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A package, LANZ, for solving the large symmetric generalized eigenproblem is described. The package was tested on four different architectures: Convex 200, CRAY Y-MP, Sun-3, and Sun-4. The package uses a Lanczos' method and is based on recent research into solving the generalized eigenproblem.
I/O issues in finite element analysis on parallel processors are addressed. Viable solutions for both local and shared memory multiprocessors are presented. The approach is simple but limited by currently available hardware and software systems. Implementation is carried out on a CRAY-2 system. Performance results are reported.
The compressible, three-dimensional, time-dependent Navier-Stokes equations are solved on a 20 processor Flex/32 computer. The code is a parallel implementation of an existing code operational on the Cray-2 at NASA Ames, which performs direct simulations of the initial stages of the transition process of wall-bounded flow at supersonic Mach numbers. Spectral collocation in all three spatial directions (Fourier along the plate and Chebyshev normal to it) ensures high accuracy of the flow variables. By hiding most of the parallelism in low-level routines, the casual user is shielded from most of the nonstandard coding constructs. Speedups of 13 out of a maximum of 16 are achieved on the largest computational grids.
In a spacecraft design, the requirements of settled propellant are different for tank pressurization, engine restart, venting, or propellant transfer. The requirement to settle or to position liquid fuel over the outlet end of the spacecraft propellant tank prior main engine restart poses a microgravity fluid behavior problem. In this paper, the dynamical behavior of liquid propellant, fluid reorientation, and propellant resettling have been carried out through the execution of supercomputer CRAY X-MP to simulate the fluid management in a microgravity environment. Results show that the resettlement of fluid can be accomplished more efficiently for fluid in rotating tank than in nonrotating tank, and also better performance for gravity jitters imposed on fluid settlement than without gravity jitters based on the amount of time needed to carry out resettlement period of time between the initiation and termination of geysering.
Techniques are described for computing matrix inverses by algorithms that are highly suited to massively parallel computation. The techniques are based on an algorithm suggested by Strassen (1969). Variations of this scheme use matrix Newton iterations and other methods to improve the numerical stability while at the same time preserving a very high level of parallelism. One-processor Cray-2 implementations of these schemes range from one that is up to 55 percent faster than a conventional library routine to one that is slower than a library routine but achieves excellent numerical stability. The problem of computing the solution to a single set of linear equations is discussed, and it is shown that this problem can also be solved efficiently using these techniques.
Various methods of calculating the internal energy of diatomic molecules are studied. An accurate and efficient method for computing the eigenvalues of the vibrational Schroedinger equation for an arbitrary potential is developed. The method is based on a finite-element discretization using the cubic Lobatto element. A combination of spectrum slicing and the Laguerre algorithm is used to solve for the eigenvalues. A simple method to compute the quasi-bound states is presented. For N2 molecules, all vibrational-rotational states of eleven available electronic potentials are computed, and summed to obtain the exact internal energy function with temperature. The total computation required 314 seconds of CPU-time on NASA's Cray 2 computer. Various approximate models are discussed and compared with the exact numerical simulation. It is shown that the splitting of the macroscopic internal energy into separate electronic, rotational, and vibrational energies is not justified at high temperatures.
An interactive adaptive remeshing algorithm utilizing a frontal grid generator and a variety of time integration schemes for the two-dimensional Euler equations on unstructured meshes is presented. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. The time integration methods available include: an explicit four stage Runge-Kutta and a fully implicit LU decomposition. A cell-centered finite volume upwind scheme utilizing Roe's approximate Riemann solver is developed. To obtain higher order accurate results a monotone linear reconstruction procedure proposed by Barth is utilized. Results for flow over a transonic circular arc and flow through a supersonic nozzle are examined.
An effort is made to characterize the tradeoffs and overheads limiting the speedup potential theoretically projected for pipeline-incorporating computer architectures, using a mathematical model of the roles played by the various parameters. Pipeline optimization proceeds by a partitioning of the pipeline into an optimum number of segments so that maximization of throughput is obtained. Inferences are drawn from the model, and potential improvements to it are identified. Substantial agreement is obtained with Kunkel and Smith's (1986) CRAY-1S simulations of pipelining.
The issue of solving the time-dependent incompressible Navier-Stokes equations on the Connection Machine 2 is addressed, for the problem of transition to turbulence of the steady flow in a channel. The spectral algorithm used serially requires O(N4) operations when solving the equations on an N x N x N grid; using the massive parallelism of the CM, it becomes an O(N2) problem. Preliminary timings of the code, written in LISP, are included and compared with a corresponding code optimized for the Cray-2 for a 128 x 128 x 101 grid.
A method is described for performing direct simulation Monte Carlo (DSMC) calculations on parallel processors using adaptive domain decomposition to distribute the computational work load. The method has been implemented on a commercially available hypercube and benchmark results are presented which show the performance of the method relative to current supercomputers. The problems studied were simulations of equilibrium conditions in a closed, stationary box, a two-dimensional vortex flow, and the hypersonic, rarefield flow in a two-dimensional channel. For these problems, the parallel DSMC method ran 5 to 13 times faster than on a single processor of a Cray-2. The adaptive decomposition method worked well in uniformly distributing the computational work over an arbitrary number of processors and reduced the average computational time by over a factor of two in certain cases.
The instability of liquid and gas interface can be induced by the presence of longitudinal and lateral accelerations, vehicle vibration, and rotational fields of spacecraft in a microgravity environment. In a spacecraft design, the requirements of settled propellant are different for tank pressurization, engine restart, venting, or propellent transfer. In this paper, the dynamical behavior of liquid propellant, fluid reorientation, and propellent resettling have been carried out through the execution of a CRAY X-MP super computer to simulate fluid management in a microgravity environment. Characteristics of slosh waves excited by the restoring force field of gravity jitters have also been investigated.
The three-dimensional flow over a projectile has been computed using an implicit, approximately factored, partially flux-split algorithm. A simple composite grid scheme has been developed in which a single grid is partitioned into a series of smaller grids for applications which require an external large memory device such as the SSD of the CRAY X-MP/48 or multi-tasking. The accuracy and stability of the composite grid scheme have been tested by numerically simulating the flow over an ellipsoid at an angle of attack and comparing the solution with a single-grid solution. The flow field over a projectile at M = 0.96 and 1.1, and 4-deg angle of attack has been computed using a fine grid and compared with experiment.
Three structural finite element programs are compared with theory, experimental data, and each other to evaluate their usefulness for modeling the thermomechanical deflection of ion engine electrodes. Two programs, NASTRAN and MARC, used a Cray XMP and the third, Algor, used an IBM compatible personal computer. The shape of the applied temperature gradient greatly affects off-axis displacement, implying that an accurate temperature distribution is required to analyze new designs. The use of bulk material constants to model the perforated electrodes was investigated. The stress and displacement predictions are shown to be sensitive to the temperature gradient and the Young's modulus, and insensitive to number of nodes, above some minimum value, and the Poisson ratio used. The models are shown to be useful tools for evaluating designs. Experimental measurement of temperatures and displacements was identified as the most critical area for further work.
TranAir is a computer code which solves the full-potential equation for transonic flow about very general and complex configurations. Piecewise flat surface panels are used to describe the surface geometry. This paneled definition is then embedded in an unstructured cartesian flow field grid. Finite elements are used in the discretization of the flow field grid in a manner which is fully conservative and second-order accurate. Since geometries may be defined with relative ease, and since the user is not involved in the generation of the flow field grid, computational results may be generated rather quickly for a wide range of geometries. For transonic cases in the cruise angle-of-attack range, TranAir has generated results which are in generally good agreement with both Euler results and wind tunnel data. A typical transonic case runs in 1 to 2 CPU hours on a Cray X-MP. For subcritical cases, the code runs in 15 to 30 CPU minutes, even for geometries in which several thousand surface panels are used in the definition. This ability to rapidly and accurately provide both subsonic and transonic predictions about very complex aircraft configurations gives TranAir the potential of being a very powerful and widely used design tool.
A finite difference code was implemented for the compressible Navier-Stokes equations on the Connection Machine, a massively parallel computer. The code is based on the ARC2D/ARC3D program and uses the implicit factored algorithm of Beam and Warming. The codes uses odd-even elimination to solve linear systems. Timings and computation rates are given for the code, and a comparison is made with a Cray XMP.
A parallelized system, ASSURE, for computing the reliability of embedded avionics flight control systems which are able to reconfigure themselves in the event of failure is described. ASSURE accepts a grammar that describes a reliability semi-Markov state-space. From this it creates a parallel program that simultaneously generates and analyzes the state-space, placing upper and lower bounds on the probability of system failure. ASSURE is implemented on a 32-node Intel iPSC/860, and has achieved high processor efficiencies on real problems. Through a combination of improved algorithms, exploitation of parallelism, and use of an advanced microprocessor architecture, ASSURE has reduced the execution time on substantial problems by a factor of one thousand over previous workstation implementations. Furthermore, ASSURE's parallel execution rate on the iPSC/860 is an order of magnitude faster than its serial execution rate on a Cray-2 supercomputer. While dynamic load balancing is necessary for ASSURE's good performance, it is needed only infrequently; the particular method of load balancing used does not substantially affect performance.
Three structural finite element programs are compared with theory, experimental data, and each other to evaluate their usefulness for modeling the thermomechanical deflection of ion engine electrodes. Two programs, NASTRAN and MARC, used a Cray XMP and the third, Algor, used an IBM compatible personal computer. The shape of the applied temperature gradient greatly affects off-axis displacement, implying that an accurate temperature distribution is required to analyze new designs. The use of bulk material constants to model the perforated electrodes was investigated. The stress and displacement predictions are shown to be sensitive to the temperature gradient and the Young's modulus, and insensitive to number of nodes, above some minimum value, and the Poisson ratio used. The models are shown to be useful tools for evaluating designs. Experimental measurements of temperatures and displacements was identified as the most critical area.
Analyses of reflector antenna surfaces use a computer program based on a discrete approximation of the radiation integral. The calculation replaces the actual surface with a triangular facet representation; the physical optics current is assumed to be constant over each facet. Described here is a method of calculation using linear-phase approximation of the surface currents of parabolas, ellipses, and shaped subreflectors and compares results with a previous program that used a constant-phase approximation of the triangular facets. The results show that the linear-phase approximation is a significant improvement over the constant-phase approximation, and enables computation of 100 to 1,000 lambda reflectors within a reasonable time on a Cray computer.