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NASA NTRS1988

Introduction to a system for implementing neural net connections on SIMD architectures

Neural networks have attracted much interest recently, and using parallel architectures to simulate neural networks is a natural and necessary application. The SIMD model of parallel computation is chosen, because systems of this type can be built with large numbers of processing elements. However, such systems are not naturally suited to generalized communication. A method is proposed that allows an implementation of neural network connections on massively parallel SIMD architectures. The key to this system is an algorithm permitting the formation of arbitrary connections between the neurons. A feature is the ability to add new connections quickly. It also has error recovery ability and is robust over a variety of network topologies. Simulations of the general connection system, and its implementation on the Connection Machine, indicate that the time and space requirements are proportional to the product of the average number of connections per neuron and the diameter of the interconnection network.

Tomboulian, Sherryl↗

NASA NTRS1988

Introduction to a system for implementing neural net connections on SIMD architectures

Neural networks have attracted much interest recently, and using parallel architectures to simulate neural networks is a natural and necessary application. The SIMD model of parallel computation is chosen, because systems of this type can be built with large numbers of processing elements. However, such systems are not naturally suited to generalized elements. A method is proposed that allows an implementation of neural network connections on massively parallel SIMD architectures. The key to this system is an algorithm permitting the formation of arbitrary connections between the neurons. A feature is the ability to add new connections quickly. It also has error recovery ability and is robust over a variety of network topologies. Simulations of the general connection system, and its implementation on the Connection Machine, indicate that the time and space requirements are proportional to the product of the average number of connections per neuron and the diameter of the interconnection network.

Tomboulian, Sherryl↗

NASA NTRS1972

Variance reduction in Monte Carlo analysis of rarefied gas diffusion

The present analysis uses the Monte Carlo method to solve the problem of rarefied diffusion between parallel walls. The diffusing molecules are evaporated or emitted from one of two parallel walls and diffused through another molecular species. The analysis treats the diffusing molecule as undergoing a Markov random walk and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs the expected Markov walk payoff is retained but its variance is reduced so that the M. C. result has a much smaller error.

Perlmutter, M.↗

NASA NTRS1982

On the inversion of block tridiagonals without storage constraints

A strategy was developed to permit trade-offs between the number of floating point operations required and the storage requirements for the solution of certain difference problems, such as block tridiagonal systems of equations. This is done by recomputing some intermediate results instead of storing them. Reducing the storage to the square root of the current requirement roughly doubles the number of computations. Reducing the storage more than this tends to make the number of computations prohibitively large. In theory, if m is the order of each sub-matrix in the block tridiagonal matrix, one can solve any linear system with only 5m(2) + 1 temporary storage cells. In many cases m is a constant and quite small. For example, in solving a factored form of the three-dimensional Navier-Stokes equations, the size m of the block tridiagonals is 5. This method lends itself to efficient use on computers with parallel processing or vector processing architectures. On these computers the larger number of floating point operations is more than offset by the decrease in I/O and the increased percentage of vector operations made possible by this algorithm.

Merriam, M. L.↗

NASA NTRS1985

On the factorization of block-tridiagonals without storage constraints

In many programs solving difference equations, problem size is restricted by the number of available memory cells. A strategy has been developed to permit trade-offs between the number of floating point operations required and storage requirements for the solution of certain problems such as block tridiagonal systems of equations. This is done by recomputing some intermediate results instead of storing them. Reducing the storage to the square root of the current requirement will roughly double the number of computations. In theory, if m is the order of each sub-matrix in the block tridiagonal matrix, one can solve any linear system with only 5 sq m + 1 temporary storage cells. This method lends itself to efficient use on computers with parallel processing or vector processing architectures. On these computers the larger number of floating point operations is more than offset by the decrease in I/O and the increased percentage of vector operations made possible by this algorithm.

Merriam, M. L.↗

NASA NTRS1985

Advances and trends in structures and dynamics; Proceedings of the Symposium, Washington, DC, October 22-25, 1984

Among the topics discussed are developments in structural engineering hardware and software, computation for fracture mechanics, trends in numerical analysis and parallel algorithms, mechanics of materials, advances in finite element methods, composite materials and structures, determinations of random motion and dynamic response, optimization theory, automotive tire modeling methods and contact problems, the damping and control of aircraft structures, and advanced structural applications. Specific topics covered include structural design expert systems, the evaluation of finite element system architectures, systolic arrays for finite element analyses, nonlinear finite element computations, hierarchical boundary elements, adaptive substructuring techniques in elastoplastic finite element analyses, automatic tracking of crack propagation, a theory of rate-dependent plasticity, the torsional stability of nonlinear eccentric structures, a computation method for fluid-structure interaction, the seismic analysis of three-dimensional soil-structure interaction, a stress analysis for a composite sandwich panel, toughness criterion identification for unidirectional composite laminates, the modeling of submerged cable dynamics, and damping synthesis for flexible spacecraft structures.

Noor, A. K.↗

NASA NTRS1986

Earth's compressional foreshock boundary revisited Observations by the ISEE 1 magnetometer

A 'solar foreshock coordinate' (SFC) system is introduced in which the positions of foreshock components can be collated with a minimum of assumptions about the physical processes involved. Location behind the interplanetary magnetic field (IMF) tangent surface to the bow shock and rotational symmetry around the solar wind flow (X) axis are the only presuppositions. The SFC system has been applied to over 300 observations of the boundary of the ULF compressional waves recorded by ISEE 1's magnetometer in 1978 and 1979. The boundary locations form a coherent pattern in the SFC frame. A selection of those cases for which the cone angle of the IMF was between 40 and 50 deg, corresponding to the average stream angle, yields a least square line whose mapping back to the solar ecliptic coordinates frame has slope of about 85 deg, very close to that of the tangent ULF boundary deduced earlier from more primitive methods with entirely different data sets. The line, being parallel to neither the IMF, the typical reflected beam, nor the shock, cannot be compatible with any model of wave production by beam-solar wind interaction that depends on uniform beam distribution or fixed growth rate. Rather, its tangency suggests the influence of a separate, escaping ion population.

Greenstadt, E. W.↗

NASA NTRS1987

Fast simulation techniques for switching converters

Techniques for simulating a switching converter are examined. The state equations for the equivalent circuits, which represent the switching converter, are presented and explained. The uses of the Newton-Raphson iteration, low ripple approximation, half-cycle symmetry, and discrete time equations to compute the interval durations are described. An example is presented in which these methods are illustrated by applying them to a parallel-loaded resonant inverter with three equivalent circuits for its continuous mode of operation.

King, Roger J.↗

NASA NTRS1989

Application of the p-version of the finite-element method to global-local problems

A brief survey is given of some recent developments in finite-element analysis technology which bear upon the three main research areas under consideration in this workshop: (1) analysis methods; (2) software testing and quality assurance; and (3) parallel processing. The variational principle incorporated in a finite-element computer program, together with a particular set of input data, determines the exact solution corresponding to that input data. Most finite-element analysis computer programs are based on the principle of virtual work. In the following, researchers consider only programs based on the principle of virtual work and denote the exact displacement vector field corresponding to some specific set of input data by vector u(EX). The exact solution vector u(EX) is independent of the design of the mesh or the choice of elements. Except for very simple problems, or specially constructed test problems, vector u(EX) is not known. Researchers perform a finite-element analysis (or any other numerical analysis) because they wish to make conclusions concerning the response of a physical system to certain imposed conditions, as if vector u(EX) were known.

Szabo, Barna A.↗

NASA NTRS1990

A block-based algorithm for the solution of compressible flows in rotor-stator combinations

A block-based solution algorithm is developed for the solution of compressible flows in rotor-stator combinations. The method allows concurrent solution of multiple solution blocks in parallel machines. It also allows a time averaged interaction at the stator-rotor interfaces. Numerical results are presented to illustrate the performance of the algorithm. The effect of the interaction between the stator and rotor is evaluated.

Akay, H. U.↗

NASA NTRS1991

A nonrecursive 'Order N' preconditioned conjugate gradient/range space formulation of MDOF dynamics

This paper addresses the requirements of present-day mechanical system simulations of algorithms that induce parallelism on a fine scale and of transient simulation methods which must be automatically load balancing for a wide collection of system topologies and hardware configurations. To this end, a combination range space/preconditioned conjugage gradient formulation of multidegree-of-freedon dynamics is developed, which, by employing regular ordering of the system connectivity graph, makes it possible to derive an extremely efficient preconditioner from the range space metric (as opposed to the system coefficient matrix). Because of the effectiveness of the preconditioner, the method can achieve performance rates that depend linearly on the number of substructures. The method, termed 'Order N' does not require the assembly of system mass or stiffness matrices, and is therefore amenable to implementation on work stations. Using this method, a 13-substructure model of the Space Station was constructed.

Kurdila, A. J.↗

NASA NTRS1991

Discrete ordinate solution of the radiative transfer equation in the 'polarization normal wave representation'

The transfer equations for normal waves in finite, inhomogeneous and plane-parallel magnetoactive media are solved using the discrete ordinate method. The physical process of absorption, emission, and multiple scattering are accounted for, and the medium may be forced both at the top and bottom boundary by anisotropic radiation as well as by internal anisotropic sources. The computational procedure is numerically stable for arbitrarily large optical depths, and the computer time is independent of optical thickness.

Kylling, A.↗

NASA NTRS1991

Heat transfer in a discrete-velocity gas

Heat transfer of a discrete-velocity gas composed of identical hard sphere molecules between two parallel plates is studied numerically. A finite-difference method recently developed by the authors is used for solving the discrete Boltzmann equations. The temperature distributions between the plates of temperature ratios 2.0 and 4.0, and the heat transfer of temperature ratio 4.0 are presented and are compared with results of other methods.

Inamuro, Takaji↗

NASA NTRS1952

Concerning the flow about ring-shaped cowlings of finite thickness Part I

It is shown how one may obtain, in a simple manner, the forms of ring-shaped bodies from existing tables of functions according to the customary method of superposition of flow due to singularities and parallel flow. A number of examples of the forms and pressure distributions of annular source bodies with and without hub body are given, and the inlet conditions of such ring-shaped cowlings are investigated. Furthermore, the annular bodies of finite length are indicated that correspond to Joukowsky profiles for the two-dimensional case. The examples are to give a basis for the design of cross-sectional forms of ring-shaped cowlings and a survey of the flows to be expected.

FLOW, INCOMPRESSIBLE↗

NASA NTRS1995

Parallel rendering

This article provides a broad introduction to the subject of parallel rendering, encompassing both hardware and software systems. The focus is on the underlying concepts and the issues which arise in the design of parallel rendering algorithms and systems. We examine the different types of parallelism and how they can be applied in rendering applications. Concepts from parallel computing, such as data decomposition, task granularity, scalability, and load balancing, are considered in relation to the rendering problem. We also explore concepts from computer graphics, such as coherence and projection, which have a significant impact on the structure of parallel rendering algorithms. Our survey covers a number of practical considerations as well, including the choice of architectural platform, communication and memory requirements, and the problem of image assembly and display. We illustrate the discussion with numerous examples from the parallel rendering literature, representing most of the principal rendering methods currently used in computer graphics.

Crockett, Thomas W.↗

NASA NTRS1995

Experimental testing using a remotely operated flap with a 2D high lift model

The problem of efficient wind tunnel testing for multi-element airfoils was first addressed by the author during a previous ASEE fellowship. A modern three element model with internal actuators to position a flap in two degrees of freedom was designed and later built. Some preliminary testing proved that the approach was viable. The purpose of this summer's work was to fully develop experimental methods including efficient data acquisition. The final goal is to develop dense data sets for both lift and drag measurements as a function of flap position for both take-off and landing configurations. The model has a span of 36 in. and chord of 18 in. and is currently being fitted for a 3 ft. x 4 ft. low speed wind tunnel. The flap was reworked to allow all pressure taps to function after initial tests showed two blocked ports. The serial method of obtaining pressures from the surface taps was found to be exceedingly slow so a new method using 12 pressure transducers and a 12 port parallel scanning valve were developed. A new automated data acquisition and control algorithm was developed using LabView software and a PC platform. Flow two-dimensionality is currently under investigation with boundary layer control by blowing; this was previously omitted for initial testing. By the end of the summer a detailed data set (uncorrected) consisting of lift coefficient versus flap position for the landing configuration should be available.

Landman, Drew↗

NASA NTRS1996

Effective Boundary Treatment for the Biharmonic Dirichlet Problem

The biharmonic equation can be rewritten as a system of two Poisson equations. Multigrid solution of this system is expected to converge with the same amount of work as solving two Poisson equations, requiring less than 70 floating point operations (scalar multiply or addition) per fine grid point to reach a solution using an FMG algorithm. For periodic boundary conditions, this goal is attained by simple, straightforward application of multigrid. For Dirichlet boundary conditions, however, convergence is impeded by poor interaction with the boundaries. Attempts to overcome the slowness without specifically addressing the boundaries have resulted in multigrid algorithms not attaining the Poisson convergence rate. We present three methods of boundary treatment with which full multigrid efficiency can be obtained. All implement an approach described by Brandt, concentrating some additional effort near the boundary. The first approach simply adds a number of relaxation sweeps over points close to the boundary. The second uses joint relaxation on near-boundary points. The third method takes something from each of the first two methods, resulting in a solver more suitable for highly parallel applications.

Brandt, A.↗

NASA NTRS1999

Parallel Aeroelastic Analysis Using ENSAERO and NASTRAN

A high fidelity parallel static structural analysis capability is created and interfaced to the multidisciplinary analysis package ENSAERO-MPI of Ames Research Center. This new module replaced ENSAERO's lower fidelity simple finite element and modal modules. Full aircraft structures may be more accurately modeled using the new finite element capability. Parallel computation is performed by breaking the full structure into multiple substructures. This approach is conceptually similar to ENSAERO's multi-zonal fluid analysis capability. The new substructure code is used to solve the structural finite element equations for each substructure in parallel. NASTRAN/COSMIC is utilized as a front end for this code. Its full library of elements can be used to create an accurate and realistic aircraft mode. It is used to create the stiffness matrices for each sub-structure. The new parallel code then uses an iterative preconditioned conjugate gradient method to solve the global structural equations for the sub-structure boundary nodes. Results are presented for a wing-body configuration.

Eldred, Lloyd B.↗