We introduce a filter-based evolutionary algorithm (FEA) for constrained optimization. The filter used by an FEA explicitly imposes the concept of dominance on a partially ordered solution set. We show that the algorithm is provably robust for both linear and nonlinear problems and constraints. FEAs use a finite pattern of mutation offsets, and our analysis is closely related to recent convergence results for pattern search methods. We discuss how properties of this pattern impact the ability of an FEA to converge to a constrained local optimum.
We have developed infrastructure, utilities and partitioning methods to improve data partitioning in linear solvers and preconditioners. Our efforts included incorporation of data repartitioning capabilities from the Zoltan toolkit into the Trilinos solver framework, (allowing dynamic repartitioning of Trilinos matrices); implementation of efficient distributed data directories and unstructured communication utilities in Zoltan and Trilinos; development of a new multi-constraint geometric partitioning algorithm (which can generate one decomposition that is good with respect to multiple criteria); and research into hypergraph partitioning algorithms (which provide up to 56% reduction of communication volume compared to graph partitioning for a number of emerging applications). This report includes descriptions of the infrastructure and algorithms developed, along with results demonstrating the effectiveness of our approaches.
The views of state of art in verification and validation (V & V) in computational physics are discussed. These views are described in the framework in which predictive capability relies on V & V, as well as other factors that affect predictive capability. Some of the research topics addressed are development of improved procedures for the use of the phenomena identification and ranking table (PIRT) for prioritizing V & V activities, and the method of manufactured solutions for code verification. It also addressed development and use of hierarchical validation diagrams, and the construction and use of validation metrics incorporating statistical measures.
It seems well understood that supercomputer simulation is an enabler for scientific discoveries, weapons, and other activities of value to society. It also seems widely believed that Moores Law will make progressively more powerful supercomputers over time and thus enable more of these contributions. This paper seeks to add detail to these arguments, revealing them to be generally correct but not a smooth and effortless progression. This paper will review some key problems that can be solved with supercomputer simulation, showing that more powerful supercomputers will be useful up to a very high yet finite limit of around 1021 FLOPS (1 Zettaflops. The review will also show the basic nature of these extreme problems. This paper will review work by others showing that the theoretical maximum supercomputer power is very high indeed, but will explain how a straightforward extrapolation of Moores Law will lead to technological maturity in a few decades. The power of a supercomputer at the maturity of Moores Law will be very high by todays standards at 1016-1019 FLOPS (100 Petaflops to 10 Exaflops, depending on architecture , but distinctly below the level required for the most ambitious applications. Having established that Moores Law will not be that last word in supercomputing, this paper will explore the nearer term issue of what a supercomputer will look like at maturity of Moores Law. Our approach will quantify the maximum performance as permitted by the laws of physics for extension of current technology and then find a design that approaches this limit closely. We study a "multi-architecture" for supercomputers that combines a microprocessor with other "advanced" concepts and find it can reach the limits as well. This approach should be quite viable in the future because the microprocessor would provide compatibility with existing codes and programming styles while the "advanced" features would provide a boost to the limits of performance.
Motivated by observations about job runtimes on the CPlant system, we use a trace-driven microsimulator to begin characterizing the performance of different classes of allocation algorithms on jobs with different communication patterns in space-shared parallel systems with mesh topology. We show that relative performance varies considerably with communication pattern. The Paging strategy using the Hilbert space-filling curve and the Best Fit heuristic performed best across several communication patterns.
CommAspen is a new agent-based model for simulating the interdependent effects of market decisions and disruptions in the telecommunications infrastructure on other critical infrastructures in the U.S. economy such as banking and finance, and electric power. CommAspen extends and modifies the capabilities of Aspen-EE, an agent-based model previously developed by Sandia National Laboratories to analyze the interdependencies between the electric power system and other critical infrastructures. CommAspen has been tested on a series of scenarios in which the communications network has been disrupted, due to congestion and outages. Analysis of the scenario results indicates that communications networks simulated by the model behave as their counterparts do in the real world. Results also show that the model could be used to analyze the economic impact of communications congestion and outages.
This document introduces the use of Trilinos, version 3.1. Trilinos has been written to support, in a rigorous manner, the solver needs of the engineering and scientific applications at Sandia National Laboratories. Aim of this manuscript is to present the basic features of some of the Trilinos packages. The presented material includes the definition of distributed matrices and vectors with Epetra, the iterative solution of linear system with AztecOO, incomplete factorizations with IFPACK, multilevel methods with ML, direct solution of linear system with Amesos, and iterative solution of nonlinear systems with NOX. With the help of several examples, some of the most important classes and methods are detailed to the inexperienced user. For the most majority, each example is largely commented throughout the text. Other comments can be found in the source of each example. This document is a companion to the Trilinos User's Guide and Trilinos Development Guides. Also, the documentation included in each of the Trilinos' packages is of fundamental importance.
Molecular analysis of cancer, at the genomic level, could lead to individualized patient diagnostics and treatments. The developments to follow will signal a significant paradigm shift in the clinical management of human cancer. Despite our initial hopes, however, it seems that simple analysis of microarray data cannot elucidate clinically significant gene functions and mechanisms. Extracting biological information from microarray data requires a complicated path involving multidisciplinary teams of biomedical researchers, computer scientists, mathematicians, statisticians, and computational linguists. The integration of the diverse outputs of each team is the limiting factor in the progress to discover candidate genes and pathways associated with the molecular biology of cancer. Specifically, one must deal with sets of significant genes identified by each method and extract whatever useful information may be found by comparing these different gene lists. Here we present our experience with such comparisons, and share methods developed in the analysis of an infant leukemia cohort studied on Affymetrix HG-U95A arrays. In particular, spatial gene clustering, hyper-dimensional projections, and computational linguistics were used to compare different gene lists. In spatial gene clustering, different gene lists are grouped together and visualized on a three-dimensional expression map, where genes with similar expressions are co-located. In another approach, projections from gene expression space onto a sphere clarify how groups of genes can jointly have more predictive power than groups of individually selected genes. Finally, online literature is automatically rearranged to present information about genes common to multiple groups, or to contrast the differences between the lists. The combination of these methods has improved our understanding of infant leukemia. While the complicated reality of the biology dashed our initial, optimistic hopes for simple answers from microarrays, we have made progress by combining very different analytic approaches.
Statistical active contour models (aka statistical pressure snakes) have attractive properties for use in mobile manipulation platforms as both a method for use in visual servoing and as a natural component of a human-computer interface. Unfortunately, the constantly changing illumination expected in outdoor environments presents problems for statistical pressure snakes and for their image gradient-based predecessors. This paper introduces a new color-based variant of statistical pressure snakes that gives superior performance under dynamic lighting conditions and improves upon the previously published results of attempts to incorporate color imagery into active deformable models.
The deformation of an infinite bar subjected to a self-equilibrated load distribution is investigated using the peridynamic formulation of elasticity theory. The peridynamic theory differs from the classical theory and other nonlocal theories in that it does not involve spatial derivatives of the displacement field. The bar problem is formulated as a linear Fredholm integral equation and solved using Fourier transform methods. The solution is shown to exhibit, in general, features that are not found in the classical result. Among these are decaying oscillations in the displacement field and progressively weakening discontinuities that propagate outside of the loading region. These features, when present, are guaranteed to decay provided that the wave speeds are real. This leads to a one-dimensional version of St. Venant's principle for peridynamic materials that ensures the increasing smoothness of the displacement field remotely from the loading region. The peridynamic result converges to the classical result in the limit of short-range forces. An example gives the solution to the concentrated load problem, and hence provides the Green's function for general loading problems.
This report documents work undertaken to endow the cognitive framework currently under development at Sandia National Laboratories with a human-like memory for specific life episodes. Capabilities have been demonstrated within the context of three separate problem areas. The first year of the project developed a capability whereby simulated robots were able to utilize a record of shared experience to perform surveillance of a building to detect a source of smoke. The second year focused on simulations of social interactions providing a queriable record of interactions such that a time series of events could be constructed and reconstructed. The third year addressed tools to promote desktop productivity, creating a capability to query episodic logs in real time allowing the model of a user to build on itself based on observations of the user's behavior.
Epetra is a package of classes for the construction and use of serial and distributed parallel linear algebra objects. It is one of the base packages in Trilinos. This document describes guidelines for Epetra coding style. The issues discussed here go beyond correct C++ syntax to address issues that make code more readable and self-consistent. The guidelines presented here are intended to aid current and future development of Epetra specifically. They reflect design decisions that were made in the early development stages of Epetra. Some of the guidelines are contrary to more commonly used conventions, but we choose to continue these practices for the purposes of self-consistency. These guidelines are intended to be complimentary to policies established in the Trilinos Developers Guide.
All ceramics and powder metals, including the ceramics components that Sandia uses in critical weapons components such as PZT voltage bars and current stacks, multi-layer ceramic MET's, ahmindmolybdenum & alumina cermets, and ZnO varistors, are manufactured by sintering. Sintering is a critical, possibly the most important, processing step during manufacturing of ceramics. The microstructural evolution, the macroscopic shrinkage, and shape distortions during sintering will control the engineering performance of the resulting ceramic component. Yet, modeling and prediction of sintering behavior is in its infancy, lagging far behind the other manufacturing models, such as powder synthesis and powder compaction models, and behind models that predict engineering properties and reliability. In this project, we developed a model that was capable of simulating microstructural evolution during sintering, providing constitutive equations for macroscale simulation of shrinkage and distortion during sintering. And we developed macroscale sintering simulation capability in JAS3D. The mesoscale model can simulate microstructural evolution in a complex powder compact of hundreds or even thousands of particles of arbitrary shape and size by 1. curvature-driven grain growth, 2. pore migration and coalescence by surface diffusion, 3. vacancy formation, grain boundary diffusion and annihilation. This model was validated by comparing predictions of the simulation to analytical predictions for simple geometries. The model was then used to simulate sintering in complex powder compacts. Sintering stress and materials viscous module were obtained from the simulations. These constitutive equations were then used by macroscopic simulations for simulating shrinkage and shape changes in FEM simulations. The continuum theory of sintering embodied in the constitutive description of Skorohod and Olevsky was combined with results from microstructure evolution simulations to model shrinkage and deformation during. The continuum portion is based on a finite element formulation that allows 3D components to be modeled using SNL's nonlinear large-deformation finite element code, JAS3D. This tool provides a capability to model sintering of complex three-dimensional components. The model was verified by comparing to simulations results published in the literature. The model was validated using experimental results from various laboratory experiments performed by Garino. In addition, the mesoscale simulations were used to study anisotropic shrinkage in aligned, elongated powder compacts. Anisotropic shrinkage occurred in all compacts with aligned, elongated particles. However, the direction of higher shrinkage was in some cases along the direction of elongation and in other cases in the perpendicular direction depending on the details of the powder compact. In compacts of simple-packed, mono-sized, elongated particles, shrinkage was higher in the direction of elongation. In compacts of close-packed, mono-sized, elongated particles and of elongated particles with a size and shape distribution, the shrinkage was lower in the direction of elongation. We also explored the concept of a sintering stress tensor rather than the traditional sintering stress scalar concept for the case of anisotropic shrinkage. A thermodynamic treatment of this is presented. A method to calculate the sintering stress tensor is also presented. A user-friendly code that can simulate microstructural evolution during sintering in 2D and in 3D was developed. This code can run on most UNIX platforms and has a motif-based GUI. The microstructural evolution is shown as the code is running and many of the microstructural features, such as grain size, pore size, the average grain boundary length (in 2D) and area (in 3D), etc. are measured and recorded as a function of time. The overall density as the function of time is also recorded.
The Unique Signal is a key constituent of Enhanced Nuclear Detonation Safety (ENDS). Although the Unique Signal approach is well prescribed and mathematically assured, there are numerous unsolved mathematical problems that could help assess the risk of deviations from the ideal approach. Some of the mathematics-based results shown in this report are: 1. The risk that two patterns with poor characteristics (easily generated by inadvertent processes) could be combined through exclusive-or mixing to generate an actual Unique Signal pattern has been investigated and found to be minimal (not significant when compared to the incompatibility metric of actual Unique Signal patterns used in nuclear weapons). 2. The risk of generating actual Unique Signal patterns with linear feedback shift registers is minimal, but the patterns in use are not as invulnerable to inadvertent generation by dependent processes as previously thought. 3. New methods of testing pair-wise incompatibility threats have resulted in no significant problems found for the set of Unique Signal patterns currently used. Any new patterns introduced would have to be carefully assessed for compatibility with existing patterns, since some new patterns under consideration were found to be deficient when associated with other patterns in use. 4. Markov models were shown to correspond to some of the engineered properties of Unique Signal sequences. This gives new support for the original design objectives. 5. Potential dependence among events (caused by a variety of communication protocols) has been studied. New evidence has been derived of the risk associated with combined communication of multiple events, and of the improvement in abnormal-environment safety that can be achieved through separate-event communication.
Prokaryotic single-cell microbes are the simplest of all self-sufficient living organisms. Yet microbes create and use much of the molecular machinery present in more complex organisms, and the macro-molecules in microbial cells interact in regulatory, metabolic, and signaling pathways that are prototypical of the reaction networks present in all cells. We have developed a simple simulation model of a prokaryotic cell that treats proteins, protein complexes, and other organic molecules as particles which diffuse via Brownian motion and react with nearby particles in accord with chemical rate equations. The code models protein motion and chemistry within an idealized cellular geometry. It has been used to simulate several simple reaction networks and compared to more idealized models which do not include spatial effects. In this report we describe an initial version of the simulation code that was developed with FY03 funding. We discuss the motivation for the model, highlight its underlying equations, and describe simulations of a 3-stage kinase cascade and a portion of the carbon fixation pathway in the Synechococcus microbe.
Algorithms for higher order accuracy modeling of kinematic behavior within the ALEGRA framework are presented. These techniques improve the behavior of the code when kinematic errors are found, ensure orthonormality of the rotation tensor at each time step, and increase the accuracy of the Lagrangian stretch and rotation tensor update algorithm. The implementation of these improvements in ALEGRA is described. A short discussion of issues related to improving the accuracy of the stress update procedures is also included.
Solidification and blood flow seemingly have little in common, but each involves a fluid in contact with a deformable solid. In these systems, the solid-fluid interface moves as the solid advects and deforms, often traversing the entire domain of interest. Currently, these problems cannot be simulated without innumerable expensive remeshing steps, mesh manipulations or decoupling the solid and fluid motion. Despite the wealth of progress recently made in mechanics modeling, this glaring inadequacy persists. We propose a new technique that tracks the interface implicitly and circumvents the need for remeshing and remapping the solution onto the new mesh. The solid-fluid boundary is tracked with a level set algorithm that changes the equation type dynamically depending on the phases present. This novel approach to coupled mechanics problems promises to give accurate stresses, displacements and velocities in both phases, simultaneously.
High throughput instruments and analysis techniques are required in order to make good use of the genomic sequences that have recently become available for many species, including humans. These instruments and methods must work with tens of thousands of genes simultaneously, and must be able to identify the small subsets of those genes that are implicated in the observed phenotypes, or, for instance, in responses to therapies. Microarrays represent one such high throughput method, which continue to find increasingly broad application. This project has improved microarray technology in several important areas. First, we developed the hyperspectral scanner, which has discovered and diagnosed numerous flaws in techniques broadly employed by microarray researchers. Second, we used a series of statistically designed experiments to identify and correct errors in our microarray data to dramatically improve the accuracy, precision, and repeatability of the microarray gene expression data. Third, our research developed new informatics techniques to identify genes with significantly different expression levels. Finally, natural language processing techniques were applied to improve our ability to make use of online literature annotating the important genes. In combination, this research has improved the reliability and precision of laboratory methods and instruments, while also enabling substantially faster analysis and discovery.
We present here the details of the implementation of the parallel tempering Monte Carlo technique into a LAMMPS, a heavily used massively parallel molecular dynamics code at Sandia. This technique allows for many replicas of a system to be run at different simulation temperatures. At various points in the simulation, configurations can be swapped between different temperature environments and then continued. This allows for large regions of energy space to be sampled very quickly, and allows for minimum energy configurations to emerge in very complex systems, such as large biomolecular systems. By including this algorithm into an existing code, we immediately gain all of the previous work that had been put into LAMMPS, and allow this technique to quickly be available to the entire Sandia and international LAMMPS community. Finally, we present an example of this code applied to folding a small protein.
Genetic programming is a powerful methodology for automatically producing solutions to problems in a variety of domains. It has been used successfully to develop behaviors for RoboCup soccer players and simple combat agents. We will attempt to use genetic programming to solve a problem in the domain of strategic combat, keeping in mind the end goal of developing sophisticated behaviors for compound defense and infiltration. The simplified problem at hand is that of two armed agents in a small room, containing obstacles, fighting against each other for survival. The base case and three changes are considered: a memory of positions using stacks, context-dependent genetic programming, and strongly typed genetic programming. Our work demonstrates slight improvements from the first two techniques, and no significant improvement from the last.
This report is based on the Statement of Work (SOW) describing the various requirements for delivering 3 new supercomputer system to Sandia National Laboratories (Sandia) as part of the Department of Energy's (DOE) Accelerated Strategic Computing Initiative (ASCI) program. This system is named Red Storm and will be a distributed memory, massively parallel processor (MPP) machine built primarily out of commodity parts. The requirements presented here distill extensive architectural and design experience accumulated over a decade and a half of research, development and production operation of similar machines at Sandia. Red Storm will have an unusually high bandwidth, low latency interconnect, specially designed hardware and software reliability features, a light weight kernel compute node operating system and the ability to rapidly switch major sections of the machine between classified and unclassified computing environments. Particular attention has been paid to architectural balance in the design of Red Storm, and it is therefore expected to achieve an atypically high fraction of its peak speed of 41 TeraOPS on real scientific computing applications. In addition, Red Storm is designed to be upgradeable to many times this initial peak capability while still retaining appropriate balance in key design dimensions. Installation of the Red Storm computer system at Sandia's New Mexico site is planned for 2004, and it is expected that the system will be operated for a minimum of five years following installation.
The Sandia Petaflops Planner is a tool for projecting the design and performance of parallel supercomputers into the future. The mathematical basis of these projections is the International Technology Roadmap for Semiconductors (ITRS, or a detailed version of Moore's Law) and DOE balance factors for supercomputer procurements. The planner is capable of various forms of scenario analysis, cost estimation, and technology analysis. The tool is described along with technology conclusions regarding PFLOPS-level supercomputers in the upcoming decade.
The Computational Plant or Cplant is a commodity-based distributed-memory supercomputer under development at Sandia National Laboratories. Distributed-memory supercomputers run many parallel programs simultaneously. Users submit their programs to a job queue. When a job is scheduled to run, it is assigned to a set of available processors. Job runtime depends not only on the number of processors but also on the particular set of processors assigned to it. Jobs should be allocated to localized clusters of processors to minimize communication costs and to avoid bandwidth contention caused by overlapping jobs. This report introduces new allocation strategies and performance metrics based on space-filling curves and one dimensional allocation strategies. These algorithms are general and simple. Preliminary simulations and Cplant experiments indicate that both space-filling curves and one-dimensional packing improve processor locality compared to the sorted free list strategy previously used on Cplant. These new allocation strategies are implemented in Release 2.0 of the Cplant System Software that was phased into the Cplant systems at Sandia by May 2002. Experimental results then demonstrated that the average number of communication hops between the processors allocated to a job strongly correlates with the job's completion time. This report also gives processor-allocation algorithms for minimizing the average number of communication hops between the assigned processors for grid architectures. The associated clustering problem is as follows: Given n points in {Re}d, find k points that minimize their average pairwise L{sub 1} distance. Exact and approximate algorithms are given for these optimization problems. One of these algorithms has been implemented on Cplant and will be included in Cplant System Software, Version 2.1, to be released. In more preliminary work, we suggest improvements to the scheduler separate from the allocator.
This report summarizes the results of a three-year LDRD project on prognostics and health management. System failure over some future time interval (an alternative definition is the capability to predict the remaining useful life of a system). Prognostics are integrated with health monitoring (through inspections, sensors, etc.) to provide an overall PHM capability that optimizes maintenance actions and results in higher availability at a lower cost. Our goal in this research was to develop PHM tools that could be applied to a wide variety of equipment (repairable, non-repairable, manufacturing, weapons, battlefield equipment, etc.) and require minimal customization to move from one system to the next. Thus, our approach was to develop a toolkit of reusable software objects/components and architecture for their use. We have developed two software tools: an Evidence Engine and a Consequence Engine. The Evidence Engine integrates information from a variety of sources in order to take into account all the evidence that impacts a prognosis for system health. The Evidence Engine has the capability for feature extraction, trend detection, information fusion through Bayesian Belief Networks (BBN), and estimation of remaining useful life. The Consequence Engine involves algorithms to analyze the consequences of various maintenance actions. The Consequence Engine takes as input a maintenance and use schedule, spares information, and time-to-failure data on components, then generates maintenance and failure events, and evaluates performance measures such as equipment availability, mission capable rate, time to failure, and cost. This report summarizes the capabilities we have developed, describes the approach and architecture of the two engines, and provides examples of their use. 'Prognostics' refers to the capability to predict the probability of
A fundamental challenge for all communication systems, engineered or living, is the problem of achieving efficient, secure, and error-free communication over noisy channels. Information theoretic principals have been used to develop effective coding theory algorithms to successfully transmit information in engineering systems. Living systems also successfully transmit biological information through genetic processes such as replication, transcription, and translation, where the genome of an organism is the contents of the transmission. Decoding of received bit streams is fairly straightforward when the channel encoding algorithms are efficient and known. If the encoding scheme is unknown or part of the data is missing or intercepted, how would one design a viable decoder for the received transmission? For such systems blind reconstruction of the encoding/decoding system would be a vital step in recovering the original message. Communication engineers may not frequently encounter this situation, but for computational biologists and biotechnologist this is an immediate challenge. The goal of this work is to develop methods for detecting and reconstructing the encoder/decoder system for engineered and biological data. Building on Sandia's strengths in discrete mathematics, algorithms, and communication theory, we use linear programming and will use evolutionary computing techniques to construct efficient algorithms for modeling the coding system for minimally errored engineered data stream and genomic regulatory DNA and RNA sequences. The objective for the initial phase of this project is to construct solid parallels between biological literature and fundamental elements of communication theory. In this light, the milestones for FY2003 were focused on defining genetic channel characteristics and providing an initial approximation for key parameters, including coding rate, memory length, and minimum distance values. A secondary objective addressed the question of determining similar parameters for a received, noisy, error-control encoded data set. In addition to these goals, we initiated exploration of algorithmic approaches to determine if a data set could be approximated with an error-control code and performed initial investigations into optimization based methodologies for extracting the encoding algorithm given the coding rate of an encoded noise-free and noisy data stream.
Evidence for the existence of discrete sub-movements underlying continuous human movement has motivated many attempts to "extract" them. Although they produce visually convincing results, all of the methodologies that have been employed are prone to produce spurious decompositions. Examples of potential failures are given. A branch-and-bound algorithm for submovement extraction, capable of global nonlinear minimization (and hence capable of avoiding spurious decompositions), is developed and demonstrated.
If we are to build a supercomputer with a speed of 10{sup 15} floating operations per second (1 PetaFLOPS), interconnect technology will need to be improved considerably over what it is today. In this report, we explore one possible interconnect design for such a network. The guiding principle in this design is the optimization of all components for the finiteness of the speed of light. To achieve a linear speedup in time over well-tested supercomputers of todays' designs will require scaling up of processor power and bandwidth and scaling down of latency. Latency scaling is the most challenging: it requires a 100 ns user-to-user latency for messages traveling the full diameter of the machine. To meet this constraint requires simultaneously minimizing wire length through 3D packaging, new low-latency electrical signaling mechanisms, extremely fast routers, and new network interfaces. In this report, we outline approaches and implementations that will meet the requirements when implemented as a system. No technology breakthroughs are required.
This paper describes a methodology for implementing disk-less cluster systems using the Network File System (NFS) that scales to thousands of nodes. This method has been successfully deployed and is currently in use on several production systems at Sandia National Labs. This paper will outline our methodology and implementation, discuss hardware and software considerations in detail and present cluster configurations with performance numbers for various management operations like booting.
A new capability for modeling thin-shell structures within the coupled Euler-Lagrange code, Zapotec, is under development. The new algorithm creates an artificial material interface for the Eulerian portion of the problem by expanding a Lagrangian shell element such that it has an effective thickness that spans one or more Eulerian cells. The algorithm implementation is discussed along with several examples involving blast loading on plates.
Implicit time integration coupled with SUPG discretization in space leads to additional terms that provide consistency and improve the phase accuracy for convection dominated flows. Recently, it has been suggested that for small Courant numbers these terms may dominate the streamline diffusion term, ostensibly causing destabilization of the SUPG method. While consistent with a straightforward finite element stability analysis, this contention is not supported by computational experiments and contradicts earlier Von-Neumann stability analyses of the semidiscrete SUPG equations. This prompts us to re-examine finite element stability of the fully discrete SUPG equations. A careful analysis of the additional terms reveals that, regardless of the time step size, they are always dominated by the consistent mass matrix. Consequently, SUPG cannot be destabilized for small Courant numbers. Numerical results that illustrate our conclusions are reported.
A recently developed Centroidal Voronoi Tessellation (CVT) unstructured sampling method is investigated here to assess its suitability for use in statistical sampling and function integration. CVT efficiently generates a highly uniform distribution of sample points over arbitrarily shaped M-Dimensional parameter spaces. It has recently been shown on several 2-D test problems to provide superior point distributions for generating locally conforming response surfaces. In this paper, its performance as a statistical sampling and function integration method is compared to that of Latin-Hypercube Sampling (LHS) and Simple Random Sampling (SRS) Monte Carlo methods, and Halton and Hammersley quasi-Monte-Carlo sequence methods. Specifically, sampling efficiencies are compared for function integration and for resolving various statistics of response in a 2-D test problem. It is found that on balance CVT performs best of all these sampling methods on our test problems.
Broadcasting messages through the earth is a daunting task. Indeed, broadcasting a normal telephone conversion through the earth by wireless means is impossible with todays technology. Most of us don't care, but some do. Industries that drill into the earth need wireless communication to broadcast navigation parameters. This allows them to steer their drill bits. They also need information about the natural formation that they are drilling. Measurements of parameters such as pressure, temperature, and gamma radiation levels can tell them if they have found a valuable resource such as a geothermal reservoir or a stratum bearing natural gas. Wireless communication methods are available to the drilling industry. Information is broadcast via either pressure waves in the drilling fluid or electromagnetic waves in the earth and well tubing. Data transmission can only travel one way at rates around a few baud. Given that normal Internet telephone modems operate near 20,000 baud, these data rates are truly very slow. Moreover, communication is often interrupted or permanently blocked by drilling conditions or natural formation properties. Here we describe a tool that communicates with stress waves traveling through the steel drill pipe and production tubing in the well. It's based on an old idea called Acoustic Telemetry. But what we present here is more than an idea. This tool exists, it's drilled several wells, and it works. Currently, it's the first and only acoustic telemetry tool that can withstand the drilling environment. It broadcasts one way over a limited range at much faster rates than existing methods, but we also know how build a system that can communicate both up and down wells of indefinite length.
We seek to understand which supercomputer architecture will be best for supercomputers at the Petaflops scale and beyond. The process we use is to predict the cost and performance of several leading architectures at various years in the future. The basis for predicting the future is an expanded version of Moore's Law called the International Technology Roadmap for Semiconductors (ITRS). We abstract leading supercomputer architectures into chips connected by wires, where the chips and wires have electrical parameters predicted by the ITRS. We then compute the cost of a supercomputer system and the run time on a key problem of interest to the DOE (radiation transport). These calculations are parameterized by the time into the future and the technology expected to be available at that point. We find the new advanced architectures have substantial performance advantages but conventional designs are likely to be less expensive (due to economies of scale). We do not find a universal ''winner'', but instead the right architectural choice is likely to involve non-technical factors such as the availability of capital and how long people are willing to wait for results.
The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries. In particular, our goal is to develop parallel solver algorithms and libraries within an object-oriented software framework for the solution of large-scale, complex multi-physics engineering and scientific applications. Our emphasis is on developing robust, scalable algorithms in a software framework, using abstract interfaces for flexible interoperability of components while providing a full-featured set of concrete classes that implement all abstract interfaces. Trilinos uses a two-level software structure designed around collections of packages. A Trilinos package is an integral unit usually developed by a small team of experts in a particular algorithms area such as algebraic preconditioners, nonlinear solvers, etc. Packages exist underneath the Trilinos top level, which provides a common look-and-feel, including configuration, documentation, licensing, and bug-tracking. Trilinos packages are primarily written in C++, but provide some C and Fortran user interface support. We provide an open architecture that allows easy integration with other solver packages and we deliver our software to the outside community via the Gnu Lesser General Public License (LGPL). This report provides an overview of Trilinos, discussing the objectives, history, current development and future plans of the project.
The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries. A new software capability is introduced into Trilinos as a package. A Trilinos package is an integral unit usually developed by a small team of experts in a particular algorithms area such as algebraic preconditioners, nonlinear solvers, etc. The Trilinos Users Guide is a resource for new and existing Trilinos users. Topics covered include how to configure and build Trilinos, what is required to integrate an existing package into Trilinos and examples of how those requirements can be met, as well as what tools and services are available to Trilinos packages. Also discussed are some common practices that are followed by many Trilinos package developers. Finally, a snapshot of current Trilinos packages and their interoperability status is provided, along with a list of supported computer platforms.
Microstructural evolution during simple solid-state sintering of two-dimensional compacts of elongated particles packed in different arrangements was simulated using a kinetic, Monte Carlo model. The model used simulates curvature-driven grain growth, pore migration by surface diffusion, vacancy formation, diffusion along grain boundaries, and annihilation. Only the shape of the particles was anisotropic; all other extensive thermodynamic and kinetic properties such as surface energies and diffusivities were isotropic. We verified our model by simulating sintering in the analytically tractable cases of simple-packed and close-packed, elongated particles and comparing the shrinkage rate anisotropies with those predicted analytically. Once our model was verified, we used it to simulate sintering in a powder compact of aligned, elongated particles of arbitrary size and shape to gain an understanding of differential shrinkage. Anisotropic shrinkage occurred in all compacts with aligned, elongated particles. However, the direction of higher shrinkage was in some cases along the direction of elongation and in other cases in the perpendicular direction, depending on the details of the powder compact. In compacts of simple-packed, mono-sized, elongated particles, shrinkage was higher in the direction of elongation. In compacts of close-packed, mono-sized, elongated particles and of elongated particles with a size and shape distribution, the shrinkage was lower in the direction of elongation. The results of these simulations are analyzed, and the implication of these results is discussed.
Protein microtubules (MTs) 25 nm in diameter and tens of micrometers long have been used as templates for the biomimetic mineralization of FeOOH. Exposure of MTs to anaerobic aqueous solutions of Fe{sup 2+} buffered to neutral pH followed by aerial oxidation leads to the formation of iron oxide coated MTs. The iron oxide layer was found to grow via a two-step process: initially formed 10-30 nm thick coatings were found to be amorphous in structure and comprised of several iron-containing species. Further growth resulted in MTs coated with highly crystalline layers of lepidocrocite with a controllable thickness of up to 125 nm. On the micrometer size scale, these coated MTs were observed to form large, irregular bundles containing hundreds of individually coated MTs. Iron oxide grew selectively on the MT surface, a result of the highly charged MT surface that provided an interface favorable for iron oxide nucleation. This result illustrates that MTs can be used as scaffolds for the in-situ production of high-aspect-ratio inorganic nanowires.
Currently, the Egyptian Atomic Energy Authority is designing a shallow-land disposal facility for low-level radioactive waste. To insure containment and prevent migration of radionuclides from the site, the use of a reactive backfill material is being considered. One material under consideration is hydroxyapatite, Ca{sub 10}(PO{sub 4}){sub 6}(OH){sub 2}, which has a high affinity for the sorption of many radionuclides. Hydroxyapatite has many properties that make it an ideal material for use as a backfill including low water solubility (K{sub sp} > 10{sup -40}), high stability under reducing and oxidizing conditions over a wide temperature range, availability, and low cost. However, there is often considerable variation in the properties of apatites depending on source and method of preparation. In this work, we characterized and compared a synthetic hydroxyapatite with hydroxyapatites prepared from cattle bone calcined at 500 C, 700 C, 900 C and 1100 C. The analysis indicated the synthetic hydroxyapatite was similar in morphology to 500 C prepared cattle hydroxyapatite. With increasing calcination temperature the crystallinity and crystal size of the hydroxyapatites increased and the BET surface area and carbonate concentration decreased. Batch sorption experiments were performed to determine the effectiveness of each material to sorb uranium. Sorption of U was strong regardless of apatite type indicating all apatite materials evaluated. Sixty day desorption experiments indicated desorption of uranium for each hydroxyapatite was negligible.
The maximum contact map overlap (MAX-CMO) between a pair of protein structures can be used as a measure of protein similarity. It is a purely topological measure and does not depend on the sequence of the pairs involved in the comparison. More importantly, the MAX-CMO present a very favorable mathematical structure which allows the formulation of integer, linear and Lagrangian models that can be used to obtain guarantees of optimality. It is not the intention of this paper to discuss the mathematical properties of MAX-CMO in detail as this has been dealt elsewhere. In this paper we compare three algorithms that can be used to obtain maximum contact map overlaps between protein structures. We will point to the weaknesses and strengths of each one. It is our hope that this paper will encourage researchers to develop new and improve methods for protein comparison based on MAX-CMO.
We consider the convergence properties of a non-elitist self-adaptive evolutionary strategy (ES) on multi-dimensional problems. In particular, we apply our recent convergence theory for a discretized (1,{lambda})-ES to design a related (1,{lambda})-ES that converges on a class of seperable, unimodal multi-dimensional problems. The distinguishing feature of self-adaptive evolutionary algorithms (EAs) is that the control parameters (like mutation step lengths) are evolved by the evolutionary algorithm. Thus the control parameters are adapted in an implicit manner that relies on the evolutionary dynamics to ensure that more effective control parameters are propagated during the search. Self-adaptation is a central feature of EAs like evolutionary stategies (ES) and evolutionary programming (EP), which are applied to continuous design spaces. Rudolph summarizes theoretical results concerning self-adaptive EAs and notes that the theoretical underpinnings for these methods are essentially unexplored. In particular, convergence theories that ensure convergence to a limit point on continuous spaces have only been developed by Rudolph, Hart, DeLaurentis and Ferguson, and Auger et al. In this paper, we illustrate how our analysis of a (1,{lambda})-ES for one-dimensional unimodal functions can be used to ensure convergence of a related ES on multidimensional functions. This (1,{lambda})-ES randomly selects a search dimension in each iteration, along which points generated. For a general class of separable functions, our analysis shows that the ES searches along each dimension independently, and thus this ES converges to the (global) minimum.
Iterated local search, or ILS, is among the most straightforward meta-heuristics for local search. ILS employs both small-step and large-step move operators. Search proceeds via iterative modifications to a single solution, in distinct alternating phases. In the first phase, local neighborhood search (typically greedy descent) is used in conjunction with the small-step operator to transform solutions into local optima. In the second phase, the large-step operator is applied to generate perturbations to the local optima obtained in the first phase. Ideally, when local neighborhood search is applied to the resulting solution, search will terminate at a different local optimum, i.e., the large-step perturbations should be sufficiently large to enable escape from the attractor basins of local optima. ILS has proven capable of delivering excellent performance on numerous N P-Hard optimization problems. [LMS03]. However, despite its implicity, very little is known about why ILS can be so effective, and under what conditions. The goal of this paper is to advance the state-of-the-art in the analysis of meta-heuristics, by providing answers to this research question. They focus on characterizing both the relationship between the structure of the underlying search space and ILS performance, and the dynamic behavior of ILS. The analysis proceeds in the context of the job-shop scheduling problem (JSP) [Tai94]. They begin by demonstrating that the attractor basins of local optima in the JSP are surprisingly weak, and can be escaped with high probaiblity by accepting a short random sequence of less-fit neighbors. this result is used to develop a new ILS algorithms for the JSP, I-JAR, whose performance is competitive with tabu search on difficult benchmark instances. They conclude by developing a very accurate behavioral model of I-JAR, which yields significant insights into the dynamics of search. The analysis is based on a set of 100 random 10 x 10 problem instances, in addition to some widely used benchmark instances. Both I-JAR and the tabu search algorithm they consider are based on the N1 move operator introduced by van Laarhoven et al. [vLAL92]. The N1 operator induces a connected search space, such that it is always possible to move from an arbitrary solution to an optimal solution; this property is integral to the development of a behavioral model of I-JAR. However, much of the analysis generalizes to other move operators, including that of Nowicki and Smutnick [NS96]. Finally the models are based on the distance between two solutions, which they take as the well-known disjunctive graph distance [MBK99].
