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NASA NTRS1988

Parallel matrix multiplication on the Connection Machine

Matrix multiplication is a computation and communication intensive problem. Six parallel algorithms for matrix multiplication on the Connection Machine are presented and compared with respect to their performance and processor usage. For n by n matrices, the algorithms have theoretical running times of O(n to the 2nd power log n), O(n log n), O(n), and O(log n), and require n, n to the 2nd power, n to the 2nd power, and n to the 3rd power processors, respectively. With careful attention to communication patterns, the theoretically predicted runtimes can indeed be achieved in practice. The parallel algorithms illustrate the tradeoffs between performance, communication cost, and processor usage.

Tichy, Walter F.↗

NASA NTRS1991

Case for real-time systems development - Quo vadis?

The paper focuses on the distinctive issues of computer-aided software engineering (CASE) products for the development of real-time systems. CASE technologies and associated standardization efforts are evolving from sets of conflicting interests. The majority of case products are intended for use in the development of management information systems. CASE products to support the development of large, complex real-time systems must provide additional capabilities. Generic concerns include the quality of the implementation of the required method for the phase of the system's development and whether the vendor is stable and committed to evolving the products in parallel with nonproprietary standards. The CASE market is undergoing considerable consolidation. The paper describes the major forces, cooperating entities, and remaining uncertainties that need to be weighed in near-term CASE procurements to limit risk of loss of investment in project time, trianing, and money.

Erb, Dona M.↗

NASA NTRS1994

Centrifugal acceleration of the polar wind

The effect of parallel ion acceleration associated with convection was first applied to energization of test particle polar ions by Cladis (1986). However, this effect is typically neglected in 'self-consistent' models of polar plasma outflow, apart from the fluid simulation by Swift (1990). Here we include approximations for this acceleration, which we broadly characterize as centrifugal in nature, in our time-dependent, semikinetic model of polar plasma outflow and describe the effects on the bulk parameter profiles and distribution functions of H+ and O+. For meridional convection across the pole the approximate parallel force along a polar magnetic field line may be written as F(sub cent, pole) = 1.5m(E(sub i))/B(sub i))squared (r(squared)/r(sup 3)(sub i)) where m is ion mass, r is geometric distance; and E(sub i), B(sub i) and r(sub i) refer to the electric and magnetic field magnitudes and geocentric distance at the ionosphere, respectively. For purely longitudinal convection along a constant L shell the parallel force is F(cent. long) = F(sub cent, pole)(1 - (r/(r(sub i)L))(sup 3/2)/(1 - 3r/(4 r(sub i)L))(sup 5/2). For high latitudes the difference between these two cases is relatively unimportant below approximately 5 R(sub E). We find that the steady state O+ bulk velocities and parallel temperatures strongly increase and decrease, respectively, with convection strength. In particular, the bulk velocities increase from near 0 km/s at 4000 km altitude to approximately 10 km/s at 5 R(sub E) geocentric distance for 50-mV/m ionospheric convection electric field. However, the centrifugal effect on the steady O+ density profiles depends on the exobase ion and electron temperatures: for low-base temperatures (T(sub i) = T(sub e) = 3000 K) the O+ density at high altitudes increases greatly with convection, while for higher base temperatures (T(sub i) = 5000 K, T(sub e) = 9000 K), the high-altitude O+ density decreases somewhat as convection is enhanced. The centrifugal force further has a pronounced effect on the escaping O+ flux, especially for cool exobase conditions; as referenced to the 4000-km altitude, the steady state O+ flux increases from 10(exp 5) ions/sq cm/s when the ionospheric convection field E(sub i) = 0 mV/m to approximately 10(exp 7) ions/sq cm/s when E(sub i) = 100 mV/m. The centrifugal effect also decreases the time scale for approach to steady-state. For example, in the plasma expansion for T(sub i) = T(sub e) = 3000 K, the O+ density at 7 R(sub E) reaches only 10(exp -7) of it final value approximately 1.5 hours after expansion onset for E(sub i) = 0. For meridional convection driven by E(sub i) = 50 mV/m, the density at the same time after initial injection is 30-50% of its asymptotic level. The centrifugal acceleration described here is a possible explanation for the large (up to approximately 10 km/s or more) o+ outflow velocities observed in the midlatitude polar magnetosphere with the Dynamics Explorer 1 and Akebono spacecraft.

Horwitz, J. L.↗

NASA NTRS1993

A parallel implementation of a multisensor feature-based range-estimation method

There are many proposed vision based methods to perform obstacle detection and avoidance for autonomous or semi-autonomous vehicles. All methods, however, will require very high processing rates to achieve real time performance. A system capable of supporting autonomous helicopter navigation will need to extract obstacle information from imagery at rates varying from ten frames per second to thirty or more frames per second depending on the vehicle speed. Such a system will need to sustain billions of operations per second. To reach such high processing rates using current technology, a parallel implementation of the obstacle detection/ranging method is required. This paper describes an efficient and flexible parallel implementation of a multisensor feature-based range-estimation algorithm, targeted for helicopter flight, realized on both a distributed-memory and shared-memory parallel computer.

Suorsa, Raymond E.↗

NASA NTRS1993

A parallel implementation of a multisensor feature-based range-estimation method

Suorsa, Raymond E.↗

NASA NTRS1998

A Domain-Decomposed Multi-Level Method for Adaptively Refined Cartesian Grids with Embedded Boundaries

The work presents a new method for on-the-fly domain decomposition technique for mapping grids and solution algorithms to parallel machines, and is applicable to both shared-memory and message-passing architectures. It will be demonstrated on the Cray T3E, HP Exemplar, and SGI Origin 2000. Computing time has been secured on all these platforms. The decomposition technique is an outgrowth of techniques used in computational physics for simulations of N-body problems and the event horizons of black holes, and has not been previously used by the CFD community. Since the technique offers on-the-fly partitioning, it offers a substantial increase in flexibility for computing in heterogeneous environments, where the number of available processors may not be known at the time of job submission. In addition, since it is dynamic it permits the job to be repartitioned without global communication in cases where additional processors become available after the simulation has begun, or in cases where dynamic mesh adaptation changes the mesh size during the course of a simulation. The platform for this partitioning strategy is a completely new Cartesian Euler solver tarcreted at parallel machines which may be used in conjunction with Ames' "Cart3D" arbitrary geometry simulation package.

Aftosmis, M. J.↗

NASA NTRS2011

Crater Flux Transfer Events: Highroad to the X Line?

We examine Cluster observations of a so-called magnetosphere crater FTE, employing data from five instruments (FGM, CIS, EDI, EFW, and WHISPER), some at the highest resolution. The aim of doing this is to deepen our understanding of the reconnection nature of these events by applying recent advances in the theory of collisionless reconnection and in detailed observational work. Our data support the hypothesis of a stratified structure with regions which we show to be spatial structures. We support the bulge-like topology of the core region (R3) made up of plasma jetting transverse to reconnected field lines. We document encounters with a magnetic separatrix as a thin layer embedded in the region (R2) just outside the bulge, where the speed of the protons flowing approximately parallel to the field maximizes: (1) short (fraction of a sec) bursts of enhanced electric field strengths (up to approximately 30 mV/m) and (2) electrons flowing against the field toward the X line at approximately the same time as the bursts of intense electric fields. R2 also contains a density decrease concomitant with an enhanced magnetic field strength. At its interface with the core region, R3, electric field activity ceases abruptly. The accelerated plasma flow profile has a catenary shape consisting of beams parallel to the field in R2 close to the R2/R3 boundary and slower jets moving across the magnetic field within the bulge region. We detail commonalities our observations of crater FTEs have with reconnection structures in other scenarios. We suggest that in view of these properties and their frequency of occurrence, crater FTEs are ideal places to study processes at the separatrices, key regions in magnetic reconnection. This is a good preparation for the MMS mission.

Farrugia, C. J.↗

NASA NTRS1999

Step Bunching: Influence of Impurities and Solution Flow

Step bunching results in striations even at relatively early stages of its development and in inclusions of mother liquor at the later stages. Therefore, eliminating step bunching is crucial for high crystal perfection. At least 5 major effects causing and influencing step bunching are known: (1) Basic morphological instability of stepped interfaces. It is caused by concentration gradient in the solution normal to the face and by the redistribution of solute tangentially to the interface which redistribution enhances occasional perturbations in step density due to various types of noise; (2) Aggravation of the above basic instability by solution flowing tangentially to the face in the same directions as the steps or stabilization of equidistant step train if these flows are antiparallel; (3) Enhanced bunching at supersaturation where step velocity v increases with relative supersaturation s much faster than linear. This v(s) dependence is believed to be associated with impurities. The impurities of which adsorption time is comparable with the time needed to deposit one lattice layer may also be responsible for bunching; (4) Very intensive solution flow stabilizes growing interface even at parallel solution and step flows; (5) Macrosteps were observed to nucleate at crystal corners and edges. Numerical simulation, assuming step-step interactions via surface diffusion also show that step bunching may be induced by random step nucleation at the facet edge and by discontinuity in the step density (a ridge) somewhere in the middle of a face. The corresponding bunching patterns produce the ones observed in experiment. The nature of step bunching generated at the corners and edges and by dislocation step sources, as well as the also relative importance and interrelations between mechanisms 1-5 is not clear, both from experimental and theoretical standpoints. Furthermore, several laws controlling the evolution of existing step bunches have been suggested, though unambiguous conclusions are still missing. Addressing these issues is the major goal of the present project. The theory addressing the above problem, experimental methods, several figures which include: (1) the spatial wave numbers at which the system is neutrally stable as a function of growth velocity for linear kinetics and supersaturation for nonlinear kinetics; (2) a schematic of the experiment of lysozyme crystal growing under conditions of natural convection; (3) fluctuations in time, t, of the normal growth rate, R(t), vicinal slope, p(t) and Fourier Spectra of R(t), discussions and conclusions are presented.

Chernov, A. A.↗

NASA NTRS1990

Wave-interactions in supersonic and hypersonic flows

Work completed under the current grant comprises the start of a theoretical and computational attack on the subharmonic route to secondary instabilities in compressible flows. The total flow field in this problem is made up of the following components: (1) a steady streamwise mean boundary layer flow which depends only on the normal space component y; (2) a two-dimensional time dependent T-S wave which moves with wavespeed c and has no spanwise dependence; and (3) a fully three-dimensional, time dependent T-S wave whose streamwise wavenumber is half of the streamwise wavenumber associated with the two-dimensional T-S wave in b. If a frame of reference is adopted which moves with the wavespeed c of the 2-D T-S wave, the time dependence of this portion of the flow can be eliminated. The effective steady mean flow in this problem is now the sum of the original parallel steady mean flow and the initial 2-D T-S instability. Dependence on the streamwise coordinate x in this mean flow can be extracted by assuming normal mode expansions involving complex exponentials and the streamwise wavenumber a. However, it is important to note that, because this is a wave-wave interaction problem, unlike the usual linear instability case, both the complex exponential, and its complex conjugate, must be retained in describing the 2-D T-S wave. The role of the perturbation to the steady mean flow is now played by the 3-D time dependent T-S wave. In treating this wave, normal modes in the streamwise and spanwise directions and time may be used. Consistent with the subharmonic nature of this transition route, the streamwise wavenumber is a/2, and complex conjugates of the complex exponential must be employed. This is not the case with the modes giving z and t dependence with wavespeed o and spanwise wavenumber B as the effective mean flow quantities are independent of z and their time dependence is accounted for by the moving frame of reference. Consequently, the wave-wave interaction which will produce mean flow modification occurs only through the streamwise exponentials.

Lakin, William D.↗

NASA NTRS1998

Current Status on the use of Parallel Computing in Turbulent Reacting Flow Computations Involving Sprays, Monte Carlo PDF and Unstructured Grids

The state of the art in multidimensional combustor modeling as evidenced by the level of sophistication employed in terms of modeling and numerical accuracy considerations, is also dictated by the available computer memory and turnaround times afforded by present-day computers. With the aim of advancing the current multi-dimensional computational tools used in the design of advanced technology combustors, a solution procedure is developed that combines the novelty of the coupled CFD/spray/scalar Monte Carlo PDF (Probability Density Function) computations on unstructured grids with the ability to run on parallel architectures. In this approach, the mean gas-phase velocity and turbulence fields are determined from a standard turbulence model, the joint composition of species and enthalpy from the solution of a modeled PDF transport equation, and a Lagrangian-based dilute spray model is used for the liquid-phase representation. The gas-turbine combustor flows are often characterized by a complex interaction between various physical processes associated with the interaction between the liquid and gas phases, droplet vaporization, turbulent mixing, heat release associated with chemical kinetics, radiative heat transfer associated with highly absorbing and radiating species, among others. The rate controlling processes often interact with each other at various disparate time 1 and length scales. In particular, turbulence plays an important role in determining the rates of mass and heat transfer, chemical reactions, and liquid phase evaporation in many practical combustion devices.

Raju, M. S.↗

NASA NTRS1981

The tectonics of anorthosite massifs

Anorthosite massifs developed approximately 1.4 to 1.5 billion years ago along an arch which developed parallel to a zone of continental separation as a block which included North America, Europe, and probably Asia separated from a block which included parts of South America, Africa, India, and Australia. Anorthosite massifs also developed at the same time along a belt which runs through the continents which comprise Gondwanaland (South America), Africa, India, Australia, and Antarctica. This was a zone of continental separation which subsequently became a zone of continental collision about 1.2 billion years ago. The northern anorthosite belt also parallels an orogenic belt which was active between 1.8 and 1.7 billion years ago. Heat generated during this mountain building period helped in the formation of the anorthosites.

Seyfert, C. K.↗

NASA NTRS1990

Constraint treatment techniques and parallel algorithms for multibody dynamic analysis

Computational procedures for kinematic and dynamic analysis of three-dimensional multibody dynamic (MBD) systems are developed from the differential-algebraic equations (DAE's) viewpoint. Constraint violations during the time integration process are minimized and penalty constraint stabilization techniques and partitioning schemes are developed. The governing equations of motion, a two-stage staggered explicit-implicit numerical algorithm, are treated which takes advantage of a partitioned solution procedure. A robust and parallelizable integration algorithm is developed. This algorithm uses a two-stage staggered central difference algorithm to integrate the translational coordinates and the angular velocities. The angular orientations of bodies in MBD systems are then obtained by using an implicit algorithm via the kinematic relationship between Euler parameters and angular velocities. It is shown that the combination of the present solution procedures yields a computationally more accurate solution. To speed up the computational procedures, parallel implementation of the present constraint treatment techniques, the two-stage staggered explicit-implicit numerical algorithm was efficiently carried out. The DAE's and the constraint treatment techniques were transformed into arrowhead matrices to which Schur complement form was derived. By fully exploiting the sparse matrix structural analysis techniques, a parallel preconditioned conjugate gradient numerical algorithm is used to solve the systems equations written in Schur complement form. A software testbed was designed and implemented in both sequential and parallel computers. This testbed was used to demonstrate the robustness and efficiency of the constraint treatment techniques, the accuracy of the two-stage staggered explicit-implicit numerical algorithm, and the speed up of the Schur-complement-based parallel preconditioned conjugate gradient algorithm on a parallel computer.

Chiou, Jin-Chern↗

NASA NTRS1995

NAS Experiences of Porting CM Fortran Codes to HPF on IBM SP2 and SGI Power Challenge

Current Connection Machine (CM) Fortran codes developed for the CM-2 and the CM-5 represent an important class of parallel applications. Several users have employed CM Fortran codes in production mode on the CM-2 and the CM-5 for the last five to six years, constituting a heavy investment in terms of cost and time. With Thinking Machines Corporation's decision to withdraw from the hardware business and with the decommissioning of many CM-2 and CM-5 machines, the best way to protect the substantial investment in CM Fortran codes is to port the codes to High Performance Fortran (HPF) on highly parallel systems. HPF is very similar to CM Fortran and thus represents a natural transition. Conversion issues involved in porting CM Fortran codes on the CM-5 to HPF are presented. In particular, the differences between data distribution directives and the CM Fortran Utility Routines Library, as well as the equivalent functionality in the HPF Library are discussed. Several CM Fortran codes (Cannon algorithm for matrix-matrix multiplication, Linear solver Ax=b, 1-D convolution for 2-D datasets, Laplace's Equation solver, and Direct Simulation Monte Carlo (DSMC) codes have been ported to Subset HPF on the IBM SP2 and the SGI Power Challenge. Speedup ratios versus number of processors for the Linear solver and DSMC code are presented.

Saini, Subhash↗

NASA NTRS2015

Biomimetic Fly Eye Sensor for Real-Time Target Tracking

The project objective is to design, build, and demonstrate a biomimetic (inspired by biology) smart sensor based on the common house fly eye for real-time target tracking in three dimensions (3-D). The sensor makes use of revolutionary optical sensor design resulting in significantly improved motion detection capabilities when compared with conventional optical sensors. The design is motivated by the parallel nature of the flys vision system and its demonstrated hyperacuity or precision of visual localization beyond the conventional resolution limit. This means that the sensor is able to accurately detect very fast motion and small changes in motion. The analog architecture of the sensor allows for real-time solution at adjustable bandwidths depending on the application. The low cost, exceptionally lightweight, small form factor, low power requirements, and low computation requirements of the sensor make it ideally suited to many aeronautics applications that have limitations on weight, power, and processing time. The sensor is modular and can be easily adapted in scale and manufactured for a wide variety of sensing applications. Advanced target tracking algorithms will be developed to allow the sensor to track a target in 3-D. These algorithms will be implemented in the smart sensors hardware to enable real-time target tracking.

wing position measurement system↗

NASA NTRS1943

Large-deflection theory of curved sheet

Equations are given for the elastic behavior of initially curved sheets in which the deflections are not small in comparison with the thickness, but at the same time small enough to justify the use of simplified formulas for curvature. These equations are solved for the case of a sheet with circular cylindrical shape simply supported along two edges parallel to the axis of the generating cylinder. Numerical results are given for three values of the curvature and for three ratios of buckle length to buckle width. The computations are carried to buckle deflections of about twice the sheet thickness. It was concluded that initial curvature may cause an appreciable increase in the buckling load but that, for edge strains which are several times the buckling strain, the initial curvature causes a negligibly small change in the effective width.

Levy, Samuel↗

NASA NTRS1996

Satellite Angular Rate Estimation From Vector Measurements

This paper presents an algorithm for estimating the angular rate vector of a satellite which is based on the time derivatives of vector measurements expressed in a reference and body coordinate. The computed derivatives are fed into a spacial Kalman filter which yields an estimate of the spacecraft angular velocity. The filter, named Extended Interlaced Kalman Filter (EIKF), is an extension of the Kalman filter which, although being linear, estimates the state of a nonlinear dynamic system. It consists of two or three parallel Kalman filters whose individual estimates are fed to one another and are considered as known inputs by the other parallel filter(s). The nonlinear dynamics stem from the nonlinear differential equation that describes the rotation of a three dimensional body. Initial results, using simulated data, and real Rossi X ray Timing Explorer (RXTE) data indicate that the algorithm is efficient and robust.

Azor, Ruth↗

NASA NTRS2004

Computation of Gust-Cascade Interaction Using the CE/SE Method

The problem 2 in Category 3 of the 4th Computational Aeroacoustic(CAA) Workshop is solved using the space-time conservation element and solution element (CE/SE) method. This problem models rotor-stator interaction in a 2D cascade. It involves complex geometries and flow physics including vortex shedding and acoustic radiation. The parallel version of the 2D nonlinear Euler solver is used with an unstructured triangular mesh to solve this problem. The Giles approach is incorporated with the CE/SE method to handle non-equal pitches of the rotor and stator. Validation on the Giles approach is performed using Problem 3.1 in the 2nd CAA Workshop. The space-time CE/SE method is a finite volume method with second-order accuracy in both space and time. The flux conservation is enforced in both space and time instead of space only. It has low numerical dissipation and dispersion errors. It uses simple non-reflecting boundary conditions and is compatible with unstructured meshes. It is simple, flexible, and generate reasonably accurate solutions. The CE/SE method has been successfully applied to solve numerous practical problems, especially aeroacoustic problems. Some preliminary numerical results of the benchmark problem 3.2 of the 4th CAA Workshop are shown. The steady-state pressure contour is plotted. The mean pressure distribution on the blade surface is compared with Turbo solution showing a good agreement. The sound pressure level versus the rotor harmonic n at the six designated positions on the blade surface, three locations at inlet plane, and three locations at the outlet plane are plotted. It can be seen that the acoustic response exists only at the excitation frequencies (n = 1,2,3). On the blade surface, the acoustic wave at n = 1 is dominant, while at the inlet and outlet planes, the sound pressure level at n = 2 becomes the largest, which is similar to the results presented. The distribution of sound pressure level at different spatial modes along the z- direction is plotted for n = 1,2,3, respectively. It shows that the spatial modes m = -32 and 22 at n = 1 exponentially decay, and the spatial modes m = 10 at n = 2, m = -42 and 12 at n = 3 propagate both upstream and downstream, which agrees with the prediction based on the linearized theory. Some oscillations are observed, which needs to be investigated further. In the final paper, the numerical results will be compared with a frequency-domain solver LINFLUX solution if it is available.

Wang, X.-Y.↗

NASA NTRS2000

A Parallel Genetic Algorithm for Automated Electronic Circuit Design

Parallelized versions of genetic algorithms (GAs) are popular primarily for three reasons: the GA is an inherently parallel algorithm, typical GA applications are very compute intensive, and powerful computing platforms, especially Beowulf-style computing clusters, are becoming more affordable and easier to implement. In addition, the low communication bandwidth required allows the use of inexpensive networking hardware such as standard office ethernet. In this paper we describe a parallel GA and its use in automated high-level circuit design. Genetic algorithms are a type of trial-and-error search technique that are guided by principles of Darwinian evolution. Just as the genetic material of two living organisms can intermix to produce offspring that are better adapted to their environment, GAs expose genetic material, frequently strings of 1s and Os, to the forces of artificial evolution: selection, mutation, recombination, etc. GAs start with a pool of randomly-generated candidate solutions which are then tested and scored with respect to their utility. Solutions are then bred by probabilistically selecting high quality parents and recombining their genetic representations to produce offspring solutions. Offspring are typically subjected to a small amount of random mutation. After a pool of offspring is produced, this process iterates until a satisfactory solution is found or an iteration limit is reached. Genetic algorithms have been applied to a wide variety of problems in many fields, including chemistry, biology, and many engineering disciplines. There are many styles of parallelism used in implementing parallel GAs. One such method is called the master-slave or processor farm approach. In this technique, slave nodes are used solely to compute fitness evaluations (the most time consuming part). The master processor collects fitness scores from the nodes and performs the genetic operators (selection, reproduction, variation, etc.). Because of dependency issues in the GA, it is possible to have idle processors. However, as long as the load at each processing node is similar, the processors are kept busy nearly all of the time. In applying GAs to circuit design, a suitable genetic representation 'is that of a circuit-construction program. We discuss one such circuit-construction programming language and show how evolution can generate useful analog circuit designs. This language has the desirable property that virtually all sets of combinations of primitives result in valid circuit graphs. Our system allows circuit size (number of devices), circuit topology, and device values to be evolved. Using a parallel genetic algorithm and circuit simulation software, we present experimental results as applied to three analog filter and two amplifier design tasks. For example, a figure shows an 85 dB amplifier design evolved by our system, and another figure shows the performance of that circuit (gain and frequency response). In all tasks, our system is able to generate circuits that achieve the target specifications.

Long, Jason D.↗