Analytic solutions are useful for code verification. Structural vibration codes approximate solutions to the eigenvalue problem for the linear elasticity equations (Navier's equations). Unfortunately the verification method of 'manufactured solutions' does not apply to vibration problems. Verification books (for example [2]) tabulate a few of the lowest modes, but are not useful for computations of large numbers of modes. A closed form solution is presented here for all the eigenvalues and eigenfunctions for a cuboid solid with isotropic material properties. The boundary conditions correspond physically to a greased wall.
We compare inexact Newton and coordinate descent methods for optimizing the quality of a mesh by repositioning the vertices, where quality is measured by the harmonic mean of the mean-ratio metric. The effects of problem size, element size heterogeneity, and various vertex displacement schemes on the performance of these algorithms are assessed for a series of tetrahedral meshes.
There is currently a large research and development effort within the high-performance computing community on advanced parallel programming models. This research can potentially have an impact on parallel applications, system software, and computing architectures in the next several years. Given Sandia's expertise and unique perspective in these areas, particularly on very large-scale systems, there are many areas in which Sandia can contribute to this effort. This technical report provides a survey of past and present parallel programming model research projects and provides a detailed description of the Partitioned Global Address Space (PGAS) programming model. The PGAS model may offer several improvements over the traditional distributed memory message passing model, which is the dominant model currently being used at Sandia. This technical report discusses these potential benefits and outlines specific areas where Sandia's expertise could contribute to current research activities. In particular, we describe several projects in the areas of high-performance networking, operating systems and parallel runtime systems, compilers, application development, and performance evaluation.
We give processor-allocation algorithms for grid architectures, where the objective is to select processors from a set of available processors to minimize the average number of communication hops. The associated clustering problem is as follows: Given n points in R{sup d}, find a size-k subset with minimum average pairwise L{sub 1} distance.We present a natural approximation algorithm and show that it is a 7/4-approximation for 2D grids. In d dimensions, the approximation guarantee is 2 - 1/2d, which is tight. We also give a polynomial-time approximation scheme (PTAS) for constant dimension d and report on experimental results.
The Trilinos{trademark} Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries. AztecOO{trademark} is a package within Trilinos that enables the use of the Aztec solver library [19] with Epetra{trademark} [13] objects. AztecOO provides access to Aztec preconditioners and solvers by implementing the Aztec 'matrix-free' interface using Epetra. While Aztec is written in C and procedure-oriented, AztecOO is written in C++ and is object-oriented. In addition to providing access to Aztec capabilities, AztecOO also provides some signficant new functionality. In particular it provides an extensible status testing capability that allows expression of sophisticated stopping criteria as is needed in production use of iterative solvers. AztecOO also provides mechanisms for using Ifpack [2], ML [20] and AztecOO itself as preconditioners.
Sundance is a system of software components that allows construction of an entire parallel simulator and its derivatives using a high-level symbolic language. With this high-level problem description, it is possible to specify a weak formulation of a PDE and its discretization method in a small amount of user-level code; furthermore, because derivatives are easily available, a simulation in Sundance is immediately suitable for accelerated PDE-constrained optimization algorithms. This paper is a tutorial for setting up and solving linear and nonlinear PDEs in Sundance. With several simple examples, we show how to set up mesh objects, geometric regions for BC application, the weak form of the PDE, and boundary conditions. Each example then illustrates use of an appropriate solver and solution visualization.
This document is intended to contain a detailed description of the mathematical formulation of Xyce, a massively parallel SPICE-style circuit simulator developed at Sandia National Laboratories. The target audience of this document are people in the role of 'service provider'. An example of such a person would be a linear solver expert who is spending a small fraction of his time developing solver algorithms for Xyce. Such a person probably is not an expert in circuit simulation, and would benefit from an description of the equations solved by Xyce. In this document, modified nodal analysis (MNA) is described in detail, with a number of examples. Issues that are unique to circuit simulation, such as voltage limiting, are also described in detail.
This SAND report is the final report on Sandia's Grand Challenge LDRD Project 27328, 'A Revolution in Lighting -- Building the Science and Technology Base for Ultra-Efficient Solid-state Lighting.' This project, which for brevity we refer to as the SSL GCLDRD, is considered one of Sandia's most successful GCLDRDs. As a result, this report reviews not only technical highlights, but also the genesis of the idea for Solid-state Lighting (SSL), the initiation of the SSL GCLDRD, and the goals, scope, success metrics, and evolution of the SSL GCLDRD over the course of its life. One way in which the SSL GCLDRD was different from other GCLDRDs was that it coincided with a larger effort by the SSL community - primarily industrial companies investing in SSL, but also universities, trade organizations, and other Department of Energy (DOE) national laboratories - to support a national initiative in SSL R&D. Sandia was a major player in publicizing the tremendous energy savings potential of SSL, and in helping to develop, unify and support community consensus for such an initiative. Hence, our activities in this area, discussed in Chapter 6, were substantial: white papers; SSL technology workshops and roadmaps; support for the Optoelectronics Industry Development Association (OIDA), DOE and Senator Bingaman's office; extensive public relations and media activities; and a worldwide SSL community website. Many science and technology advances and breakthroughs were also enabled under this GCLDRD, resulting in: 55 publications; 124 presentations; 10 book chapters and reports; 5 U.S. patent applications including 1 already issued; and 14 patent disclosures not yet applied for. Twenty-six invited talks were given, at prestigious venues such as the American Physical Society Meeting, the Materials Research Society Meeting, the AVS International Symposium, and the Electrochemical Society Meeting. This report contains a summary of these science and technology advances and breakthroughs, with Chapters 1-5 devoted to the five technical task areas: 1 Fundamental Materials Physics; 2 111-Nitride Growth Chemistry and Substrate Physics; 3 111-Nitride MOCVD Reactor Design and In-Situ Monitoring; 4 Advanced Light-Emitting Devices; and 5 Phosphors and Encapsulants. Chapter 7 (Appendix A) contains a listing of publications, presentations, and patents. Finally, the SSL GCLDRD resulted in numerous actual and pending follow-on programs for Sandia, including multiple grants from DOE and the Defense Advanced Research Projects Agency (DARPA), and Cooperative Research and Development Agreements (CRADAs) with SSL companies. Many of these follow-on programs arose out of contacts developed through our External Advisory Committee (EAC). In h s and other ways, the EAC played a very important role. Chapter 8 (Appendix B) contains the full (unedited) text of the EAC reviews that were held periodically during the course of the project.
In theory, it should be possible to infer realistic genetic networks from time series microarray data. In practice, however, network discovery has proved problematic. The three major challenges are: (1) inferring the network; (2) estimating the stability of the inferred network; and (3) making the network visually accessible to the user. Here we describe a method, tested on publicly available time series microarray data, which addresses these concerns. The inference of genetic networks from genome-wide experimental data is an important biological problem which has received much attention. Approaches to this problem have typically included application of clustering algorithms [6]; the use of Boolean networks [12, 1, 10]; the use of Bayesian networks [8, 11]; and the use of continuous models [21, 14, 19]. Overviews of the problem and general approaches to network inference can be found in [4, 3]. Our approach to network inference is similar to earlier methods in that we use both clustering and Boolean network inference. However, we have attempted to extend the process to better serve the end-user, the biologist. In particular, we have incorporated a system to assess the reliability of our network, and we have developed tools which allow interactive visualization of the proposed network.
This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been designed as a SPICE-compatible, high-performance analog circuit simulator capable of simulating electrical circuits at a variety of abstraction levels. Primarily, Xyce has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability the current state-of-the-art in the following areas: {sm_bullet} Capability to solve extremely large circuit problems by supporting large-scale parallel computing platforms (up to thousands of processors). Note that this includes support for most popular parallel and serial computers. {sm_bullet} Improved performance for all numerical kernels (e.g., time integrator, nonlinear and linear solvers) through state-of-the-art algorithms and novel techniques. {sm_bullet} Device models which are specifically tailored to meet Sandia's needs, including many radiation-aware devices. {sm_bullet} A client-server or multi-tiered operating model wherein the numerical kernel can operate independently of the graphical user interface (GUI). {sm_bullet} Object-oriented code design and implementation using modern coding practices that ensure that the Xyce Parallel Electronic Simulator will be maintainable and extensible far into the future. Xyce is a parallel code in the most general sense of the phrase - a message passing of computing platforms. These include serial, shared-memory and distributed-memory parallel implementation - which allows it to run efficiently on the widest possible number parallel as well as heterogeneous platforms. Careful attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows. One feature required by designers is the ability to add device models, many specific to the needs of Sandia, to the code. To this end, the device package in the Xyce These input formats include standard analytical models, behavioral models look-up Parallel Electronic Simulator is designed to support a variety of device model inputs. tables, and mesh-level PDE device models. Combined with this flexible interface is an architectural design that greatly simplifies the addition of circuit models. One of the most important feature of Xyce is in providing a platform for computational research and development aimed specifically at the needs of the Laboratory. With Xyce, Sandia now has an 'in-house' capability with which both new electrical (e.g., device model development) and algorithmic (e.g., faster time-integration methods) research and development can be performed. Ultimately, these capabilities are migrated to end users.
This document is a reference guide to the Xyce Parallel Electronic Simulator, and is a companion document to the Xyce Users' Guide. The focus of this document is (to the extent possible) exhaustively list device parameters, solver options, parser options, and other usage details of Xyce. This document is not intended to be a tutorial. Users who are new to circuit simulation are better served by the Xyce Users' Guide.
The surface micromachining processes used to manufacture MEMS devices and integrated circuits transpire at such small length scales and are sufficiently complex that a theoretical analysis of them is particularly inviting. Under development at Sandia National Laboratories (SNL) is Chemically Induced Surface Evolution with Level Sets (ChISELS), a level-set based feature-scale modeler of such processes. The theoretical models used, a description of the software and some example results are presented here. The focus to date has been of low-pressure and plasma enhanced chemical vapor deposition (low-pressure chemical vapor deposition, LPCVD and PECVD) processes. Both are employed in SNLs SUMMiT V technology. Examples of step coverage of SiO{sub 2} into a trench by each of the LPCVD and PECVD process are presented.
