Publications

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Proliferation of degrees-of-freedom has plagued discontinuous Galerkin methodology from its inception over 30 years ago. This paper develops a new computational formulation that combines the advantages of discontinuous Galerkin methods with the data structure of their continuous Galerkin counterparts. The new method uses local, element-wise problems to project a continuous finite element space into a given discontinuous space, and then applies a discontinuous Galerkin formulation. The projection leads to parameterization of the discontinuous degrees-of-freedom by their continuous counterparts and has a variational multiscale interpretation. This significantly reduces the computational burden and, at the same time, little or no degradation of the solution occurs. In fact, the new method produces improved solutions compared with the traditional discontinuous Galerkin method in some situations. © 2005 Elsevier B.V. All rights reserved.

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This document provides verification test results for normal, lognormal, and uniform distributions that are used in Sandia's Latin Hypercube Sampling (LHS) software. The purpose of this testing is to verify that the sample values being generated in LHS are distributed according to the desired distribution types. The testing of distribution correctness is done by examining summary statistics, graphical comparisons using quantile-quantile plots, and format statistical tests such as the Chisquare test, the Kolmogorov-Smirnov test, and the Anderson-Darling test. The overall results from the testing indicate that the generation of normal, lognormal, and uniform distributions in LHS is acceptable.

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We propose two new multilinear operators for expressing the matrix compositions that are needed in the Tucker and PARAFAC (CANDECOMP) decompositions. The first operator, which we call the Tucker operator, is shorthand for performing an n-mode matrix multiplication for every mode of a given tensor and can be employed to concisely express the Tucker decomposition. The second operator, which we call the Kruskal operator, is shorthand for the sum of the outer-products of the columns of N matrices and allows a divorce from a matricized representation and a very concise expression of the PARAFAC decomposition. We explore the properties of the Tucker and Kruskal operators independently of the related decompositions. Additionally, we provide a review of the matrix and tensor operations that are frequently used in the context of tensor decompositions.

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We report the implementation of an iterative scheme for calculating the Optimized Effective Potential (OEP). Given an energy functional that depends explicitly on the Kohn-Sham wave functions, and therefore, implicitly on the local effective potential appearing in the Kohn-Sham equations, a gradient-based minimization is used to find the potential that minimizes the energy. Previous work has shown how to find the gradient of such an energy with respect to the effective potential in the zero-temperature limit. We discuss a density-matrix-based derivation of the gradient that generalizes the previous results to the finite temperature regime, and we describe important optimizations used in our implementation. We have applied our OEP approach to the Hartree-Fock energy expression to perform Exact Exchange (EXX) calculations. We report our EXX results for common semiconductors and ordered phases of hydrogen at zero and finite electronic temperatures. We also discuss issues involved in the implementation of forces within the OEP/EXX approach.

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We present a series of related robust optimization models for placing sensors in municipal water networks to detect contaminants that are maliciously or accidentally injected. We formulate sensor placement problems as mixed-integer programs, for which the objective coefficients are not known with certainty. We consider a restricted absolute robustness criteria that is motivated by natural restrictions on the uncertain data, and we define three robust optimization models that differ in how the coefficients in the objective vary. Under one set of assumptions there exists a sensor placement that is optimal for all admissible realizations of the coefficients. Under other assumptions, we can apply sorting to solve each worst-case realization efficiently, or we can apply duality to integrate the worst-case outcome and have one integer program. The most difficult case is where the objective parameters are bilinear, and we prove its complexity is NP-hard even under simplifying assumptions. We consider a relaxation that provides an approximation, giving an overall guarantee of near-optimality when used with branch-and-bound search. We present preliminary computational experiments that illustrate the computational complexity of solving these robust formulations on sensor placement applications.

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A new multi-scale, stabilized method for Q1/P0 finite element computations of Lagrangian shock hydrodynamics is presented. Instabilities (of hourglass type) are controlled by a stabilizing operator derived using the variational multi-scale analysis paradigm. The resulting stabilizing term takes the form of a pressure correction. With respect to currently implemented hourglass control approaches, the novelty of the method resides in its residual-based character. The stabilizing residual has a definite physical meaning, since it embeds a discrete form of the Clausius-Duhem inequality. Effectively, the proposed stabilization samples and acts to counter the production of entropy due to numerical instabilities. The proposed technique is applicable to materials with no shear strength, for which there exists a caloric equation of state. The stabilization operator is incorporated into a mid-point, predictor/multi-corrector time integration algorithm, which conserves mass, momentum and total energy. Encouraging numerical results in the context of compressible gas dynamics confirm the potential of the method.

Verdict is a collection of subroutines for evaluating the geometric qualities of triangles, quadrilaterals, tetrahedra, and hexahedra using a variety of metrics. A metric is a real number assigned to one of these shapes depending on its particular vertex coordinates. These metrics are used to evaluate the input to finite element, finite volume, boundary element, and other types of solvers that approximate the solution to partial differential equations defined over regions of space. The geometric qualities of these regions is usually strongly tied to the accuracy these solvers are able to obtain in their approximations. The subroutines are written in C++ and have a simple C interface. Each metric may be evaluated individually or in combination. When multiple metrics are evaluated at once, they share common calculations to lower the cost of the evaluation.

Germanium telluride undergoes rapid transition between polycrystalline and amorphous states under either optical or electrical excitation. While the crystalline phases are predicted to be semiconductors, polycrystalline germanium telluride always exhibits p -type metallic conductivity. We present a study of the electronic structure and formation energies of the vacancy and antisite defects in both known crystalline phases. We show that these intrinsic defects determine the nature of free-carrier transport in crystalline germanium telluride. Germanium vacancies require roughly one-third the energy of the other three defects to form, making this by far the most favorable intrinsic defect. While the tellurium antisite and vacancy induce gap states, the germanium counterparts do not. A simple counting argument, reinforced by integration over the density of states, predicts that the germanium vacancy leads to empty states at the top of the valence band, thus giving a complete explanation of the observed p -type metallic conduction.

Over 300 Asian life scientists were surveyed to provide insight into work with infectious agents. This report provides the reader with a more complete understanding of the current practices employed to study infectious agents by laboratories located in Asian countries--segmented by level of biotechnology sophistication. The respondents have a variety of research objectives and study over 60 different pathogens and toxins. Many of the respondents indicated that their work was hampered by lack of adequate resources and the difficulty of accessing critical resources. The survey results also demonstrate that there appears to be better awareness of laboratory biosafety issues compared to laboratory biosecurity. Perhaps not surprisingly, many of these researchers work with pathogens and toxins under less stringent laboratory biosafety and biosecurity conditions than would be typical for laboratories in the West.

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This report evaluates a newly-available, high-definition, video camera coupled with a zoom optical system for microscopic imaging of micro-electro-mechanical systems. We did this work to support configuration of three document-camera-like stations as part of an installation in a new Microsystems building at Sandia National Laboratories. The video display walls to be installed as part of these three presentation and training stations are of extraordinary resolution and quality. The new availability of a reasonably-priced, cinema-quality, high-definition video camera offers the prospect of filling these displays with full-motion imaging of Sandia's microscopic products at a quality substantially beyond the quality of typical video microscopes. Simple and robust operation of the microscope stations will allow the extraordinary-quality imaging to contribute to Sandia's day-to-day research and training operations. This report illustrates the disappointing image quality from a camera/lens system comprised of a Sony HDC-X310 high-definition video camera coupled to a Navitar Zoom 6000 lens. We determined that this Sony camera is capable of substantially more image quality than the Navitar optic can deliver. We identified an optical doubler lens from Navitar as the component of their optical system that accounts for a substantial part of the image quality problem. While work continues to incrementally improve performance of the Navitar system, we are also evaluating optical systems from other vendors to couple to this Sony camera.

This paper summarizes the results of a theoretical and experimental program at Sandia National Laboratories aimed at identifying and modeling key physical features of rocks and rock-like materials at the laboratory scale over a broad range of strain rates. The mathematical development of a constitutive model is discussed and model predictions versus experimental data are given for a suite of laboratory tests. Concurrent pore collapse and cracking at the microscale are seen as competitive micromechanisms that give rise to the well-known macroscale phenomenon of a transition from volumetric compaction to dilatation under quasistatic triaxial compression. For high-rate loading, this competition between pore collapse and microcracking also seems to account for recently identified differences in strain-rate sensitivity between uniaxial-strain 'plate slap' data compared to uniaxial-stress Kolsky bar data. A description is given of how this work supports ongoing efforts to develop a predictive capability in simulating deformation and failure of natural geological materials, including those that contain structural features such as joints and other spatial heterogeneities.

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This SAND report provides the technical progress through April 2005 of the Sandia-led project, "Carbon Sequestration in Synechococcus Sp.: From Molecular Machines to Hierarchical Modeling," funded by the DOE Office of Science Genomics:GTL Program. Understanding, predicting, and perhaps manipulating carbon fixation in the oceans has long been a major focus of biological oceanography and has more recently been of interest to a broader audience of scientists and policy makers. It is clear that the oceanic sinks and sources of CO2 are important terms in the global environmental response to anthropogenic atmospheric inputs of CO2 and that oceanic microorganisms play a key role in this response. However, the relationship between this global phenomenon and the biochemical mechanisms of carbon fixation in these microorganisms is poorly understood. In this project, we will investigate the carbon sequestration behavior of Synechococcus Sp., an abundant marine cyanobacteria known to be important to environmental responses to carbon dioxide levels, through experimental and computational methods. This project is a combined experimental and computational effort with emphasis on developing and applying new computational tools and methods. Our experimental effort will provide the biology and data to drive the computational efforts and include significant investment in developing new experimental methods for uncovering protein partners, characterizing protein complexes, identifying new binding domains. We will also develop and apply new data measurement and statistical methods for analyzing microarray experiments. Computational tools will be essential to our efforts to discover and characterize the function of the molecular machines of Synechococcus. To this end, molecular simulation methods will be coupled with knowledge discovery from diverse biological data sets for high-throughput discovery and characterization of protein-protein complexes. In addition, we will develop a set of novel capabilities for inference of regulatory pathways in microbial genomes across multiple sources of information through the integration of computational and experimental technologies. These capabilities will be applied to Synechococcus regulatory pathways to characterize their interaction map and identify component proteins in these - 4 -pathways. We will also investigate methods for combining experimental and computational results with visualization and natural language tools to accelerate discovery of regulatory pathways. The ultimate goal of this effort is develop and apply new experimental and computational methods needed to generate a new level of understanding of how the Synechococcus genome affects carbon fixation at the global scale. Anticipated experimental and computational methods will provide ever-increasing insight about the individual elements and steps in the carbon fixation process, however relating an organism's genome to its cellular response in the presence of varying environments will require systems biology approaches. Thus a primary goal for this effort is to integrate the genomic data generated from experiments and lower level simulations with data from the existing body of literature into a whole cell model. We plan to accomplish this by developing and applying a set of tools for capturing the carbon fixation behavior of complex of Synechococcus at different levels of resolution. Finally, the explosion of data being produced by high-throughput experiments requires data analysis and models which are more computationally complex, more heterogeneous, and require coupling to ever increasing amounts of experimentally obtained data in varying formats. These challenges are unprecedented in high performance scientific computing and necessitate the development of a companion computational infrastructure to support this effort. More information about this project can be found at www.genomes-to-life.org Acknowledgment We want to gratefully acknowledge the contributions of: Grant Heffelfinger1*, Anthony Martino2, Brian Palenik6, Andrey Gorin3, Ying Xu10,3, Mark Daniel Rintoul1, Al Geist3, Matthew Ennis1, with Pratul Agrawal3, Hashim Al-Hashimi8, Andrea Belgrano12, Mike Brown1, Xin Chen9, Paul Crozier1, PguongAn Dam10, Jean-Loup Faulon2, Damian Gessler12, David Haaland1, Victor Havin4, C.F. Huang5, Tao Jiang9, Howland Jones1, David Jung3, Katherine Kang14, Michael Langston15, Shawn Martin1, Shawn Means1, Vijaya Natarajan4, Roy Nielson5, Frank Olken4, Victor Olman10, Ian Paulsen14, Steve Plimpton1, Andreas Reichsteiner5, Nagiza Samatova3, Arie Shoshani4, Michael Sinclair1, Alex Slepoy1, Shawn Stevens8, Charlie Strauss5, Zhengchang Su10, Ed Thomas1, Jerilyn Timlin1, WimVermaas13, Xiufeng Wan11, HongWei Wu10, Dong Xu11, Grover Yip8, Erik Zuiderweg8 *Author to whom correspondence should be addressed (gsheffe@sandia.gov) 1. Sandia National Laboratories, Albuquerque, NM 2. Sandia National Laboratories, Livermore, CA 3. Oak Ridge National Laboratory, Oak Ridge, TN 4. Lawrence Berkeley National Laboratory, Berkeley, CA 5. Los Alamos National Laboratory, Los Alamos, NM 6. University of California, San Diego 7. University of Illinois, Urbana/Champaign 8. University of Michigan, Ann Arbor 9. University of California, Riverside 10. University of Georgia, Athens 11. University of Missouri, Columbia 12. National Center for Genome Resources, Santa Fe, NM 13. Arizona State University 14. The Institute for Genomic Research 15. University of Tennessee 5 Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL8500.

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Given the logic density of modern FPGAs, it is feasible to use FPGAs for floating-point applications. However, it is important that any floating-point units that are used be highly optimized. This paper introduces an open source library of highly optimized floating-point units for Xilinx FPGAs. The units are fully IEEE compliant and achieve approximately 230 MHz operation frequency for double-precision add and multiply in a Xilinx Virtex-2-Pro FPGA (-7 speed grade). This speed is achieved with a 10 stage adder pipeline and a 12 stage multiplier pipeline. The area requirement is 571 slices for the adder and 905 slices for the multiplier.

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PyTrilinos provides python access to selected Trilinos packages: emerging from early stages, portability, completeness; parallelism; rapid prototyping; application development; unit testing; and numeric compatibility (migrating to NumPy). PyTrilinos complements and supplements the SciPy package.

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The Independent Network Model (INM) has proven to be a useful tool for understanding the development of permanent set in strained elastomers. Our previous work showed the applicability of the INM to our simulations of polymer systems crosslinking in strained states. This study looks at the INM applied to theoretical models incorporating entanglement effects, including Flory's constrained junction model and more recent tube models. The effect of entanglements has been treated as a separate network formed at gelation, with additional curing treated as traditional phantom contributions. Theoretical predictions are compared with large-scale molecular dynamics simulations.

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