Elie Track (IEEE Council on Superconductivity) and Tom Conte (Computer Society). RC takes a holistic approach, considering revolutionary as well as evolutionary solutions needed to advance computer technologies. Three summits have been held in 2013 and 2014, discussing different technologies, from emerging devices to user interface, from security to energy efficiency, from neuromorphic to reversible computing. The first part of this paper introduces RC to the design automation community and solicits revolutionary ideas from the community for the directions of future computer research. Energy efficiency is identified as one of the most important challenges in future computer technologies. The importance of energy efficiency spans from miniature embedded sensors to wearable computers, from individual desktops to data centers. To gauge the state of the art, the RC Committee organized the first Low Power Image Recognition Challenge (LPIRC). Each image contains one or multiple objects, among 200 categories. A contestant has to provide a working system that can recognize the objects and report the bounding boxes of the objects. The second part of this paper explains LPIRC and the solutions from the top two winners.

As discussed in the previous chapter, the purpose of peridynamics is to unify the mechanics of continuous media, continuous media with evolving discontinuities, and discrete particles. To accomplish this, peridynamics avoids the use of partial derivatives of the deformation with respect to spatial coordinates. Instead, it uses integral equations that remain valid on discontinuities. Discrete particles, as will be discussed later in this chapter, are treated using Dirac delta functions.

Solving Laplacian linear systems is an important task in a variety of practical and theoretical applications. This problem is known to have solutions that perform in linear times polylogarithmic work in theory, but these algorithms are difficult to implement in practice. We examine existing solution techniques in order to determine the best methods currently available and for which types of problems are they useful. We perform timing experiments using a variety of solvers on a variety of problems and present our results. We discover differing solver behavior between web graphs and a class of synthetic graphs designed to model them.

It is well known that the derivative-based classical approach to strain is problematic when the displacement field is irregular, noisy, or discontinuous. Difficulties arise wherever the displacements are not differentiable. We present an alternative, nonlocal approach to calculating strain from digital image correlation (DIC) data that is well-defined and robust, even for the pathological cases that undermine the classical strain measure. This integral formulation for strain has no spatial derivatives and when the displacement field is smooth, the nonlocal strain and the classical strain are identical. We submit that this approach to computing strains from displacements will greatly improve the fidelity and efficacy of DIC for new application spaces previously untenable in the classical framework.

We present a local search strategy to improve the coordinate-based mapping of a parallel job's tasks to the MPI ranks of its parallel allocation in order to reduce network congestion and the job's communication time. The goal is to reduce the number of network hops between communicating pairs of ranks. Our target is applications with a nearest-neighbor stencil communication pattern running on mesh systems with non-contiguous processor allocation, such as Cray XE and XK Systems. Using the miniGhost mini-app, which models the shock physics application CTH, we demonstrate that our strategy reduces application running time while also reducing the runtime variability. We further show that mapping quality can vary based on the selected allocation algorithm, even between allocation algorithms of similar apparent quality.

Magnetohydrodynamic (MHD) representations are used to model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. The resulting linear systems that arise from discretization and linearization of the nonlinear problem are generally difficult to solve. In this paper, we investigate multigrid preconditioners for this system. We consider two well-known multigrid relaxation methods for incompressible fluid dynamics: Braess-Sarazin relaxation and Vanka relaxation. We first extend these to the context of steady-state one-fluid viscoresistive MHD. Then we compare the two relaxation procedures within a multigrid-preconditioned GMRES method employed within Newton's method. To isolate the effects of the different relaxation methods, we use structured grids, inf-sup stable finite elements, and geometric interpolation. We present convergence and timing results for a two-dimensional, steady-state test problem.

The exponential increase in data over the last decade presents a significant challenge to analytics efforts that seek to process and interpret such data for various applications. Neural-inspired computing approaches are being developed in order to leverage the computational properties of the analog, low-power data processing observed in biological systems. Analog resistive memory crossbars can perform a parallel read or a vector-matrix multiplication as well as a parallel write or a rank-1 update with high computational efficiency. For an N × N crossbar, these two kernels can be O(N) more energy efficient than a conventional digital memory-based architecture. If the read operation is noise limited, the energy to read a column can be independent of the crossbar size (O(1)). These two kernels form the basis of many neuromorphic algorithms such as image, text, and speech recognition. For instance, these kernels can be applied to a neural sparse coding algorithm to give an O(N) reduction in energy for the entire algorithm when run with finite precision. Sparse coding is a rich problem with a host of applications including computer vision, object tracking, and more generally unsupervised learning.

This paper describes the design of Teko, an object-oriented C++ library for implementing advanced block preconditioners. Mathematical design criteria that elucidate the needs of block preconditioning libraries and techniques are explained and shown to motivate the structure of Teko. For instance, a principal design choice was for Teko to strongly reflect the mathematical statement of the preconditioners to reduce development burden and permit focus on the numerics. Additional mechanisms are explained that provide a pathway to developing an optimized production capable block preconditioning capability with Teko. Finally, Teko is demonstrated on fluid flow and magnetohydrodynamics applications. In addition to highlighting the features of the Teko library, these new results illustrate the effectiveness of recent preconditioning developments applied to advanced discretization approaches.

This work presents a new Krylov-subspace-recycling method for efficiently solving sequences of linear systems of equations characterized by varying right-hand sides and symmetric-positive-definite matrices. As opposed to typical truncation strategies used in recycling such as deflation, we propose a truncation method inspired by goal-oriented proper orthogonal decomposition (POD) from model reduction. This idea is based on the observation that model reduction aims to compute a low-dimensional subspace that contains an accurate solution; as such, we expect the proposed method to generate a low-dimensional subspace that is well suited for computing solutions that can satisfy inexact tolerances. In particular, we propose specific goal-oriented POD "ingredients" that align the optimality properties of POD with the objective of Krylov-subspace recycling. To compute solutions in the resulting "augmented" POD subspace, we propose a hybrid direct/iterative three-stage method that leverages (1) the optimal ordering of POD basis vectors, and (2) well-conditioned reduced matrices. Numerical experiments performed on solid-mechanics problems highlight the benefits of the proposed method over existing approaches for Krylov-subspace recycling.

We present a synthetic study investigating the resolution limits of Full Wavefield Inversion (FWI) when applied to data generated from a visco-TTI-elastic (VTE) model. We compare VTE inversion having fixed Q and TTI, with acoustic inversion of acoustically generated data and elastic inversion of elastically generated data.

The need to better represent the material properties within the earth's interior has driven the development of higherfidelity physics, e.g., visco-tilted-transversely-isotropic (visco- TTI) elastic media and material interfaces, such as the ocean bottom and salt boundaries. This is especially true for full waveform inversion (FWI), where one would like to reproduce the real-world effects and invert on unprocessed raw data. Here we present a numerical formulation using a Discontinuous Galerkin (DG) finite-element (FE) method, which incorporates the desired high-fidelity physics and material interfaces. To offset the additional costs of this material representation, we include a variety of techniques (e.g., non-conformal meshing, and local polynomial refinement), which reduce the overall costs with little effect on the solution accuracy.