Publications

This study compares several block-oriented preconditioners for the stabilized finite element discretization of the incompressible Navier-Stokes equations. This includes standard additive Schwarz domain decomposition methods, aggressive coarsening multigrid, and three preconditioners based on an approximate block LU factorization, specifically SIMPLEC, LSC, and PCD. Robustness is considered with a particular focus on the impact that different stabilization methods have on preconditioner performance. Additionally, parallel scaling studies are undertaken. The numerical results indicate that aggressive coarsening multigrid, LSC and PCD all have good algorithmic scalability. Coupling this with the fact that block methods can be applied to systems arising from stable mixed discretizations implies that these techniques are a promising direction for developing scalable methods for Navier-Stokes. © 2011.

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We present a methodology for optimally locating disinfectant booster stations for response to contamination events in water distribution systems. A stochastic programming problem considering uncertainty in both the location and time of the contamination event is formulated resulting in an extensive form that is equivalent to the weighted maximum coverage problem. Although the original full-space problem is intractably large, we show a series of reductions that reduce the size of the problem by five orders of magnitude and allow solutions of the optimal placement problem for realistically sized water network models. © 2012 Elsevier B.V.

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PyTrilinos is a set of Python interfaces to compiled Trilinos packages. This collection supports serial and parallel dense linear algebra, serial and parallel sparse linear algebra, direct and iterative linear solution techniques, algebraic and multilevel preconditioners, nonlinear solvers and continuation algorithms, eigensolvers and partitioning algorithms. Also included are a variety of related utility functions and classes, including distributed I/O, coloring algorithms and matrix generation. PyTrilinos vector objects are compatible with the popular NumPy Python package. As a Python front end to compiled libraries, PyTrilinos takes advantage of the flexibility and ease of use of Python, and the efficiency of the underlying C++, C and Fortran numerical kernels. This paper covers recent, previously unpublished advances in the PyTrilinos package.

An approach for incorporating embedded simulation and analysis capabilities in complex simulation codes through template-based generic programming is presented. This approach relies on templating and operator overloading within the C++ language to transform a given calculation into one that can compute a variety of additional quantities that are necessary for many state-of-the-art simulation and analysis algorithms. An approach for incorporating these ideas into complex simulation codes through general graph-based assembly is also presented. These ideas have been implemented within a set of packages in the Trilinos framework and are demonstrated on a simple problem from chemical engineering. © 2012 - IOS Press and the authors. All rights reserved.

Modal-based methods for structural health monitoring require the identification of characteristic frequencies associated with a structure's primary modes of failure. A major difficulty is the extraction of damage-related frequency shifts from the large set of often benign frequency shifts observed experimentally. In this study, we apply peridynamics in combination with modal analysis for the prediction of characteristic frequency shifts throughout the damage evolution process. Peridynamics, a nonlocal extension of continuum mechanics, is unique in its ability to capture progressive material damage. The application of modal analysis to peridynamic models enables the tracking of structural modes and characteristic frequencies over the course of a simulation. Shifts in characteristic frequencies resulting from evolving structural damage can then be isolated and utilized in the analysis of frequency responses observed experimentally. We present a methodology for quasi-static peridynamic analyses, including the solution of the eigenvalue problem for identification of structural modes. Repeated solution of the eigenvalue problem over the course of a transient simulation yields a data set from which critical shifts in modal frequencies can be isolated. The application of peridynamics to modal analysis is demonstrated on the benchmark problem of a simply-supported beam. The computed natural frequencies of an undamaged beam are found to agree well with the classical local solution. Analyses in the presence of cracks of various lengths are shown to reveal frequency shifts associated with structural damage. Copyright © 2012 by ASME.

Density Functional Theory (DFT) based Equation of State (EOS) construction is a prominent part of Sandia's capabilities to support engineering sciences. This capability is based on amending experimental data with information gained from computational investigations, in parts of the phase space where experimental data is hard, dangerous, or expensive to obtain. A prominent materials area where such computational investigations are hard to perform today because of limited accuracy is actinide and lanthanide materials. The Science of Extreme Environment Lab Directed Research and Development project described in this Report has had the aim to cure this accuracy problem. We have focused on the two major factors which would allow for accurate computational investigations of actinide and lanthanide materials: (1) The fully relativistic treatment needed for materials containing heavy atoms, and (2) the needed improved performance of DFT exchange-correlation functionals. We have implemented a fully relativistic treatment based on the Dirac Equation into the LANL code RSPt and we have shown that such a treatment is imperative when calculating properties of materials containing actinides and/or lanthanides. The present standard treatment that only includes some of the relativistic terms is not accurate enough and can even give misleading results. Compared to calculations previously considered state of the art, the Dirac treatment gives a substantial change in equilibrium volume predictions for materials with large spin-orbit coupling. For actinide and lanthanide materials, a Dirac treatment is thus a fundamental requirement in any computational investigation, including those for DFT-based EOS construction. For a full capability, a DFT functional capable of describing strongly correlated systems such as actinide materials need to be developed. Using the previously successful subsystem functional scheme developed by Mattsson et.al., we have created such a functional. In this functional the Harmonic Oscillator Gas is providing the necessary reference system for the strong correlation and localization occurring in actinides. Preliminary testing shows that the new Hao-Armiento-Mattsson (HAM) functional gives a trend towards improved results for the crystalline copper oxide test system we have chosen. This test system exhibits the same exchange-correlation physics as the actinide systems do, but without the relativistic effects, giving access to a pure testing ground for functionals. During the work important insights have been gained. An example is that currently available functionals, contrary to common belief, make large errors in so called hybridization regions where electrons from different ions interact and form new states. Together with the new understanding of functional issues, the Dirac implementation into the RSPt code will permit us to gain more fundamental understanding, both quantitatively and qualitatively, of materials of importance for Sandia and the rest of the Nuclear Weapons complex.

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This document reports on the research of Kenneth Letendre, the recipient of a Sandia Graduate Research Fellowship at the University of New Mexico. Warfare is an extreme form of intergroup competition in which individuals make extreme sacrifices for the benefit of their nation or other group to which they belong. Among animals, limited, non-lethal competition is the norm. It is not fully understood what factors lead to warfare. We studied the global variation in the frequency of civil conflict among countries of the world, and its positive association with variation in the intensity of infectious disease. We demonstrated that the burden of human infectious disease importantly predicts the frequency of civil conflict and tested a causal model for this association based on the parasite-stress theory of sociality. We also investigated the organization of social foraging by colonies of harvester ants in the genus Pogonomyrmex, using both field studies and computer models.

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This report gives an overview of the work done as part of an Early Career LDRD aimed at modeling flow induced damage of materials involving chemical reactions, deformation of the porous matrix, and complex flow phenomena. The numerical formulation is motivated by a mixture theory or theory of interacting continua type approach to coupling the behavior of the fluid and the porous matrix. Results for the proposed method are presented for several engineering problems of interest including carbon dioxide sequestration, hydraulic fracturing, and energetic materials applications. This work is intended to create a general framework for flow induced damage that can be further developed in each of the particular areas addressed below. The results show both convincing proof of the methodologies potential and the need for further validation of the models developed.