Publications

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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.

Attitudes play a significant role in determining how individuals process information and behave. In this paper we have developed a new computational model of population wide attitude change that captures the social level: how individuals interact and communicate information, and the cognitive level: how attitudes and concept interact with each other. The model captures the cognitive aspect by representing each individuals as a parallel constraint satisfaction network. The dynamics of this model are explored through a simple attitude change experiment where we vary the social network and distribution of attitudes in a population. Copyright © 2010, Association for the Advancement of Artificial Intelligence. All rights reserved.