Publications

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Alkali nitrate eutectic mixtures are finding application as industrial heat transfer fluids in concentrated solar power generation systems. An important property for such applications is the melting point, or phase coexistence temperature. We have computed melting points for lithium, sodium and potassium nitrate from molecular dynamics simulations using a recently developed method, which uses thermodynamic integration to compute the free energy difference between the solid and liquid phases. The computed melting point for NaNO3 was within 15K of its experimental value, while for LiNO3 and KNO3, the computed melting points were within 100K of the experimental values [4]. We are currently extending the approach to calculate melting temperatures for binary mixtures of lithium and sodium nitrate.

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This document provides common best practices for the efficient utilization of parallel file systems for analysts and application developers. A multi-program, parallel supercomputer is able to provide effective compute power by aggregating a host of lower-power processors using a network. The idea, in general, is that one either constructs the application to distribute parts to the different nodes and processors available and then collects the result (a parallel application), or one launches a large number of small jobs, each doing similar work on different subsets (a campaign). The I/O system on these machines is usually implemented as a tightly-coupled, parallel application itself. It is providing the concept of a 'file' to the host applications. The 'file' is an addressable store of bytes and that address space is global in nature. In essence, it is providing a global address space. Beyond the simple reality that the I/O system is normally composed of a small, less capable, collection of hardware, that concept of a global address space will cause problems if not very carefully utilized. How much of a problem and the ways in which those problems manifest will be different, but that it is problem prone has been well established. Worse, the file system is a shared resource on the machine - a system service. What an application does when it uses the file system impacts all users. It is not the case that some portion of the available resource is reserved. Instead, the I/O system responds to requests by scheduling and queuing based on instantaneous demand. Using the system well contributes to the overall throughput on the machine. From a solely self-centered perspective, using it well reduces the time that the application or campaign is subject to impact by others. The developer's goal should be to accomplish I/O in a way that minimizes interaction with the I/O system, maximizes the amount of data moved per call, and provides the I/O system the most information about the I/O transfer per request.

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This report describes the activities and results of a Sandia LDRD project whose objective was to develop and demonstrate foundational aspects of a next-generation nuclear reactor safety code that leverages advanced computational technology. The project scope was directed towards the systems-level modeling and simulation of an advanced, sodium cooled fast reactor, but the approach developed has a more general applicability. The major accomplishments of the LDRD are centered around the following two activities. (1) The development and testing of LIME, a Lightweight Integrating Multi-physics Environment for coupling codes that is designed to enable both 'legacy' and 'new' physics codes to be combined and strongly coupled using advanced nonlinear solution methods. (2) The development and initial demonstration of BRISC, a prototype next-generation nuclear reactor integrated safety code. BRISC leverages LIME to tightly couple the physics models in several different codes (written in a variety of languages) into one integrated package for simulating accident scenarios in a liquid sodium cooled 'burner' nuclear reactor. Other activities and accomplishments of the LDRD include (a) further development, application and demonstration of the 'non-linear elimination' strategy to enable physics codes that do not provide residuals to be incorporated into LIME, (b) significant extensions of the RIO CFD code capabilities, (c) complex 3D solid modeling and meshing of major fast reactor components and regions, and (d) an approach for multi-physics coupling across non-conformal mesh interfaces.

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We examine a new method of producing reduced order models for LTI systems which attempts to minimize a bound on the peak error between t he original and reduced order models subject to a bound on the peak value of the input. The method, which can be implemented by solving a set of linear programming problems that are parameterized v ia a single scalar quantity, is able to minimize an error bound subject to a number of moment matc hing constraints. Moreover, because all optimization is performed in the time domain, the method can also be used to perform model reduction for infinite dimensional systems, rather than being restricted to finite order state space descriptions. We begin by contrasting the method we present her e with two classes of standard model reduction algorithms, namely, moment matching algorithms and singular value-based methods. After motivating the class of reduction tools we propose, we describe the algorithm (which minimizes the Ll norm of the difference between the original and reduced order impulse responses) and formulate the corresponding linear programming problem that is solved during each iteration of the algorithm. We then prove that, for a certain class of LTI systems, the metho d we propose can be used to produce reduced order models of arbitrary accuracy even when the original system is infinite dimensional. We then show how to incorporate moment matching constraints into the basic error bound minimization algorithm, and present three examples which utilize the techni ques described herein. We conclude with some comments on extensions to multi-input, multi-output systems, as well as some general comments for future work. © 2010 Society for Industrial and Applied Mathematics.

We examine a new method of producing reduced order models for LTI systems which attempts to minimize a bound on the peak error between the original and reduced order models subject to a bound on the peak value of the input. The method, which can be implemented by solving a set of linear programming problems that are parameterized via a single scalar quantity, is able to minimize an error bound subject to a number of moment matching constraints.Moreover, because all optimization is performed in the time-domain, the method can also be used to perform model reduction for infinite dimensional systems, rather than being restricted to finite order state space descriptions. We begin by contrasting the method we present here to two classes of standard model reduction algorithms, namely moment matching algorithms and singularvalue- based methods. After motivating the class of reduction tools we propose, we describe the algorithm (which minimizes the L1 norm of the difference between the original and reduced order impulse responses) and formulate the corresponding linear programming problem that is solved during each iteration of the algorithm. We then show how to incorporate moment matching constraints into the basic error bound minimization algorithm, and present an example which utilizes the techniques described herein. We conclude with some general comments for future work, including a nonlinear programming formulation with potential implementation benefits. © 2010 AACC.

Inspired by prior work in the design of switched feedback controllers for second order systems, we develop a switched state feedback control law for the stabilization of LTI systems of arbitrary dimension. The control law operates by switching between two static gain vectors in such a way that the state trajectory is driven onto a stable n - 1 dimensional hyperplane (where n represents the system dimension). We begin by briefly examining relevant geometric properties of the phase portraits in the case of two-dimensional systems and show how these geometric properties can be expressed as algebraic constraints on the switched vector fields that are applicable to LTI systems of arbitrary dimension. We then describe an explicit procedure for designing stabilizing controllers and illustrate the closed-loop transient performance via two examples. © 2010 AACC.

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The peridynamic theory of mechanics attempts to unite the mathematical modeling of continuous media, cracks, and particles within a single framework. It does this by replacing the partial differential equations of the classical theory of solid mechanics with integral or integro-differential equations. These equations are based on a model of internal forces within a body in which material points interact with each other directly over finite distances. The classical theory of solid mechanics is based on the assumption of a continuous distribution of mass within a body. It further assumes that all internal forces are contact forces that act across zero distance. The mathematical description of a solid that follows from these assumptions relies on partial differential equations that additionally assume sufficient smoothness of the deformation for the PDEs to make sense in either their strong or weak forms. The classical theory has been demonstrated to provide a good approximation to the response of real materials down to small length scales, particularly in single crystals, provided these assumptions are met. Nevertheless, technology increasingly involves the design and fabrication of devices at smaller and smaller length scales, even interatomic dimensions. Therefore, it is worthwhile to investigate whether the classical theory can be extended to permit relaxed assumptions of continuity, to include the modeling of discrete particles such as atoms, and to allow the explicit modeling of nonlocal forces that are known to strongly influence the behavior of real materials.

Motivated by the needs of seismic inversion and building on our prior experience for fluid-dynamics systems, we present a high-order discontinuous Galerkin (DG) Runge-Kutta method applied to isotropic, linearized elasto-dynamics. Unlike other DG methods recently presented in the literature, our method allows for inhomogeneous material variations within each element that enables representation of realistic earth models — a feature critical for future use in seismic inversion. Likewise, our method supports curved elements and hybrid meshes that include both simplicial and nonsimplicial elements. We demonstrate the capabilities of this method through a series of numerical experiments including hybrid mesh discretizations of the Marmousi2 model as well as a modified Marmousi2 model with a oscillatory ocean bottom that is exactly captured by our discretization.

This abstract explores the potential advantages of discontinuous Galerkin (DG) methods for the time-domain inversion of media parameters within the earth’s interior. In particular, DG methods enable local polynomial refinement to better capture localized geological features within an area of interest while also allowing the use of unstructured meshes that can accurately capture discontinuous material interfaces. This abstract describes our initial findings when using DG methods combined with Runge-Kutta time integration and adjoint-based optimization algorithms for full-waveform inversion. Our initial results suggest that DG methods allow great flexibility in matching the media characteristics (faults, ocean bottom and salt structures) while also providing higher fidelity representations in target regions.

Peridynamics is a nonlocal extension of classical solid mechanics that allows for the modeling of bodies in which discontinuities occur spontaneously. Because the peridynamic expression for the balance of linear momentum does not contain spatial derivatives and is instead based on an integral equation, it is well suited for modeling phenomena involving spatial discontinuities such as crack formation and fracture. In this study, both peridynamics and classical finite element analysis are applied to simulate material response under dynamic blast loading conditions. A combined approach is utilized in which the portion of the simulation modeled with peridynamics interacts with the finite element portion of the model via a contact algorithm. The peridynamic portion of the analysis utilizes an elastic-plastic constitutive model with linear hardening. The peridynamic interface to the constitutive model is based on the calculation of an approximate deformation gradient, requiring the suppression of possible zero-energy modes. The classical finite element portion of the model utilizes a Johnson-Cook constitutive model. Simulation results are validated by direct comparison to expanding tube experiments. The coupled modeling approach successfully captures material response at the surface of the tube and the emerging fracture pattern. Copyright © 2010 by ASME.

As scientific simulations scale to use petascale machines and beyond, the data volumes generated pose a dual problem. First, with increasing machine sizes, the careful tuning of IO routines becomes more and more important to keep the time spent in IO acceptable. It is not uncommon, for instance, to have 20% of an application's runtime spent performing IO in a 'tuned' system. Careful management of the IO routines can move that to 5% or even less in some cases. Second, the data volumes are so large, on the order of 10s to 100s of TB, that trying to discover the scientifically valid contributions requires assistance at runtime to both organize and annotate the data. Waiting for offline processing is not feasible due both to the impact on the IO system and the time required. To reduce this load and improve the ability of scientists to use the large amounts of data being produced, new techniques for data management are required. First, there is a need for techniques for efficient movement of data from the compute space to storage. These techniques should understand the underlying system infrastructure and adapt to changing system conditions. Technologies include aggregation networks, data staging nodes for a closer parity to the IO subsystem, and autonomic IO routines that can detect system bottlenecks and choose different approaches, such as splitting the output into multiple targets, staggering output processes. Such methods must be end-to-end, meaning that even with properly managed asynchronous techniques, it is still essential to properly manage the later synchronous interaction with the storage system to maintain acceptable performance. Second, for the data being generated, annotations and other metadata must be incorporated to help the scientist understand output data for the simulation run as a whole, to select data and data features without concern for what files or other storage technologies were employed. All of these features should be attained while maintaining a simple deployment for the science code and eliminating the need for allocation of additional computational resources.

The next generation of capability-class, massively parallel processing (MPP) systems is expected to have hundreds of thousands to millions of processors, In such environments, it is critical to have fault-tolerance mechanisms, including checkpoint/restart, that scale with the size of applications and the percentage of the system on which the applications execute. For application-driven, periodic checkpoint operations, the state-of-the-art does not provide a scalable solution. For example, on today's massive-scale systems that execute applications which consume most of the memory of the employed compute nodes, checkpoint operations generate I/O that consumes nearly 80% of the total I/O usage. Motivated by this observation, this project aims to improve I/O performance for application-directed checkpoints through the use of lightweight storage architectures and overlay networks. Lightweight storage provide direct access to underlying storage devices. Overlay networks provide caching and processing capabilities in the compute-node fabric. The combination has potential to signifcantly reduce I/O overhead for large-scale applications. This report describes our combined efforts to model and understand overheads for application-directed checkpoints, as well as implementation and performance analysis of a checkpoint service that uses available compute nodes as a network cache for checkpoint operations.

The sensor placement problem in contamination warning system design for municipal water distribution networks involves maximizing the protection level afforded by limited numbers of sensors, typically quantified as the expected impact of a contamination event; the issue of how to mitigate against high-consequence events is either handled implicitly or ignored entirely. Consequently, expected-case sensor placements run the risk of failing to protect against high-consequence 9/11-style attacks. In contrast, robust sensor placements address this concern by focusing strictly on high-consequence events and placing sensors to minimize the impact of these events. We introduce several robust variations of the sensor placement problem, distinguished by how they quantify the potential damage due to high-consequence events. We explore the nature of robust versus expected-case sensor placements on three real-world large-scale distribution networks. We find that robust sensor placements can yield large reductions in the number and magnitude of high-consequence events, with only modest increases in expected impact. The ability to trade-off between robust and expected-case impacts is a key unexplored dimension in contamination warning system design. © 2009 ASCE.

Extensive experimentation over the past decade has shown that fabricated physical systems that are intended to be identical, and are nominally identical, in fact, differ from one another, and sometimes substantially. This fact makes it difficult to validate a mathematical model for any system and results in the requirement to characterize physical system behavior using the tools of uncertainty quantification. Further, because of the existence of system, component, and material uncertainty, the mathematical models of these elements sometimes seek to reflect the uncertainty. This presentation introduces some of the methods of probability and statistics, and shows how they can be applied in engineering modeling and data analysis. The ideas of randomness and some basic means for measuring and modeling it are presented. The ideas of random experiment, random variable, mean, variance and standard deviation, and probability distribution are introduced. The ideas are introduced in the framework of a practical, yet simple, example; measured data are included. This presentation is the third in a sequence of tutorial discussions on mathematical model validation. The example introduced here is also used in later presentations. © 2009 Society for Experimental Mechanics Inc.

This paper presents a basic tutorial on epistemic uncertainty quantification methods. Epistemic uncertainty, characterizing lack-of-knowledge, is often prevalent in engineering applications. However, the methods we have for analyzing and propagating epistemic uncertainty are not as nearly widely used or well-understood as methods to propagate aleatory uncertainty (e.g. inherent variability characterized by probability distributions). We examine three methods used in propagating epistemic uncertainties: interval analysis, Dempster-Shafer evidence theory, and second-order probability. We demonstrate examples of their use on a problem in structural dynamics. © 2009 Society for Experimental Mechanics Inc.

Xenon is not only a technologically important element used in laser technologies and jet propulsion, but it is also one of the most accessible materials in which to study the metal-insulator transition with increasing pressure. Because of its closed shell electronic configuration, xenon is often assumed to be chemically inert, interacting almost entirely through the van der Waals interaction, and at liquid density, is typically modeled well using Leonard-Jones potentials. However, such modeling has a limited range of validity as xenon is known to form compounds under normal conditions and likely exhibits considerably more chemistry at higher densities when hybridization of occupied orbitals becomes significant. We present DFT-MD simulations of shocked liquid xenon with the goal of developing an improved equation of state. The calculated Hugoniot to 2 MPa compares well with available experimental shock data. Sandia is a mul-tiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. © 2009 American Institute of Physics.

Grid-based mesh generation methods have been available for many years and can provide a reliable method for meshing arbitrary geometries with hexahedral elements. The principal use for these methods has mostly been limited to biological-type models where topology that may incorporate sharp edges and curve definitions are not critical. While these applications have been effective, robust generation of hexahedral meshes on mechanical models, where the topology is typically of prime importance, impose difficulties that existing grid-based methods have not yet effectively addressed. This work introduces a set of procedures that can be used in resolving the features of a geometric model for grid-based hexahedral mesh generation for mechanical or topology-rich models.

Xenon is not only a technologically important element used in laser technologies and jet propulsion, but it is also one of the most accessible materials in which to study the metal-insulator transition with increasing pressure. Because of its closed shell electronic configuration, xenon is often assumed to be chemically inert, interacting almost entirely through the van der Waals interaction, and at liquid density, is typically modeled well using Leonard-Jones potentials. However, such modeling has a limited range of validity as xenon is known to form compounds under normal conditions and likely exhibits considerably more chemistry at higher densities when hybridization of occupied orbitals becomes significant. We present DFT-MD simulations of shocked liquid xenon with the goal of developing an improved equation of state. The calculated Hugoniot to 2 MPa compares well with available experimental shock data. Sandia is a mul-tiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. © 2009 American Institute of Physics.

Mappings from a master element to the physical mesh element, in conjunction with local metrics such as those appearing in the Target-matrix paradigm, are used to measure quality at points within an element. The approach is applied to both linear and quadratic triangular elements; this enables, for example, one to measure quality within a quadratic finite element. Quality within an element may also be measured on a set of symmetry points, leading to so-called symmetry metrics. An important issue having to do with the labeling of the element vertices is relevant to mesh quality tools such as Verdict and Mesquite. Certain quality measures like area, volume, and shape should be label-invariant, while others such as aspect ratio and orientation should not. It is shown that local metrics whose Jacobian matrix is non-constant are label-invariant only at the center of the element, while symmetry metrics can be label-invariant anywhere within the element, provided the reference element is properly restricted.

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