Publications

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: