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At least 703 records · Page 39

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NASA NTRS2001

Efficient Cache use for Stencil Operations on Structured Discretization Grids

We derive tight bounds on the cache misses for evaluation of explicit stencil operators on structured grids. Our lower bound is based on the isoperimetrical property of the discrete octahedron. Our upper bound is based on a good surface to volume ratio of a parallelepiped spanned by a reduced basis of the interference lattice of a grid. Measurements show that our algorithm typically reduces the number of cache misses by a factor of three, relative to a compiler optimized code. We show that stencil calculations on grids whose interference lattice have a short vector feature abnormally high numbers of cache misses. We call such grids unfavorable and suggest to avoid these in computations by appropriate padding. By direct measurements on a MIPS R10000 processor we show a good correlation between abnormally high numbers of cache misses and unfavorable three-dimensional grids.

Frumkin, Michael↗

NASA NTRS2001

Energy Stable Flux Formulas For The Discontinuous Galerkin Discretization Of First Order Nonlinear Conservation Laws

We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable.

Barth, Timothy↗

NASA NTRS2001

Nanotube Tunneling as a Consequence of Probable Discrete Trajectories

It has been recently reported that the electrical charge in a semiconductive carbon nanotube is not evenly distributed, but is divided into charge "islands." A clear understanding of tunneling phenomena can be useful to elucidate the mechanism for electrical conduction in nanotubes. This paper represents the first attempt to shed light on the aforementioned phenomenon through viewing tunneling as a natural consequence of "discrete trajectories." The relevance of this analysis is that it may provide further insight into the higher rate of tunneling processes, which makes tunneling devices attractive. In a situation involving particles impinging on a classically impenetrable barrier, the result of quantum mechanics that the probability of detecting transmitted particles falls off exponentially is derived without wave theory. This paper should provide a basis for calculating the charge profile over the length of the tube so that nanoscale devices' conductive properties may be fully exploited.

Robinson, Daryl C.↗

NASA NTRS2001

Discrete-State Simulated Annealing For Traveling-Wave Tube Slow-Wave Circuit Optimization

Algorithms based on the global optimization technique of simulated annealing (SA) have proven useful in designing traveling-wave tube (TWT) slow-wave circuits for high RF power efficiency. The characteristic of SA that enables it to determine a globally optimized solution is its ability to accept non-improving moves in a controlled manner. In the initial stages of the optimization, the algorithm moves freely through configuration space, accepting most of the proposed designs. This freedom of movement allows non-intuitive designs to be explored rather than restricting the optimization to local improvement upon the initial configuration. As the optimization proceeds, the rate of acceptance of non-improving moves is gradually reduced until the algorithm converges to the optimized solution. The rate at which the freedom of movement is decreased is known as the annealing or cooling schedule of the SA algorithm. The main disadvantage of SA is that there is not a rigorous theoretical foundation for determining the parameters of the cooling schedule. The choice of these parameters is highly problem dependent and the designer needs to experiment in order to determine values that will provide a good optimization in a reasonable amount of computational time. This experimentation can absorb a large amount of time especially when the algorithm is being applied to a new type of design. In order to eliminate this disadvantage, a variation of SA known as discrete-state simulated annealing (DSSA), was recently developed. DSSA provides the theoretical foundation for a generic cooling schedule which is problem independent, Results of similar quality to SA can be obtained, but without the extra computational time required to tune the cooling parameters. Two algorithm variations based on DSSA were developed and programmed into a Microsoft Excel spreadsheet graphical user interface (GUI) to the two-dimensional nonlinear multisignal helix traveling-wave amplifier analysis program TWA3. The algorithms were used to optimize the computed RF efficiency of a TWT by determining the phase velocity profile of the slow-wave circuit. The mathematical theory and computational details of the DSSA algorithms will be presented and results will be compared to those obtained with a SA algorithm.

Wilson, Jeffrey D.↗

NASA NTRS2001

Synchronous Parallel System for Emulation and Discrete Event Simulation

A synchronous parallel system for emulation and discrete event simulation having parallel nodes responds to received messages at each node by generating event objects having individual time stamps, stores only the changes to the state variables of the simulation object attributable to the event object and produces corresponding messages. The system refrains from transmitting the messages and changing the state variables while it determines whether the changes are superseded, and then stores the unchanged state variables in the event object for later restoral to the simulation object if called for. This determination preferably includes sensing the time stamp of each new event object and determining which new event object has the earliest time stamp as the local event horizon, determining the earliest local event horizon of the nodes as the global event horizon, and ignoring events whose time stamps are less than the global event horizon. Host processing between the system and external terminals enables such a terminal to query, monitor, command or participate with a simulation object during the simulation process.

Jeffrey S Steinman↗

NASA NTRS2001

Continuous Measurements and Quantitative Constraints: Challenge Problems for Discrete Modeling Techniques

We present some diagnosis and control problems that are difficult to solve with discrete or purely qualitative techniques. We analyze the nature of the problems, classify them and explain why they are frequently encountered in systems with closed loop control. This paper illustrates the problem with several examples drawn from industrial and aerospace applications and presents detailed information on one important application: In-Situ Resource Utilization (ISRU) on Mars. The model for an ISRU plant is analyzed showing where qualitative techniques are inadequate to identify certain failure modes and to maintain control of the system in degraded environments. We show why the solution to the problem will result in significantly more robust and reliable control systems. Finally, we illustrate requirements for a solution to the problem by means of examples.

Goodrich, Charles H.↗

NASA NTRS1999

Practical Aspects of Stabilized FEM Discretizations of Nonlinear Conservation Law Systems with Convex Extension

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the Galerkin least-squares (GLS) and the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the POE system. Central to the development of the simplified GLS and DG methods is the Degenerative Scaling Theorem which characterizes right symmetrizes of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobean matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler, Navier-Stokes, and magnetohydrodynamic (MHD) equations. Linear and nonlinear energy stability is proven for the simplified GLS and DG methods. Spatial convergence properties of the simplified GLS and DO methods are numerical evaluated via the computation of Ringleb flow on a sequence of successively refined triangulations. Finally, we consider a posteriori error estimates for the GLS and DG demoralization assuming error functionals related to the integrated lift and drag of a body. Sample calculations in 20 are shown to validate the theory and implementation.

Barth, Timothy↗

NASA NTRS2002

A Discrete-Vortex Method for Studying the Wing Rock of Delta Wings

A discrete-vortex method is developed to investigate the wing rock problem associated with highly swept wings. The method uses two logarithmic vortices placed above the wing to represent the vortex flow field and uses boundary conditions based on conical flow, vortex rate of change of momentum, and other considerations to position the vortices and determine their strengths. A relationship based on the time analogy and conical-flow assumptions is used to determine the hysteretic positions of the vortices during roll oscillations. Static and dynamic vortex positions and wing rock amplitudes and frequencies calculated by using the method are generally in good agreement with available experimental data. The results verify that wing rock is caused by hysteretic deflections of the vortices and indicate that the stabilizing moments that limit wing rock amplitudes are the result of the one primary vortex moving outboard of the wing where it has little influence on the wing.

Gainer, Thomas G.↗

NASA NTRS2003

Compressed Semi-Discrete Central-Upwind Schemes for Hamilton-Jacobi Equations

We introduce a new family of Godunov-type semi-discrete central schemes for multidimensional Hamilton-Jacobi equations. These schemes are a less dissipative generalization of the central-upwind schemes that have been recently proposed in series of works. We provide the details of the new family of methods in one, two, and three space dimensions, and then verify their expected low-dissipative property in a variety of examples.

Bryson, Steve↗

NASA NTRS2004

Discrete Spring Model for Predicting Delamination Growth in Z-Fiber Reinforced DCB Specimens

Beam theory analysis was applied to predict delamination growth in DCB specimens reinforced in the thickness direction with pultruded pins, known as Z-fibers. The specimen arms were modeled as cantilever beams supported by discrete springs, which were included to represent the pins. A bi-linear, irreversible damage law was used to represent Z-fiber damage, the parameters of which were obtained from previous experiments. Closed-form solutions were developed for specimen compliance and displacements corresponding to Z-fiber row locations. A solution strategy was formulated to predict delamination growth, in which the parent laminate mode I fracture toughness was used as the criterion for delamination growth. The solution procedure was coded into FORTRAN 90, giving a dedicated software tool for performing the delamination prediction. Comparison of analysis results with previous analysis and experiment showed good agreement, yielding an initial verification for the analytical procedure.

Ratcliffe, James G.↗

NASA NTRS2004

Optimal Discrete Event Supervisory Control of Aircraft Gas Turbine Engines

This report presents an application of the recently developed theory of optimal Discrete Event Supervisory (DES) control that is based on a signed real measure of regular languages. The DES control techniques are validated on an aircraft gas turbine engine simulation test bed. The test bed is implemented on a networked computer system in which two computers operate in the client-server mode. Several DES controllers have been tested for engine performance and reliability.

Litt, Jonathan↗

NASA NTRS1999

Analysis of Discrete-Source Damage Progression in a Tensile Stiffened Composite Panel

This paper demonstrates the progressive failure analysis capability in NASA Langley s COMET-AR finite element analysis code on a large-scale built-up composite structure. A large-scale five stringer composite panel with a 7-in. long discrete source damage was analyzed from initial loading to final failure including the geometric and material nonlinearities. Predictions using different mesh sizes, different saw cut modeling approaches, and different failure criteria were performed and assessed. All failure predictions have a reasonably good correlation with the test result.

Wang, John T.↗

NASA NTRS1997

Correspondence between discrete and continuous models of excitable media: trigger waves

We present a theoretical framework for relating continuous partial differential equation (PDE) models of excitable media to discrete cellular automata (CA) models on a randomized lattice. These relations establish a quantitative link between the CA model and the specific physical system under study. We derive expressions for the CA model's plane wave speed, critical curvature, and effective diffusion constant in terms of the model's internal parameters (the interaction radius, excitation threshold, and time step). We then equate these expressions to the corresponding quantities obtained from solution of the PDEs (for a fixed excitability). This yields a set of coupled equations with a unique solution for the required CA parameter values. Here we restrict our analysis to "trigger" wave solutions obtained in the limiting case of a two-dimensional excitable medium with no recovery processes. We tested the correspondence between our CA model and two PDE models (the FitzHugh-Nagumo medium and a medium with a "sawtooth" nonlinear reaction source) and found good agreement with the numerical solutions of the PDEs. Our results suggest that the behavior of trigger waves is actually controlled by a small number of parameters.

Non-NASA Center↗

NASA NTRS1996

A Framework for the Optimization of Discrete-Event Simulation Models

With the growing use of computer modeling and simulation, in all aspects of engineering, the scope of traditional optimization has to be extended to include simulation models. Some unique aspects have to be addressed while optimizing via stochastic simulation models. The optimization procedure has to explicitly account for the randomness inherent in the stochastic measures predicted by the model. This paper outlines a general purpose framework for optimization of terminating discrete-event simulation models. The methodology combines a chance constraint approach for problem formulation, together with standard statistical estimation and analyses techniques. The applicability of the optimization framework is illustrated by minimizing the operation and support resources of a launch vehicle, through a simulation model.

Joshi, B. D.↗

NASA NTRS2004

Discrete Spring Model for Predicting Delamination Growth in Z-Fiber Reinforced DCB Specimens

Beam theory analysis was applied to predict delamination growth in Double Cantilever Beam (DCB) specimens reinforced in the thickness direction with pultruded pins, known as Z-fibers. The specimen arms were modeled as cantilever beams supported by discrete springs, which were included to represent the pins. A bi-linear, irreversible damage law was used to represent Z-fiber damage, the parameters of which were obtained from previous experiments. Closed-form solutions were developed for specimen compliance and displacements corresponding to Z-fiber row locations. A solution strategy was formulated to predict delamination growth, in which the parent laminate mode I critical strain energy release rate was used as the criterion for delamination growth. The solution procedure was coded into FORTRAN 90, giving a dedicated software tool for performing the delamination prediction. Comparison of analysis results with previous analysis and experiment showed good agreement, yielding an initial verification for the analytical procedure.

Ratcliffe, James G.↗

NASA NTRS2004

A Discussion of Using a Reconfigurable Processor to Implement the Discrete Fourier Transform

This paper presents the design and implementation of the Discrete Fourier Transform (DFT) algorithm on a reconfigurable processor system. While highly applicable to many engineering problems, the DFT is an extremely computationally intensive algorithm. Consequently, the eventual goal of this work is to enhance the execution of a floating-point precision DFT algorithm by off loading the algorithm from the computing system. This computing system, within the context of this research, is a typical high performance desktop computer with an may of field programmable gate arrays (FPGAs). FPGAs are hardware devices that are configured by software to execute an algorithm. If it is desired to change the algorithm, the software is changed to reflect the modification, then download to the FPGA, which is then itself modified. This paper will discuss methodology for developing the DFT algorithm to be implemented on the FPGA. We will discuss the algorithm, the FPGA code effort, and the results to date.

White, Michael J.↗

NASA NTRS2001

Gamma-Weighted Discrete Ordinate Two-Stream Approximation for Computation of Domain Averaged Solar Irradiance

An algorithm is developed for the gamma-weighted discrete ordinate two-stream approximation that computes profiles of domain-averaged shortwave irradiances for horizontally inhomogeneous cloudy atmospheres. The algorithm assumes that frequency distributions of cloud optical depth at unresolved scales can be represented by a gamma distribution though it neglects net horizontal transport of radiation. This algorithm is an alternative to the one used in earlier studies that adopted the adding method. At present, only overcast cloudy layers are permitted.

Kato, S.↗

NASA NTRS2005

Discrete X-Ray Source Populations and Star Formation History in Nearby Galaxies

This program aims in understanding the connection between the discrete X-ray source populations observed in nearby galaxies and the history of star-formation in these galaxies. The ultimate goal is to use this knowledge in order to constrain X-ray binary evolution channels. For this reason although the program is primarily observational it has a significant modeling component. During the second year of this study we focused on detailed studies of the Antennae galaxies and the Small Magellanic Cloud (SMC). We also performed the initial analysis of the 5 galaxies forming a starburst-age sequence.

Zezas, Andreas↗