Publications

Abstract not provided.

Abstract not provided.

The goal of this report is to provide a comprehensive status report of the research & development conducted in the context of the DARMA project by the end of the first quarter of fiscal year 2020. It follows in particular [LBS+19] and [PL19].

Credibility of end-to-end CompSim (Computational Simulation) models and their agile execution requires an expressive framework to describe, communicate and execute complex computational tool chains representing the model. All stakeholders from system engineering and customers through model developers and V&V partners need views and functionalities of the workflow representing the model in a manner that is natural to their discipline. In the milestone and in this report we define workflow as a network of computation simulation activities executed autonomously on a distributed set of computational platforms. The FY19 ASC L2 Milestone (6802) for the Integrated Workflow (IWF) project was designed to integrate and improve existing capabilities or develop new functionalities to provide a wide range of stakeholders a coherent and intuitive platform capable of defining and executing CompSim modeling from analysis workflow definition to complex ensemble calculations. The main goal of the milestone was to advance the integrated workflow capabilities to support the weapon system analysts with a production deployment in FY20. Ensemble calculations supporting program decisions include sensitivity analysis, optimization and uncertainty quantification. The goal of the L2 milestone aligned with the ultimate goal of the IWF project is to foster cultural and technical shift toward and integrated CompSim capability based on automated workflows. Specific deliverables were defined in five broad categories: 1) Infrastructure, including development of distributed-computing workflow capability, 2) integration of Dakota (Sandia's sensitivity, optimization and UQ engine) with SAW (Sandia Analysis Workbench), 3) ARG (Automatic Report Generator introspecting analysis artifacts and generating human-readable extensible and archivable reports), 4) Libraries and Repositories aiding capability reuse, and 5) Exemplars to support training, capturing best practices and stress testing of the platform. A set of exemplars was defined to represent typical weapon system qualification CompSim projects. Analyzing the required capabilities and using the findings to plan implementation of required capabilities ensured optimal allocation of development resources focused on production deployment after the L2 is completed. It was recognized early that the end-to-end modeling applications pose a considerable number of diverse risks, and a formal risk tracking process was implemented. The project leveraged products, capabilities and development tasks of IWF partners. SAW, Dakota, Cubit, Sierra, Slycat, and NGA (NexGen Analytics, a small business) contributed to the integrated platform developed during this milestone effort. New products delivered include: a) NGW (Next Generation Workflow) for robust workflow definition and execution, b) Dakota wizards, editor and results visualization, and c) the automatic report generator ARG. User engagement was initiated early in the development process eliciting concrete requirements and actionable feedback to assure that the integrated CompSim capability will have high user acceptance and impact. The current integrated capabilities have been demonstrated and are continually being tested by a set of exemplars ranging from training scenarios to computationally demanding uncertainty analyses. The integrated workflow platform has been deployed on both SRN (Sandia Restricted Network) and SCN (Sandia Classified Network). Computational platforms where the system has been demonstrated span from Windows (Creo the CAD platform chosen by Sandia) to Trinity HPC (Sierra and CTH solvers). Follow up work will focus on deployment at SNL and other sites in the nuclear enterprise (LLNL, KCNSC), training and consulting support to democratize the analysis agility, process health and knowledge management benefits the NGW platform provides. ACKNOWLEDGEMENTS The IWF team would like to acknowledge the consistent support from the ASC sponsors: Scott Hutchinson, Walt Witkowski, Ken Alvin, Tom Klitsner, Jeremy Templeton, Erik Strack, and Amanda Dodd. Without their support this integrated effort would not have been possible. We would also like to thank the milestone review panel for their insightful feedback and guidance throughout the year: Martin Heinstein, Patty Hough, Jay Dike, Dan Laney (LLNL), and Jay Billings (ORNL). And of course, without the hard work of the IWF team none of this would have happened.

Abstract not provided.

Abstract not provided.

Abstract not provided.

This is the DARMA FY19-Q1 interim report. This page intentionally left blank. This document was generated with the Automatic Report Generator (ARG). This page intentionally left blank.

This report is a sequel to [PC18], where we provided the detailed installation and testing instructions of Sandia's currently-being-developed Automatic Report Genera- tor (ARG), for both Linux and macOS target platforms. In the current report, we extend these instructions to the case of Windows systems.

Abstract not provided.

Abstract not provided.

In this report we propose a new, extensible and flexible methodology to describe the structure of documents for the Automatic Report Generator (ARG) currently being developed at Sandia.

This report is a sequel to [PB16], in which we provided a first progress report on research and development towards a scalable, asynchronous many-task, in situ statistical analysis engine using the Legion runtime system. This earlier work included a prototype implementation of a proposed solution, using a proxy mini-application as a surrogate for a full-scale scientific simulation code. The first scalability studies were conducted with the above on modestly-sized experimental clusters. In contrast, in the current work we have integrated our in situ analysis engines with a full-size scientific application (S3D, using the Legion-SPMD model), and have conducted nu- merical tests on the largest computational platform currently available for DOE science ap- plications. We also provide details regarding the design and development of a light-weight asynchronous collectives library. We describe how this library is utilized within our SPMD- Legion S3D workflow, and compare the data aggregation technique deployed herein to the approach taken within our previous work.

Abstract not provided.

Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application.

Abstract not provided.

In this report, we propose a framework for the design and implementation of in-situ analy- ses using an asynchronous many-task (AMT) model, using the Legion programming model together with the MiniAero mini-application as a surrogate for full-scale parallel scientific computing applications. The bulk of this work consists of converting the Learn/Derive/Assess model which we had initially developed for parallel statistical analysis using MPI [PTBM11], from a SPMD to an AMT model. In this goal, we propose an original use of the concept of Legion logical regions as a replacement for the parallel communication schemes used for the only operation of the statistics engines that require explicit communication. We then evaluate this proposed scheme in a shared memory environment, using the Legion port of MiniAero as a proxy for a full-scale scientific application, as a means to provide input data sets of variable size for the in-situ statistical analyses in an AMT context. We demonstrate in particular that the approach has merit, and warrants further investigation, in collaboration with ongoing efforts to improve the overall parallel performance of the Legion system.

Abstract not provided.

Abstract not provided.

This report follows the series of previous documents ([PT08, BPRT09b, PT09, BPT09, PT10, PB13], where we presented the parallel descriptive, correlative, multi-correlative, principal component analysis, contingency, k -means, order and auto-correlative statistics engines which we developed within the Visualization Tool Kit ( VTK ) as a scalable, parallel and versatile statistics package. We now report on a new engine which we developed for the calculation of divergence statistics, a concept which we hereafter explain and whose main goal is to quantify the discrepancy, in a stasticial manner akin to measuring a distance, between an observed empirical distribution and a theoretical, "ideal" one. The ease of use of the new diverence statistics engine is illustrated by the means of C++ code snippets. Although this new engine does not yet have a parallel implementation, it has already been applied to HPC performance analysis, of which we provide an example.

This brief report explains the method used for parameter calibration and model validation in SST/Macro and the set of tools and workflow developed for this purpose.

This document presents current technical progress and dissemination of results for the Mathematics for Analysis of Petascale Data (MAPD) project titled "Topology for Statistical Modeling of Petascale Data", funded by the Office of Science Advanced Scientific Computing Research (ASCR) Applied Math program.

Abstract not provided.

This document presents current technical progress and dissemination of results for the Mathematics for Analysis of Petascale Data (MAPD) project titled 'Topology for Statistical Modeling of Petascale Data', funded by the Office of Science Advanced Scientific Computing Research (ASCR) Applied Math program. Many commonly used algorithms for mathematical analysis do not scale well enough to accommodate the size or complexity of petascale data produced by computational simulations. The primary goal of this project is thus to develop new mathematical tools that address both the petascale size and uncertain nature of current data. At a high level, our approach is based on the complementary techniques of combinatorial topology and statistical modeling. In particular, we use combinatorial topology to filter out spurious data that would otherwise skew statistical modeling techniques, and we employ advanced algorithms from algebraic statistics to efficiently find globally optimal fits to statistical models. This document summarizes the technical advances we have made to date that were made possible in whole or in part by MAPD funding. These technical contributions can be divided loosely into three categories: (1) advances in the field of combinatorial topology, (2) advances in statistical modeling, and (3) new integrated topological and statistical methods.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

This document describes how to obtain, install, use, and enjoy a better life with OVIS version 3.2. The OVIS project targets scalable, real-time analysis of very large data sets. We characterize the behaviors of elements and aggregations of elements (e.g., across space and time) in data sets in order to detect meaningful conditions and anomalous behaviors. We are particularly interested in determining anomalous behaviors that can be used as advance indicators of significant events of which notification can be made or upon which action can be taken or invoked. The OVIS open source tool (BSD license) is available for download at ovis.ca.sandia.gov. While we intend for it to support a variety of application domains, the OVIS tool was initially developed for, and continues to be primarily tuned for, the investigation of High Performance Compute (HPC) cluster system health. In this application it is intended to be both a system administrator tool for monitoring and a system engineer tool for exploring the system state in depth. OVIS 3.2 provides a variety of statistical tools for examining the behavior of elements in a cluster (e.g., nodes, racks) and associated resources (e.g., storage appliances and network switches). It provides an interactive 3-D physical view in which the cluster elements can be colored by raw or derived element values (e.g., temperatures, memory errors). The visual display allows the user to easily determine abnormal or outlier behaviors. Additionally, it provides search capabilities for certain scheduler logs. The OVIS capabilities were designed to be highly interactive - for example, the job search may drive an analysis which in turn may drive the user generation of a derived value which would then be examined on the physical display. The OVIS project envisions the capabilities of its tools applied to compute cluster monitoring. In the future, integration with the scheduler or resource manager will be included in a release to enable intelligent resource utilization. For example, nodes that are deemed less healthy (i.e., nodes that exhibit outlier behavior with respect to some set of variables shown to be correlated with future failure) can be discovered and assigned to shorter duration or less important jobs. Further, HPC applications with fault-tolerant capabilities would respond to changes in resource health and other OVIS notifications as needed, rather than undertaking preventative measures (e.g. checkpointing) at regular intervals unnecessarily.

Abstract not provided.

As HPC systems grow in size and complexity, diagnosing problems and understanding system behavior, including failure modes, becomes increasingly difficult and time consuming. At Sandia National Laboratories we have developed a tool, OVIS, to facilitate large scale HPC system understanding. OVIS incorporates an intuitive graphical user interface, an extensive and extendable data analysis suite, and a 3-D visualization engine that allows visual inspection of both raw and derived data on a geometrically correct representation of a HPC system. This talk will cover system instrumentation, data collection (including log files and the complications of meaningful parsing), analysis, visualization of both raw and derived information, and how data can be combined to increase system understanding and efficiency.

Consider a classic hierarchy tree as a basic model of a 'system-of-systems' network, where each node represents a component system (which may itself consist of a set of sub-systems). For this general composite system, we present a technique for computing the optimal testing strategy, which is based on Bayesian decision analysis. In previous work, we developed a Bayesian approach for computing the distribution of the reliability of a system-of-systems structure that uses test data and prior information. This allows for the determination of both an estimate of the reliability and a quantification of confidence in the estimate. Improving the accuracy of the reliability estimate and increasing the corresponding confidence require the collection of additional data. However, testing all possible sub-systems may not be cost-effective, feasible, or even necessary to achieve an improvement in the reliability estimate. To address this sampling issue, we formulate a Bayesian methodology that systematically determines the optimal sampling strategy under specified constraints and costs that will maximally improve the reliability estimate of the composite system, e.g., by reducing the variance of the reliability distribution. This methodology involves calculating the 'Bayes risk of a decision rule' for each available sampling strategy, where risk quantifies the relative effect that each sampling strategy could have on the reliability estimate. A general numerical algorithm is developed and tested using an example multicomponent system. The results show that the procedure scales linearly with the number of components available for testing.

Statistical analysis is typically used to reduce the dimensionality of and infer meaning from data. A key challenge of any statistical analysis package aimed at large-scale, distributed data is to address the orthogonal issues of parallel scalability and numerical stability. Many statistical techniques, e.g., descriptive statistics or principal component analysis, are based on moments and co-moments and, using robust online update formulas, can be computed in an embarrassingly parallel manner, amenable to a map-reduce style implementation. In this paper we focus on contingency tables, through which numerous derived statistics such as joint and marginal probability, point-wise mutual information, information entropy, and {chi}{sup 2} independence statistics can be directly obtained. However, contingency tables can become large as data size increases, requiring a correspondingly large amount of communication between processors. This potential increase in communication prevents optimal parallel speedup and is the main difference with moment-based statistics where the amount of inter-processor communication is independent of data size. Here we present the design trade-offs which we made to implement the computation of contingency tables in parallel.We also study the parallel speedup and scalability properties of our open source implementation. In particular, we observe optimal speed-up and scalability when the contingency statistics are used in their appropriate context, namely, when the data input is not quasi-diffuse.

This report summarizes the current statistical analysis capability of OVIS and how it works in conjunction with the OVIS data readers and interpolators. It also documents how to extend these capabilities. OVIS is a tool for parallel statistical analysis of sensor data to improve system reliability. Parallelism is achieved using a distributed data model: many sensors on similar components (metaphorically sheep) insert measurements into a series of databases on computers reserved for analyzing the measurements (metaphorically shepherds). Each shepherd node then processes the sheep data stored locally and the results are aggregated across all shepherds. OVIS uses the Visualization Tool Kit (VTK) statistics algorithm class hierarchy to perform analysis of each process's data but avoids VTK's model aggregation stage which uses the Message Passing Interface (MPI); this is because if a single process in an MPI job fails, the entire job will fail. Instead, OVIS uses asynchronous database replication to aggregate statistical models. OVIS has several additional features beyond those present in VTK that, first, accommodate its particular data format and, second, improve the memory and speed of the statistical analyses. First, because many statistical algorithms are multivariate in nature and sensor data is typically univariate, interpolation of data is required to provide simultaneous observations of metrics. Note that in this report, we will refer to a single value obtained from a sensor as a measurement while a collection of multiple sensor values simultaneously present in the system is an observation. A base class for interpolation is provided that abstracts the operation of converting multiple sensor measurements into simultaneous observations. A concrete implementation is provided that performs piecewise constant temporal interpolation of multiple metrics across a single component. Secondly, because calculations may summarize data too large to fit in memory OVIS analyses batches of observations at a time and aggregates these intermediate intra-process models as it goes before storing the final model for inter-process aggregation via database replication. This reduces the memory footprint of the analysis, interpolation, and the database client and server query processing. This also interleaves processing with the disk I/O required to fetch data from the database - also improving speed. This report documents how OVIS performs analyses and how to create additional analysis components that fetch measurements from the database, perform interpolation, or perform operations on streamed observations (such as model updates or assessments). The rest of this section outlines the OVIS analysis algorithm and is followed by sections specific to each subtask. Note that we are limiting our discussion for now to the creation of a model from a set of measurements, and not including the assessment of observations using a model. The same framework can be used for assessment but that use case is not detailed in this report.

Statistical analysis is typically used to reduce the dimensionality of and infer meaning from data. A key challenge of any statistical analysis package aimed at large-scale, distributed data is to address the orthogonal issues of parallel scalability and numerical stability. Many statistical techniques, e.g., descriptive statistics or principal component analysis, are based on moments and co-moments and, using robust online update formulas, can be computed in an embarrassingly parallel manner, amenable to a map-reduce style implementation. In this paper we focus on contingency tables, through which numerous derived statistics such as joint and marginal probability, point-wise mutual information, information entropy, and {chi}{sup 2} independence statistics can be directly obtained. However, contingency tables can become large as data size increases, requiring a correspondingly large amount of communication between processors. This potential increase in communication prevents optimal parallel speedup and is the main difference with moment-based statistics (which we discussed in [1]) where the amount of inter-processor communication is independent of data size. Here we present the design trade-offs which we made to implement the computation of contingency tables in parallel. We also study the parallel speedup and scalability properties of our open source implementation. In particular, we observe optimal speed-up and scalability when the contingency statistics are used in their appropriate context, namely, when the data input is not quasi-diffuse.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

This report summarizes existing statistical engines in VTK/Titan and presents both the serial and parallel k-means statistics engines. It is a sequel to [PT08], [BPRT09], and [PT09] which studied the parallel descriptive, correlative, multi-correlative, principal component analysis, and contingency engines. The ease of use of the new parallel k-means engine is illustrated by the means of C++ code snippets and algorithm verification is provided. This report justifies the design of the statistics engines with parallel scalability in mind, and provides scalability and speed-up analysis results for the k-means engine.

Abstract not provided.

Abstract not provided.

Abstract not provided.

This report summarizes existing statistical engines in VTK/Titan and presents the recently parallelized contingency statistics engine. It is a sequel to [PT08] and [BPRT09] which studied the parallel descriptive, correlative, multi-correlative, and principal component analysis engines. The ease of use of this new parallel engines is illustrated by the means of C++ code snippets. Furthermore, this report justifies the design of these engines with parallel scalability in mind; however, the very nature of contingency tables prevent this new engine from exhibiting optimal parallel speed-up as the aforementioned engines do. This report therefore discusses the design trade-offs we made and study performance with up to 200 processors.

Abstract not provided.

Abstract not provided.

The purpose of this project was to investigate the use of Bayesian methods for the estimation of the reliability of complex systems. The goals were to find methods for dealing with continuous data, rather than simple pass/fail data; to avoid assumptions of specific probability distributions, especially Gaussian, or normal, distributions; to compute not only an estimate of the reliability of the system, but also a measure of the confidence in that estimate; to develop procedures to address time-dependent or aging aspects in such systems, and to use these models and results to derive optimal testing strategies. The system is assumed to be a system of systems, i.e., a system with discrete components that are themselves systems. Furthermore, the system is 'engineered' in the sense that each node is designed to do something and that we have a mathematical description of that process. In the time-dependent case, the assumption is that we have a general, nonlinear, time-dependent function describing the process. The major results of the project are described in this report. In summary, we developed a sophisticated mathematical framework based on modern probability theory and Bayesian analysis. This framework encompasses all aspects of epistemic uncertainty and easily incorporates steady-state and time-dependent systems. Based on Markov chain, Monte Carlo methods, we devised a computational strategy for general probability density estimation in the steady-state case. This enabled us to compute a distribution of the reliability from which many questions, including confidence, could be addressed. We then extended this to the time domain and implemented procedures to estimate the reliability over time, including the use of the method to predict the reliability at a future time. Finally, we used certain aspects of Bayesian decision analysis to create a novel method for determining an optimal testing strategy, e.g., we can estimate the 'best' location to take the next test to minimize the risk of making a wrong decision about the fitness of a system. We conclude this report by proposing additional fruitful areas of research.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

This document describes how to obtain, install, use, and enjoy a better life with OVIS version 2.0. The OVIS project targets scalable, real-time analysis of very large data sets. We characterize the behaviors of elements and aggregations of elements (e.g., across space and time) in data sets in order to detect anomalous behaviors. We are particularly interested in determining anomalous behaviors that can be used as advance indicators of significant events of which notification can be made or upon which action can be taken or invoked. The OVIS open source tool (BSD license) is available for download at ovis.ca.sandia.gov. While we intend for it to support a variety of application domains, the OVIS tool was initially developed for, and continues to be primarily tuned for, the investigation of High Performance Compute (HPC) cluster system health. In this application it is intended to be both a system administrator tool for monitoring and a system engineer tool for exploring the system state in depth. OVIS 2.0 provides a variety of statistical tools for examining the behavior of elements in a cluster (e.g., nodes, racks) and associated resources (e.g., storage appliances and network switches). It calculates and reports model values and outliers relative to those models. Additionally, it provides an interactive 3D physical view in which the cluster elements can be colored by raw element values (e.g., temperatures, memory errors) or by the comparison of those values to a given model. The analysis tools and the visual display allow the user to easily determine abnormal or outlier behaviors. The OVIS project envisions the OVIS tool, when applied to compute cluster monitoring, to be used in conjunction with the scheduler or resource manager in order to enable intelligent resource utilization. For example, nodes that are deemed less healthy, that is, nodes that exhibit outlier behavior in some variable, or set of variables, that has shown to be correlated with future failure, can be discovered and assigned to shorter duration or less important jobs. Further, applications with fault-tolerant capabilities can invoke those mechanisms on demand, based upon notification of a node exhibiting impending failure conditions, rather than performing such mechanisms (e.g. checkpointing) at regular intervals unnecessarily.

Abstract not provided.

This is a progress report on polynomial system solving for statistical modeling. This is a progress report on polynomial system solving for statistical modeling. This quarter we have developed our first model of shock response data and an algorithm for identifying the chamber cone containing a polynomial system in n variables with n+k terms within polynomial time - a significant improvement over previous algorithms, all having exponential worst-case complexity. We have implemented and verified the chamber cone algorithm for n+3 and are working to extend the implementation to handle arbitrary k. Later sections of this report explain chamber cones in more detail; the next section provides an overview of the project and how the current progress fits into it.

Abstract not provided.

Abstract not provided.

In this report, we present the novel functionality of parallel tetrahedral mesh refinement which we have implemented in MOAB. This report details work done to implement parallel, edge-based, tetrahedral refinement into MOAB. The theoretical basis for this work is contained in [PT04, PT05, TP06] while information on design, performance, and operation specific to MOAB are contained herein. As MOAB is intended mainly for use in pre-processing and simulation (as opposed to the post-processing bent of previous papers), the primary use case is different: rather than refining elements with non-linear basis functions, the goal is to increase the number of degrees of freedom in some region in order to more accurately represent the solution to some system of equations that cannot be solved analytically. Also, MOAB has a unique mesh representation which impacts the algorithm. This introduction contains a brief review of streaming edge-based tetrahedral refinement. The remainder of the report is broken into three sections: design and implementation, performance, and conclusions. Appendix A contains instructions for end users (simulation authors) on how to employ the refiner.

This report summarizes the existing statistical engines in VTK/Titan and presents the parallel versions thereof which have already been implemented. The ease of use of these parallel engines is illustrated by the means of C++ code snippets. Furthermore, this report justifies the design of these engines with parallel scalability in mind; then, this theoretical property is verified with test runs that demonstrate optimal parallel speed-up with up to 200 processors.

We present a formula for the pairwise update of arbitrary-order centered statistical moments. This formula is of particular interest to compute such moments in parallel for large-scale, distributed data sets. As a corollary, we indicate a specialization of this formula for incremental updates, of particular interest to streaming implementations. Finally, we provide pairwise and incremental update formulas for the covariance. Centered statistical moments are one of the most widely used tools in descriptive statistics. It is therefore essential for statistical analysis packages that robust and efficient algorithms be devised and implemented. However, robustness and speed of execution, in this context as well as in others, tend to be orthogonal. For instance, it is well known1 that algorithms for calculating centered statistical moments that utilize sum of powers for the sake of execution speed (one-pass algorithms) lead to unacceptable numerical instability.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

This report specifies the way in which Gauss points shall be named and ordered when storing them in an EXODUS II file so that they may be properly interpreted by visualization tools. This naming convention covers hexahedra and tetrahedra. Future revisions of this document will cover quadrilaterals, triangles, and shell elements.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Current work on the Integrated Stockpile Evaluation (ISE) project is evidence of Sandia's commitment to maintaining the integrity of the nuclear weapons stockpile. In this report, we undertake a key element in that process: development of an analytical framework for determining the reliability of the stockpile in a realistic environment of time-variance, inherent uncertainty, and sparse available information. This framework is probabilistic in nature and is founded on a novel combination of classical and computational Bayesian analysis, Bayesian networks, and polynomial chaos expansions. We note that, while the focus of the effort is stockpile-related, it is applicable to any reasonably-structured hierarchical system, including systems with feedback.

The purpose of this report is to define a standard interface for storing and retrieving novel, non-traditional partial differential equation (PDE) discretizations. Although it focuses specifically on finite elements where state is associated with edges and faces of volumetric elements rather than nodes and the elements themselves (as implemented in ALEGRA), the proposed interface should be general enough to accommodate most discretizations, including hp-adaptive finite elements and even mimetic techniques that define fields over arbitrary polyhedra. This report reviews the representation of edge and face elements as implemented by ALEGRA. It then specifies a convention for storing these elements in EXODUS files by extending the EXODUS API to include edge and face blocks in addition to element blocks. Finally, it presents several techniques for rendering edge and face elements using VTK and ParaView, including the use of VTK's generic dataset interface for interpolating values interior to edges and faces.

Traditional cluster monitoring approaches consider nodes in singleton, using manufacturer-specified extreme limits as thresholds for failure ''prediction''. We have developed a tool, OVIS, for monitoring and analysis of large computational platforms which, instead, uses a statistical approach to characterize single device behaviors from those of a large number of statistically similar devices. Baseline capabilities of OVIS include the visual display of deterministic information about state variables (e.g., temperature, CPU utilization, fan speed) and their aggregate statistics. Visual consideration of the cluster as a comparative ensemble, rather than as singleton nodes, is an easy and useful method for tuning cluster configuration and determining effects of real-time changes.

Abstract not provided.

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.

This report contains an algorithm for decomposing higher-order finite elementsinto regions appropriate for isosurfacing and proves the conditions under which thealgorithm will terminate. Finite elements are used to create piecewise polynomialapproximants to the solution of partial differential equations for which no analyticalsolution exists. These polynomials represent fields such as pressure, stress, and mo-mentim. In the past, these polynomials have been linear in each parametric coordinate.Each polynomial coefficient must be uniquely determined by a simulation, and thesecoefficients are called degrees of freedom. When there are not enough degrees of free-dom, simulations will typically fail to produce a valid approximation to the solution.Recent work has shown that increasing the number of degrees of freedom by increas-ing the order of the polynomial approximation (instead of increasing the number offinite elements, each of which has its own set of coefficients) can allow some typesof simulations to produce a valid approximation with many fewer degrees of freedomthan increasing the number of finite elements alone. However, once the simulation hasdetermined the values of all the coefficients in a higher-order approximant, tools donot exist for visual inspection of the solution.This report focuses on a technique for the visual inspection of higher-order finiteelement simulation results based on decomposing each finite element into simplicialregions where existing visualization algorithms such as isosurfacing will work. Therequirements of the isosurfacing algorithm are enumerated and related to the placeswhere the partial derivatives of the polynomial become zero. The original isosurfacingalgorithm is then applied to each of these regions in turn.3 AcknowledgementThe authors would like to thank David Day and Louis Romero for their insight into poly-nomial system solvers and the LDRD Senior Council for the opportunity to pursue thisresearch. The authors were supported by the United States Department of Energy, Officeof Defense Programs by the Labratory Directed Research and Development Senior Coun-cil, project 90499. Sandia is a multiprogram laboratory operated by Sandia Corporation,a Lockheed-Martin Company, for the United States Department of Energy under contractDE-AC04-94-AL85000.4

This report contains an algorithm for decomposing higher-order finite elements into regions appropriate for isosurfacing and proves the conditions under which the algorithm will terminate. Finite elements are used to create piecewise polynomial approximants to the solution of partial differential equations for which no analytical solution exists. These polynomials represent fields such as pressure, stress, and momentum. In the past, these polynomials have been linear in each parametric coordinate. Each polynomial coefficient must be uniquely determined by a simulation, and these coefficients are called degrees of freedom. When there are not enough degrees of freedom, simulations will typically fail to produce a valid approximation to the solution. Recent work has shown that increasing the number of degrees of freedom by increasing the order of the polynomial approximation (instead of increasing the number of finite elements, each of which has its own set of coefficients) can allow some types of simulations to produce a valid approximation with many fewer degrees of freedom than increasing the number of finite elements alone. However, once the simulation has determined the values of all the coefficients in a higher-order approximant, tools do not exist for visual inspection of the solution. This report focuses on a technique for the visual inspection of higher-order finite element simulation results based on decomposing each finite element into simplicial regions where existing visualization algorithms such as isosurfacing will work. The requirements of the isosurfacing algorithm are enumerated and related to the places where the partial derivatives of the polynomial become zero. The original isosurfacing algorithm is then applied to each of these regions in turn.

Effective monitoring of large computational clusters demands the analysis of a vast amount of raw data from a large number of machines. The fundamental interactions of the system are not, however, well-defined, making it difficult to draw meaningful conclusions from this data, even if one were able to efficiently handle and process it. In this paper we show that computational clusters, because they are comprised of a large number of identical machines, behave in a statistically meaningful fashion. We therefore can employ normal statistical methods to derive information about individual systems and their environment and to detect problems sooner than with traditional mechanisms. We discuss design details necessary to use these methods on a large system in a timely and low-impact fashion.

Abstract not provided.

Abstract not provided.

In SAND report 2004-1617, we outline a method for edge-based tetrahedral subdivision that does not rely on saving state or communication to produce compatible tetrahedralizations. This report analyzes the performance of the technique by characterizing (a) mesh quality, (b) execution time, and (c) traits of the algorithm that could affect quality or execution time differently for different meshes. It also details the method used to debug the several hundred subdivision templates that the algorithm relies upon. Mesh quality is on par with other similar refinement schemes and throughput on modern hardware can exceed 600,000 output tetrahedra per second. But if you want to understand the traits of the algorithm, you have to read the report!

This is a basic documentation explaining how to use the SANDmath macros with a LATEX 2{var_epsilon} document pertaining to the SANDreport class.

Abstract not provided.

Finite element meshes are used to approximate the solution to some differential equation when no exact solution exists. A finite element mesh consists of many small (but finite, not infinitesimal or differential) regions of space that partition the problem domain, {Omega}. Each region, or element, or cell has an associated polynomial map, {Phi}, that converts the coordinates of any point, x = ( x y z ), in the element into another value, f(x), that is an approximate solution to the differential equation, as in Figure 1(a). This representation works quite well for axis-aligned regions of space, but when there are curved boundaries on the problem domain, {Omega}, it becomes algorithmically much more difficult to define {Phi} in terms of x. Rather, we define an archetypal element in a new coordinate space, r = ( r s t ), which has a simple, axis-aligned boundary (see Figure 1(b)) and place two maps onto our archetypal element: