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At least 703 records · Page 39

Finding New Math Identities by Computer

Recently a number of interesting new mathematical identities have been discovered by means of numerical searches on high performance computers, using some newly discovered algorithms. These include the following: pi = ((sup oo)(sub k=0))(Sigma) (1 / 16) (sup k) ((4 / 8k+1) - (2 / 8k+4) - (1 / 8k+5) - (1 / 8k+6)) and ((17 pi(exp 4)) / 360) = ((sup oo)(sub k=1))(Sigma) (1 + (1/2) + (1/3) + ... + (1/k))(exp 2) k(exp -2), zeta(3, 1, 3, 1, ..., 3, 1) = (2 pi(exp 4m) / (4m+2)! where m = number of (3,1) pairs. and where zeta(n1,n2,...,nr) = (sub k1 (is greater than) k2 (is greater than) ... (is greater than) kr)(Sigma) (1 / (k1 (sup n1) k2 (sup n2) ... kr (sup nr). The first identity is remarkable in that it permits one to compute the n-th binary or hexadecimal digit of pu directly, without computing any of the previous digits, and without using multiple precision arithmetic. Recently the ten billionth hexadecimal digit of pi was computed using this formula. The third identity has connections to quantum field theory. (The first and second of these been formally established; the third is affirmed by numerical evidence only.) The background and results of this work will be described, including an overview of the algorithms and computer techniques used in these studies.

Bailey, David H.↗

Onward to Petaflops Computing

With the recent demonstration of a computing rate of one Tflop/s at Sandia National Lab, one might ask what lies ahead for high-end computing. The next major milestone is a sustained rate of one Pflop/s (also written one petaflops, or 10(exp 15) floating-point operations per second). It should be emphasized that we could just as well use the term "peta-ops", since it appears that large scientific systems will be required to perform intensive integer and logical computation in addition to floating-point operations, and completely non- floating-point applications are likely to be important as well. In addition to prodigiously high computational performance, such systems must of necessity feature very large main memories, between ten Tbyte (10(exp 13) byte) and one Pbyte (10 (exp 15) byte) depending on application, as well as commensurate I/O bandwidth and huge mass storage facilities. The current consensus of scientists who have performed initial studies in this field is that "affordable" petaflops systems may be feasible by the year 2010, assuming that certain key technologies continue to progress at current rates. A sustained petaflops computing capability however is a daunting challenge; it appears significantly more challenging from today's state-of-the-art than achieving one Tflop/s has been from the level of one Gflop/s about 12 years ago. Challenges are faced in the arena of device technology, system architecture, system software, algorithms and applications. This talk will give an overview of some of these challenges, and describe some of the recent initiatives to address them.

Bailey, David H.↗

Computational Aeroacoustic Analysis System Development

Many industrial and commercial products operate in a dynamic flow environment and the aerodynamically generated noise has become a very important factor in the design of these products. In light of the importance in characterizing this dynamic environment, Rocketdyne has initiated a multiyear effort to develop an advanced general-purpose Computational Aeroacoustic Analysis System (CAAS) to address these issues. This system will provide a high fidelity predictive capability for aeroacoustic design and analysis. The numerical platform is able to provide high temporal and spatial accuracy that is required for aeroacoustic calculations through the development of a high order spectral element numerical algorithm. The analysis system is integrated with well-established CAE tools, such as a graphical user interface (GUI) through PATRAN, to provide cost-effective access to all of the necessary tools. These include preprocessing (geometry import, grid generation and boundary condition specification), code set up (problem specification, user parameter definition, etc.), and postprocessing. The purpose of the present paper is to assess the feasibility of such a system and to demonstrate the efficiency and accuracy of the numerical algorithm through numerical examples. Computations of vortex shedding noise were carried out in the context of a two-dimensional low Mach number turbulent flow past a square cylinder. The computational aeroacoustic approach that is used in CAAS relies on coupling a base flow solver to the acoustic solver throughout a computational cycle. The unsteady fluid motion, which is responsible for both the generation and propagation of acoustic waves, is calculated using a high order flow solver. The results of the flow field are then passed to the acoustic solver through an interpolator to map the field values into the acoustic grid. The acoustic field, which is governed by the linearized Euler equations, is then calculated using the flow results computed from the flow solver.

Hadid, A.↗

An Overview of Computational Aeroacoustic Modeling at NASA Langley

The use of computational techniques in the area of acoustics is known as computational aeroacoustics and has shown great promise in recent years. Although an ultimate goal is to use computational simulations as a virtual wind tunnel, the problem is so complex that blind applications of traditional algorithms are typically unable to produce acceptable results. The phenomena of interest are inherently unsteady and cover a wide range of frequencies and amplitudes. Nonetheless, with appropriate simplifications and special care to resolve specific phenomena, currently available methods can be used to solve important acoustic problems. These simulations can be used to complement experiments, and often give much more detailed information than can be obtained in a wind tunnel. The use of acoustic analogy methods to inexpensively determine far-field acoustics from near-field unsteadiness has greatly reduced the computational requirements. A few examples of current applications of computational aeroacoustics at NASA Langley are given. There remains a large class of problems that require more accurate and efficient methods. Research to develop more advanced methods that are able to handle the geometric complexity of realistic problems using block-structured and unstructured grids are highlighted.

Lockard, David P.↗

Quantum Computation Using Optically Coupled Quantum Dot Arrays

A solid state model for quantum computation has potential advantages in terms of the ease of fabrication, characterization, and integration. The fundamental requirements for a quantum computer involve the realization of basic processing units (qubits), and a scheme for controlled switching and coupling among the qubits, which enables one to perform controlled operations on qubits. We propose a model for quantum computation based on optically coupled quantum dot arrays, which is computationally similar to the atomic model proposed by Cirac and Zoller. In this model, individual qubits are comprised of two coupled quantum dots, and an array of these basic units is placed in an optical cavity. Switching among the states of the individual units is done by controlled laser pulses via near field interaction using the NSOM technology. Controlled rotations involving two or more qubits are performed via common cavity mode photon. We have calculated critical times, including the spontaneous emission and switching times, and show that they are comparable to the best times projected for other proposed models of quantum computation. We have also shown the feasibility of accessing individual quantum dots using the NSOM technology by calculating the photon density at the tip, and estimating the power necessary to perform the basic controlled operations. We are currently in the process of estimating the decoherence times for this system; however, we have formulated initial arguments which seem to indicate that the decoherence times will be comparable, if not longer, than many other proposed models.

Pradhan, Prabhakar↗

Computational Approach for Developing Blood Pump

This viewgraph presentation provides an overview of the computational approach to developing a ventricular assist device (VAD) which utilizes NASA aerospace technology. The VAD is used as a temporary support to sick ventricles for those who suffer from late stage congestive heart failure (CHF). The need for donor hearts is much greater than their availability, and the VAD is seen as a bridge-to-transplant. The computational issues confronting the design of a more advanced, reliable VAD include the modelling of viscous incompressible flow. A computational approach provides the possibility of quantifying the flow characteristics, which is especially valuable for analyzing compact design with highly sensitive operating conditions. Computational fluid dynamics (CFD) and rocket engine technology has been applied to modify the design of a VAD which enabled human transplantation. The computing requirement for this project is still large, however, and the unsteady analysis of the entire system from natural heart to aorta involves several hundred revolutions of the impeller. Further study is needed to assess the impact of mechanical VADs on the human body

Kwak, Dochan↗

Application of Reconfigurable Computing Technology to Multi-KiloHertz Micro-Laser Altimeter (MMLA) Data Processing

The Multi-KiloHertz Micro-Laser Altimeter (MMLA) is an aircraft based instrument developed by NASA Goddard Space Flight Center with several potential spaceflight applications. This presentation describes how reconfigurable computing technology was employed to perform MMLA signal extraction in real-time under realistic operating constraints. The MMLA is a "single-photon-counting" airborne laser altimeter that is used to measure land surface features such as topography and vegetation canopy height. This instrument has to date flown a number of times aboard the NASA P3 aircraft acquiring data at a number of sites in the Mid-Atlantic region. This instrument pulses a relatively low-powered laser at a very high rate (10 kHz) and then measures the time-of-flight of discrete returns from the target surface. The instrument then bins these measurements into a two-dimensional array (vertical height vs. horizontal ground track) and selects the most likely signal path through the array. Return data that does not correspond to the selected signal path are classified as noise returns and are then discarded. The MMLA signal extraction algorithm is very compute intensive in that a score must be computed for every possible path through the two dimensional array in order to select the most likely signal path. Given a typical array size with 50 x 6, up to 33 arrays must be processed per second. And for each of these arrays, roughly 12,000 individual paths must be scored. Furthermore, the number of paths increases exponentially with the horizontal size of the array, and linearly with the vertical size. Yet, increasing the horizontal and vertical sizes of the array offer science advantages such as improved range, resolution, and noise rejection. Due to the volume of return data and the compute intensive signal extraction algorithm, the existing PC-based MMLA data system has been unable to perform signal extraction in real-time unless the array is limited in size to one column, This limits the ability of the MMLA to operate in environments with sparse signal returns and a high number of noise return. However, under an IR&D project, an FPGA-based, reconfigurable computing data system has been developed that has been demonstrated to perform real-time signal extraction under realistic operating constraints. This reconfigurable data system is based on the commercially available Firebird Board from Annapolis Microsystems. This PCI board consists of a Xilinx Virtex 2000E FPGA along with 36 MB of SRAM arranged in five separately addressable banks. This board is housed in a rackmount PC with dual 850MHz Pentium processors running the Windows 2000 operating system. This data system performs all signal extraction in hardware on the Firebird, but also runs the existing "software based" signal extraction in tandem for comparison purposes. Using a relatively small amount of the Virtex XCV2000E resources, the reconfigurable data system has demonstrated to improve performance improvement over the existing software based data system by an order of magnitude. Performance could be further improved by employing parallelism. Ground testing and a preliminary engineering test flight aboard the NASA P3 has been performed, during which the reconfigurable data system has been demonstrated to match the results of the existing data system.

Powell, Wesley↗

Development of Computational Aeroacoustics Code for Jet Noise and Flow Prediction

Accurate prediction of jet fan and exhaust plume flow and noise generation and propagation is very important in developing advanced aircraft engines that will pass current and future noise regulations. In jet fan flows as well as exhaust plumes, two major sources of noise are present: large-scale, coherent instabilities and small-scale turbulent eddies. In previous work for the NASA Glenn Research Center, three strategies have been explored in an effort to computationally predict the noise radiation from supersonic jet exhaust plumes. In order from the least expensive computationally to the most expensive computationally, these are: 1) Linearized Euler equations (LEE). 2) Very Large Eddy Simulations (VLES). 3) Large Eddy Simulations (LES). The first method solves the linearized Euler equations (LEE). These equations are obtained by linearizing about a given mean flow and the neglecting viscous effects. In this way, the noise from large-scale instabilities can be found for a given mean flow. The linearized Euler equations are computationally inexpensive, and have produced good noise results for supersonic jets where the large-scale instability noise dominates, as well as for the tone noise from a jet engine blade row. However, these linear equations do not predict the absolute magnitude of the noise; instead, only the relative magnitude is predicted. Also, the predicted disturbances do not modify the mean flow, removing a physical mechanism by which the amplitude of the disturbance may be controlled. Recent research for isolated airfoils' indicates that this may not affect the solution greatly at low frequencies. The second method addresses some of the concerns raised by the LEE method. In this approach, called Very Large Eddy Simulation (VLES), the unsteady Reynolds averaged Navier-Stokes equations are solved directly using a high-accuracy computational aeroacoustics numerical scheme. With the addition of a two-equation turbulence model and the use of a relatively coarse grid, the numerical solution is effectively filtered into a directly calculated mean flow with the small-scale turbulence being modeled, and an unsteady large-scale component that is also being directly calculated. In this way, the unsteady disturbances are calculated in a nonlinear way, with a direct effect on the mean flow. This method is not as fast as the LEE approach, but does have many advantages to recommend it; however, like the LEE approach, only the effect of the largest unsteady structures will be captured. An initial calculation was performed on a supersonic jet exhaust plume, with promising results, but the calculation was hampered by the explicit time marching scheme that was employed. This explicit scheme required a very small time step to resolve the nozzle boundary layer, which caused a long run time. Current work is focused on testing a lower-order implicit time marching method to combat this problem.

Keith, Theo G., Jr.↗

Portable Computer

SPOC, a navigation monitoring computer used by NASA in a 1983 mission, was a modification of a commercial computer called GRiD Compass, produced by GRiD Systems Corporation. SPOC was chosen because of its small size, large storage capacity, and high processing speed. The principal modification required was a fan to cool the computer. SPOC automatically computes position, orbital paths, communication locations, etc. Some of the modifications were adapted for commercial applications. The computer is presently used in offices for conferences, for on-site development, and by the army as part of a field communications systems.

Source record↗

The Computing and Data Grid Approach: Infrastructure for Distributed Science Applications

With the advent of Grids - infrastructure for using and managing widely distributed computing and data resources in the science environment - there is now an opportunity to provide a standard, large-scale, computing, data, instrument, and collaboration environment for science that spans many different projects and provides the required infrastructure and services in a relatively uniform and supportable way. Grid technology has evolved over the past several years to provide the services and infrastructure needed for building 'virtual' systems and organizations. We argue that Grid technology provides an excellent basis for the creation of the integrated environments that can combine the resources needed to support the large- scale science projects located at multiple laboratories and universities. We present some science case studies that indicate that a paradigm shift in the process of science will come about as a result of Grids providing transparent and secure access to advanced and integrated information and technologies infrastructure: powerful computing systems, large-scale data archives, scientific instruments, and collaboration tools. These changes will be in the form of services that can be integrated with the user's work environment, and that enable uniform and highly capable access to these computers, data, and instruments, regardless of the location or exact nature of these resources. These services will integrate transient-use resources like computing systems, scientific instruments, and data caches (e.g., as they are needed to perform a simulation or analyze data from a single experiment); persistent-use resources. such as databases, data catalogues, and archives, and; collaborators, whose involvement will continue for the lifetime of a project or longer. While we largely address large-scale science in this paper, Grids, particularly when combined with Web Services, will address a broad spectrum of science scenarios. both large and small scale.

Johnston, William E.↗

Changing the Paradigm: Preparing Students for the Computing Profession in the 21st Century

The dramatic technological developments of the past decade have led to a tremendous growth in the demand for computer science professionals well-versed in advanced technology and techniques. NASA, traditionally a haven for cutting-edge innovators, is now competing with every industrial and government sector for computer science talent. The computer science program at University of Texas at San Antonio (UTSA) faces challenges beyond those intrinsically presented by rapid technological change, because a significant number of UTSA students come from low-income families with no Internet or computer access at home. An examination of enrollment statistics for the computer science program at UTSA showed that very few students who entered as freshmen successfully graduated. The upper division courses appeared to be populated by graduate students removing deficiencies and by transfer students. The faculty was also concerned that the students who did graduate from the program did not have the strong technical and programming skills that the CS program had been noted for in the community during the 1980's.

Robbins, Kay A.↗

Computational Aeroelasticity: Success, Progress, Challenge

The formal term Computational Aeroelasticity (CAE) has only been recently adopted to describe aeroelastic analysis methods coupling high-level computational fluid dynamics codes with structural dynamics techniques. However, the general field of aeroelastic computations has enjoyed a rich history of development and application since the first hand-calculations performed in the mid 1930 s. This paper portrays a much broader definition of Computational Aeroelasticity; one that encompasses all levels of aeroelastic computation from the simplest linear aerodynamic modeling to the highest levels of viscous unsteady aerodynamics, from the most basic linear beam structural models to state-of-the-art Finite Element Model (FEM) structural analysis. This paper is not written as a comprehensive history of CAE, but rather serves to review the development and application of aeroelastic analysis methods. It describes techniques and example applications that are viewed as relatively mature and accepted, the "successes" of CAE. Cases where CAE has been successfully applied to unique or emerging problems, but the resulting techniques have proven to be one-of-a-kind analyses or areas where the techniques have yet to evolve into a routinely applied methodology are covered as "progress" in CAE. Finally the true value of this paper is rooted in the description of problems where CAE falls short in its ability to provide relevant tools for industry, the so-called "challenges" to CAE.

Schuster, David M.↗

Evaluation of Cache-based Superscalar and Cacheless Vector Architectures for Scientific Computations

The growing gap between sustained and peak performance for scientific applications has become a well-known problem in high performance computing. The recent development of parallel vector systems offers the potential to bridge this gap for a significant number of computational science codes and deliver a substantial increase in computing capabilities. This paper examines the intranode performance of the NEC SX6 vector processor and the cache-based IBM Power3/4 superscalar architectures across a number of key scientific computing areas. First, we present the performance of a microbenchmark suite that examines a full spectrum of low-level machine characteristics. Next, we study the behavior of the NAS Parallel Benchmarks using some simple optimizations. Finally, we evaluate the perfor- mance of several numerical codes from key scientific computing domains. Overall results demonstrate that the SX6 achieves high performance on a large fraction of our application suite and in many cases significantly outperforms the RISC-based architectures. However, certain classes of applications are not easily amenable to vectorization and would likely require extensive reengineering of both algorithm and implementation to utilize the SX6 effectively.

Oliker, Leonid↗

Computational Aero-acoustics As a Tool For Turbo-machinery Noise Reduction

This talk will provide an overview of the field of computational aero-acoustics and its use in fan noise prediction. After a brief history of computational fluid dynamics, some of the recent developments in computational aero-acoustics will be explored. Computational issues concerning sound wave production, propagation, and reflection in practical turbo-machinery applications will be discussed including: (a) High order/High Resolution Numerical Techniques. (b) High Resolution Boundary Conditions. [c] MIMD Parallel Computing. [d] Form of Governing Equations Useful for Simulations. In addition, the basic design of our Broadband Analysis Stator Simulator (BASS) code and its application to a 2 D rotor wake-stator interaction will be shown. An example of the noise produced by the wakes from a rotor impinging upon a stator cascade will be shown.

Dyson, Rodger W.↗

A Computational Icing Effects Study for a Three-Dimensional Wing: Comparison with Experimental Data and Investigation of Spanwise Variation

Steady-state solutions of the Reynolds-averaged Navier-Stokes (RANS) equations were computed using the Colbalt flow solver for a constant-section, rectangular wing based on an extruded two-dimensional glaze ice shape. The one equation Spalart-Allmaras turbulence model was used. The results were compared with data obtained from a recent wind tunnel test. Computed results indicate that the steady RANS solutions do not accurately capture the recirculating region downstream of the ice accretion, even after a mesh refinement. The resulting predicted reattachment is farther downstream than indicated by the experimental data. Additionally, the solutions computed on a relatively coarse baseline mesh had detailed flow characteristics that were different from those computed on the refined mesh or the experimental data. Steady RANS solutions were also computed to investigate the effects of spanwise variation in the ice shape. The spanwise variation was obtained via a bleeding function that merged the ice shape with the clean wing using a sinusoidal spanwise variation. For these configurations, the results predicted for the extruded shape provided conservative estimates for the performance degradation of the wing. Additionally, the spanwise variation in the ice shape and the resulting differences in the flow fields did not significantly change the location of the primary reattachment.

Thompson, D.↗

Characterization of Unsteady Flow Structures Near Landing-Edge Slat: 2D Computations - Part 2

In our previous computational studies of a generic high-lift configuration, quasi-laminar (as opposed to fully turbulent) treatment of the slat cove region proved to be an effective approach for capturing the unsteady dynamics of the cove flow field. Combined with acoustic propagation via Ffowes Williams and Hawkings formulation, the quasi-laminar simulations captured some important features of the slat cove noise measured with microphone array techniques. However. a direct assessment of the computed cove flow field was not feasible due to the unavailability of off-surface flow measurements. To remedy this shortcoming, we have undertaken a combined experiment and computational study aimed at characterizing the flow structures and fluid mechanical processes within the slat cove region. Part I of this paper outlines the experimental aspects of this investigation focused on the 30P30N high-lift configuration; the present paper describes the accompanying computational results including a comparison between computation and experiment at various angles of attack. Even through predictions of the time-averaged flow field agree well with the measured data, the study indicates the need for further refinement of the zonal turbulence approach in order to capture the full dynamics of the cove's fluctuating flow field.

Khorrami, Mehdi↗

Computational Aerodynamics of Shuttle Orbiter Damage Scenarios in Support of the Columbia Accident Investigation

In support of the Columbia Accident Investigation, inviscid computations of the aerodynamic characteristics for various Shuttle Orbiter damage scenarios were performed using the FELISA unstructured CFD solver. Computed delta aerodynamics were compared with the reconstructed delta aerodynamics in order to postulate a progression of damage through the flight trajectory. By performing computations at hypervelocity flight and CF4 tunnel conditions, a bridge was provided between wind tunnel testing in Langley's 20-Inch CF4 facility and the flight environment experienced by Columbia during re-entry. The rapid modeling capability of the unstructured methodology allowed the computational effort to keep pace with the wind tunnel and, at times, guide the wind tunnel efforts. These computations provided a detailed view of the flowfield characteristics and the contribution of orbiter components (such as the vertical tail and wing) to aerodynamic forces and moments that were unavailable from wind tunnel testing. The damage scenarios are grouped into three categories. Initially, single and multiple missing full RCC panels were analyzed to determine the effect of damage location and magnitude on the aerodynamics. Next is a series of cases with progressive damage, increasing in severity, in the region of RCC panel 9. The final group is a set of wing leading edge and windward surface deformations that model possible structural deformation of the wing skin due to internal heating of the wing structure. By matching the aerodynamics from selected damage scenarios to the reconstructed flight aerodynamics, a progression of damage that is consistent with the flight data, debris forensics, and wind tunnel data is postulated.

Bibb, Karen L.↗

Control Law Design in a Computational Aeroelasticity Environment

A methodology for designing active control laws in a computational aeroelasticity environment is given. The methodology involves employing a systems identification technique to develop an explicit state-space model for control law design from the output of a computational aeroelasticity code. The particular computational aeroelasticity code employed in this paper solves the transonic small disturbance aerodynamic equation using a time-accurate, finite-difference scheme. Linear structural dynamics equations are integrated simultaneously with the computational fluid dynamics equations to determine the time responses of the structure. These structural responses are employed as the input to a modern systems identification technique that determines the Markov parameters of an "equivalent linear system". The Eigensystem Realization Algorithm is then employed to develop an explicit state-space model of the equivalent linear system. The Linear Quadratic Guassian control law design technique is employed to design a control law. The computational aeroelasticity code is modified to accept control laws and perform closed-loop simulations. Flutter control of a rectangular wing model is chosen to demonstrate the methodology. Various cases are used to illustrate the usefulness of the methodology as the nonlinearity of the aeroelastic system is increased through increased angle-of-attack changes.

Newsom, Jerry R.↗