Publications

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The shallow water equations are used as a test for many atmospheric models because the solution mimics the horizontal aspects of atmospheric dynamics while the simplicity of the equations make them useful for numerical experiments. This study describes a high-order element-based Galerkin method for the global shallow water equations using absolute vorticity, divergence, and fluid depth (atmospheric thickness) as the prognostic variables, while the wind field is a diagnostic variable that can be calculated from the stream function and velocity potential (the Laplacians of which are the vorticity and divergence, respectively). The numerical method employed to solve the shallow water system is based on the discontinuous Galerkin and spectral element methods. The discontinuous Galerkin method, which is inherently conservative, is used to solve the equations governing two conservative variables - absolute vorticity and atmospheric thickness (mass). The spectral element method is used to solve the divergence equation and the Poisson equations for the velocity potential and the stream function. Time integration is done with an explicit strong stability-preserving second-order Runge-Kutta scheme and the wind field is updated directly from the vorticity and divergence at each stage, and the computational domain is the cubed sphere. A stable steady-state test is run and convergence results are provided, showing that the method is high-order accurate. Additionally, two tests without analytic solutions are run with comparable results to previous high-resolution runs found in the literature.

The outline of this presentation is: (1) High-level view of Zoltan; (2) Requirements, data models, and interface; (3) Load Balancing and Partitioning; (4) Matrix Ordering, Graph Coloring; (5) Utilities; (6) Isorropia; and (7) Zoltan2.

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The objectives of this presentation are: (1) Learn how to partition a problem using Zoltan; (2) Understand the following (a) Basic process of partitioning with Zoltan, (b) Setting Zoltan parameters, (c) Registering query functions, (d) Writing query functions, (e) Zoltan-LB-Partition and its input/output; and (3) Be able to integrate Zoltan into your own applications.

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We fabricated a split-gate defined point contact in a double gate enhancement mode Si-MOS device, and implanted Sb donor atoms using a self-aligned process. E-beam lithography in combination with a timed implant gives us excellent control over the placement of dopant atoms, and acts as a stepping stone to focused ion beam implantation of single donors. Our approach allows us considerable latitude in experimental design in-situ. We have identified two resonance conditions in the point contact conductance as a function of split gate voltage. Using tunneling spectroscopy, we probed their electronic structure as a function of temperature and magnetic field. We also determine the capacitive coupling between the resonant feature and several gates. Comparison between experimental values and extensive quasi-classical simulations constrain the location and energy of the resonant level. We discuss our results and how they may apply to resonant tunneling through a single donor.

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The cubed sphere geometry, obtained by inscribing a cube in a sphere and mapping points between the two surfaces using a gnomonic (central) projection, is commonly used in atmospheric models because it is free of polar singularities and is well-suited for parallel computing. Global meshes on the cubed-sphere typically project uniform (square) grids from each face of the cube onto the sphere, and if refinement is desired then it is done with non-conforming meshes - overlaying the area of interest with a finer uniform mesh, which introduces so-called hanging nodes on edges along the boundary of the fine resolution area. An alternate technique is to tile each face of the cube with quadrilaterals without requiring the quads to be rectangular. These meshes allow for refinement in areas of interest with a conforming mesh, providing a smoother transition between high and low resolution portions of the grid than non-conforming refinement. The conforming meshes are demonstrated in HOMME, NCAR's High Order Method Modeling Environment, where two modifications have been made: the dependence on uniform meshes has been removed, and the ability to read arbitrary quadrilateral meshes from a previously-generated file has been added. Numerical results come from a conservative spectral element method modeling a selection of the standard shallow water test cases.

Periodic, coordinated, checkpointing to disk is the most prevalent fault tolerance method used in modern large-scale, capability class, high-performance computing (HPC) systems. Previous work has shown that as the system grows in size, the inherent synchronization of coordinated checkpoint/restart (CR) limits application scalability; at large node counts the application spends most of its time checkpointing instead of executing useful work. Furthermore, a single component failure forces an application restart from the last correct checkpoint. Suggested alternatives to coordinated CR include uncoordinated CR with message logging, redundant computation, and RAID-inspired, in-memory distributed checkpointing schemes. Each of these alternatives have differing overheads that are dependent on both the scale and communication characteristics of the application. In this work, using the Structural Simulation Toolkit (SST) simulator, we compare the performance characteristics of each of these resilience methods for a number of HPC application patterns on a number of proposed exascale machines. The result of this work provides valuable guidance on the most efficient resilience methods for exascale systems.

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Trilinos is an object-oriented software framework to enabled the solution of large-scale, complex multiphysics engineering and scientific problems. Different Trilinos packages build on each other to create a stack providing the necessary capability: (1) Non-linear solver; (2) Linear solver/preconditioner; (3) Distributed linear algebra; and (4) Local linear algebra.

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Palacios is a new open-source VMM under development at Northwestern University and the University of New Mexico that enables applications executing in a virtualized environment to achieve scalable high performance on large machines. Palacios functions as a modularized extension to Kitten, a high performance operating system being developed at Sandia National Laboratories to support large-scale supercomputing applications. Together, Palacios and Kitten provide a thin layer over the hardware to support full-featured virtualized environments alongside Kitten's lightweight native environment. Palacios supports existing, unmodified applications and operating systems by using the hardware virtualization technologies in recent AMD and Intel processors. Additionally, Palacios leverages Kitten's simple memory management scheme to enable low-overhead pass-through of native devices to a virtualized environment. We describe the design, implementation, and integration of Palacios and Kitten. Our benchmarks show that Palacios provides near native (within 5%), scalable performance for virtualized environments running important parallel applications. This new architecture provides an incremental path for applications to use supercomputers, running specialized lightweight host operating systems, that is not significantly performance-compromised. © 2010 IEEE.

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Enumerating triangles (3-cycles) in graphs is a kernel operation for social network analysis. For example, many community detection methods depend upon finding common neighbors of two related entities. We consider Cohen's simple and elegant solution for listing triangles: give each node a 'bucket.' Place each edge into the bucket of its endpoint of lowest degree, breaking ties consistently. Each node then checks each pair of edges in its bucket, testing for the adjacency that would complete that triangle. Cohen presents an informal argument that his algorithm should run well on real graphs. We formalize this argument by providing an analysis for the expected running time on a class of random graphs, including power law graphs. We consider a rigorously defined method for generating a random simple graph, the erased configuration model (ECM). In the ECM each node draws a degree independently from a marginal degree distribution, endpoints pair randomly, and we erase self loops and multiedges. If the marginal degree distribution has a finite second moment, it follows immediately that Cohen's algorithm runs in expected linear time. Furthermore, it can still run in expected linear time even when the degree distribution has such a heavy tail that the second moment is not finite. We prove that Cohen's algorithm runs in expected linear time when the marginal degree distribution has finite 4/3 moment and no vertex has degree larger than {radical}n. In fact we give the precise asymptotic value of the expected number of edge pairs per bucket. A finite 4/3 moment is required; if it is unbounded, then so is the number of pairs. The marginal degree distribution of a power law graph has bounded 4/3 moment when its exponent {alpha} is more than 7/3. Thus for this class of power law graphs, with degree at most {radical}n, Cohen's algorithm runs in expected linear time. This is precisely the value of {alpha} for which the clustering coefficient tends to zero asymptotically, and it is in the range that is relevant for the degree distribution of the World-Wide Web.

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Automated analysis of unstructured text documents (e.g., web pages, newswire articles, research publications, business reports) is a key capability for solving important problems in areas including decision making, risk assessment, social network analysis, intelligence analysis, scholarly research and others. However, as data sizes continue to grow in these areas, scalable processing, modeling, and semantic analysis of text collections becomes essential. In this paper, we present the ParaText text analysis engine, a distributed memory software framework for processing, modeling, and analyzing collections of unstructured text documents. Results on several document collections using hundreds of processors are presented to illustrate the exibility, extensibility, and scalability of the the entire process of text modeling from raw data ingestion to application analysis.

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The aim of this project is to develop low dimension parametric (deterministic) models of complex networks, to use compressive sensing (CS) and multiscale analysis to do so and to exploit the structure of complex networks (some are self-similar under coarsening). CS provides a new way of sampling and reconstructing networks. The approach is based on multiresolution decomposition of the adjacency matrix and its efficient sampling. It requires preprocessing of the adjacency matrix to make it 'blocky' which is the biggest (combinatorial) algorithm challenge. Current CS reconstruction algorithm makes no use of the structure of a graph, its very general (and so not very efficient/customized). Other model-based CS techniques exist, but not yet adapted to networks. Obvious starting point for future work is to increase the efficiency of reconstruction.

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This paper compares three approaches for model selection: classical least squares methods, information theoretic criteria, and Bayesian approaches. Least squares methods are not model selection methods although one can select the model that yields the smallest sum-of-squared error function. Information theoretic approaches balance overfitting with model accuracy by incorporating terms that penalize more parameters with a log-likelihood term to reflect goodness of fit. Bayesian model selection involves calculating the posterior probability that each model is correct, given experimental data and prior probabilities that each model is correct. As part of this calculation, one often calibrates the parameters of each model and this is included in the Bayesian calculations. Our approach is demonstrated on a structural dynamics example with models for energy dissipation and peak force across a bolted joint. The three approaches are compared and the influence of the log-likelihood term in all approaches is discussed.

The problem of incomplete data - i.e., data with missing or unknown values - in multi-way arrays is ubiquitous in biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision, communication networks, etc. We consider the problem of how to factorize data sets with missing values with the goal of capturing the underlying latent structure of the data and possibly reconstructing missing values (i.e., tensor completion). We focus on one of the most well-known tensor factorizations that captures multi-linear structure, CANDECOMP/PARAFAC (CP). In the presence of missing data, CP can be formulated as a weighted least squares problem that models only the known entries. We develop an algorithm called CP-WOPT (CP Weighted OPTimization) that uses a first-order optimization approach to solve the weighted least squares problem. Based on extensive numerical experiments, our algorithm is shown to successfully factorize tensors with noise and up to 99% missing data. A unique aspect of our approach is that it scales to sparse large-scale data, e.g., 1000 x 1000 x 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP-WOPT on two real-world applications: a novel EEG (electroencephalogram) application where missing data is frequently encountered due to disconnections of electrodes and the problem of modeling computer network traffic where data may be absent due to the expense of the data collection process.

Co-design has been identified as a key strategy for achieving Exascale computing in this decade. This paper describes the need for co-design in High Performance Computing related research in embedded computing the development of hardware/software co-simulation methods.

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The analysis of networked activities is dramatically more challenging than many traditional kinds of analysis. A network is defined by a set of entities (people, organizations, banks, computers, etc.) linked by various types of relationships. These entities and relationships are often uninteresting alone, and only become significant in aggregate. The analysis and visualization of these networks is one of the driving factors behind the creation of the Titan Toolkit. Given the broad set of problem domains and the wide ranging databases in use by the information analysis community, the Titan Toolkit's flexible, component based pipeline provides an excellent platform for constructing specific combinations of network algorithms and visualizations.

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