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This paper examines the applications most commonly run on the supercomputers at the Numerical Aerospace Simulation (NAS) facility. It analyzes the extent to which such applications are fundamentally oriented to vector computers, and whether or not they can be efficiently implemented on hierarchical memory machines, such as systems with cache memories and highly parallel, distributed memory systems.
Numerical procedures formulated for the analysis of 3D jet mixing problems, as incorporated in the computer model, SCIP3D, are described. The overall methodology closely parallels that developed in the earlier 2D axisymmetric jet mixing model, SCIPVIS. SCIP3D integrates the 3D parabolized Navier-Stokes (PNS) jet mixing equations, cast in mapped cartesian or cylindrical coordinates, employing the explicit MacCormack Algorithm. A pressure split variant of this algorithm is employed in subsonic regions with a sublayer approximation utilized for treating the streamwise pressure component. SCIP3D contains both the ks and kW turbulence models, and employs a two component mixture approach to treat jet exhausts of arbitrary composition. Specialized grid procedures are used to adjust the grid growth in accordance with the growth of the jet, including a hybrid cartesian/cylindrical grid procedure for rectangular jets which moves the hybrid coordinate origin towards the flow origin as the jet transitions from a rectangular to circular shape. Numerous calculations are presented for rectangular mixing problems, as well as for a variety of basic unit problems exhibiting overall capabilities of SCIP3D.
With traditional event-list techniques, evaluating a detailed discrete-event simulation-model can often require hours or even days of computation time. By eliminating the event list and maintaining only sufficient synchronization to ensure causality, parallel simulation can potentially provide speedups that are linear in the numbers of processors. A set of shared-memory experiments, using the Chandy-Misra distributed-simulation algorithm, to simulate networks of queues is presented. Parameters of the study include queueing network topology and routing probabilities, number of processors, and assignment of network nodes to processors. These experiments show that Chandy-Misra distributed simulation is a questionable alternative to sequential-simulation of most queueing network models.
The Engineering Orbit Analysis Unit at GE Valley Forge used an Intel Hypercube Parallel Processor to investigate the performance and gain experience of parallel processors with a multi-satellite orbit determination problem. A general study was selected in which major blocks of computation for the multi-satellite orbit computations were used as units to be assigned to the various processors on the Hypercube. Problems encountered or successes achieved in addressing the orbit determination problem would be more likely to be transferable to other parallel processors. The prime objective was to study the algorithm to allow processing of observations later in time than those employed in the state update. Expertise in ephemeris determination was exploited in addressing these problems and the facility used to bring a realism to the study which would highlight the problems which may not otherwise be anticipated. Secondary objectives were to gain experience of a non-trivial problem in a parallel processor environment, to explore the necessary interplay of serial and parallel sections of the algorithm in terms of timing studies, to explore the granularity (coarse vs. fine grain) to discover the granularity limit above which there would be a risk of starvation where the majority of nodes would be idle or under the limit where the overhead associated with splitting the problem may require more work and communication time than is useful.
A highly parallel graph mapping technique that enables one to efficiently solve unstructured grid problems on massively parallel computers is presented. Many implicit and explicit methods for solving discretized partial differential equations require each point in the discretization to exchange data with its neighboring points every time step or iteration. The cost of this communication can negate the high performance promised by massively parallel computing. To eliminate this bottleneck, the graph of the irregular problem is mapped into the graph representing the interconnection topology of the computer such that the sum of the distances that the messages travel is minimized. It is shown that using the heuristic mapping algorithm significantly reduces the communication time compared to a naive assignment of processes to processors.
A self-organizing, monomorphic data type denoted a sequence has been conceived to address certain concerns that arise in programming parallel computers. A sequence in the present sense can be regarded abstractly as a vector, set, bag, queue, or other construct. Heretofore, in programming a parallel computer, it has been necessary for the programmer to state explicitly, at the outset, what parts of the program and the underlying data structures must be represented in parallel form. Not only is this requirement not optimal from the perspective of implementation; it entails an additional requirement that the programmer have intimate understanding of the underlying parallel structure. The present sequence data type overcomes both the implementation and parallel structure obstacles. In so doing, the sequence data type provides unified means by which the programmer can represent a data structure for natural and automatic decomposition to a parallel computing architecture. Sequences exhibit the behavioral and structural characteristics of vectors, but the underlying representations are automatically synthesized from combinations of programmers advice and execution use metrics. Sequences can vary bidirectionally between sparseness and density, making them excellent choices for many kinds of algorithms. The novelty and benefit of this behavior lies in the fact that it can relieve programmers of the details of implementations. The creation of a sequence enables decoupling of a conceptual representation from an implementation. The underlying representation of a sequence is a hybrid of representations composed of vectors, linked lists, connected blocks, and hash tables. The internal structure of a sequence can automatically change from time to time on the basis of how it is being used. Those portions of a sequence where elements have not been added or removed can be as efficient as vectors. As elements are inserted and removed in a given portion, then different methods are utilized to provide both an access and memory strategy that is optimized for that portion and the use to which it is put.
A vision system that includes a specially designed video camera and an image-data-processing computer is under development as a prototype of robotic systems for visual inspection of the interior surfaces of pipes and especially of gas pipelines. The system is capable of providing both forward views and mosaicked radial views that can be displayed in real time or after inspection. To avoid the complexities associated with moving parts and to provide simultaneous forward and radial views, the video camera is equipped with a wide-angle (>165 ) fish-eye lens aimed along the axis of a pipe to be inspected. Nine white-light-emitting diodes (LEDs) placed just outside the field of view of the lens (see Figure 1) provide ample diffuse illumination for a high-contrast image of the interior pipe wall. The video camera contains a 2/3-in. (1.7-cm) charge-coupled-device (CCD) photodetector array and functions according to the National Television Standards Committee (NTSC) standard. The video output of the camera is sent to an off-the-shelf video capture board (frame grabber) by use of a peripheral component interconnect (PCI) interface in the computer, which is of the 400-MHz, Pentium II (or equivalent) class. Prior video-mosaicking techniques are applicable to narrow-field-of-view (low-distortion) images of evenly illuminated, relatively flat surfaces viewed along approximately perpendicular lines by cameras that do not rotate and that move approximately parallel to the viewed surfaces. One such technique for real-time creation of mosaic images of the ocean floor involves the use of visual correspondences based on area correlation, during both the acquisition of separate images of adjacent areas and the consolidation (equivalently, integration) of the separate images into a mosaic image, in order to insure that there are no gaps in the mosaic image. The data-processing technique used for mosaicking in the present system also involves area correlation, but with several notable differences: Because the wide-angle lens introduces considerable distortion, the image data must be processed to effectively unwarp the images (see Figure 2). The computer executes special software that includes an unwarping algorithm that takes explicit account of the cylindrical pipe geometry. To reduce the processing time needed for unwarping, parameters of the geometric mapping between the circular view of a fisheye lens and pipe wall are determined in advance from calibration images and compiled into an electronic lookup table. The software incorporates the assumption that the optical axis of the camera is parallel (rather than perpendicular) to the direction of motion of the camera. The software also compensates for the decrease in illumination with distance from the ring of LEDs.
A domain decomposition method for implicit schemes that require significantly less storage and is several times faster than factorization algorithms is proposed. The transient domain decomposition method is an extension of the finite element tearing and interconnecting (FETI) method for the solution of static problems. Serial and parallel performance results obtained using the CRAY Y-MP/8 and the iPSC-860/128 systems demonstrate that the FETI method is superior to both serial and parallel direct methods.
A large-eddy simulation (LES) code was developed at the NASA Glenn Research Center to provide more accurate and detailed computational analyses of propulsion flow fields. The accuracy of current computational fluid dynamics (CFD) methods is limited primarily by their inability to properly account for the turbulent motion present in virtually all propulsion flows. Because the efficiency and performance of a propulsion system are highly dependent on the details of this turbulent motion, it is critical for CFD to accurately model it. The LES code promises to give new CFD simulations an advantage over older methods by directly computing the large turbulent eddies, to correctly predict their effect on a propulsion system. Turbulent motion is a random, unsteady process whose behavior is difficult to predict through computer simulations. Current methods are based on Reynolds-Averaged Navier- Stokes (RANS) analyses that rely on models to represent the effect of turbulence within a flow field. The quality of the results depends on the quality of the model and its applicability to the type of flow field being studied. LES promises to be more accurate because it drastically reduces the amount of modeling necessary. It is the logical step toward improving turbulent flow predictions. In LES, the large-scale dominant turbulent motion is computed directly, leaving only the less significant small turbulent scales to be modeled. As part of the prediction, the LES method generates detailed information on the turbulence itself, providing important information for other applications, such as aeroacoustics. The LES code developed at Glenn for propulsion flow fields is being used to both analyze propulsion system components and test improved LES algorithms (subgrid-scale models, filters, and numerical schemes). The code solves the compressible Favre-filtered Navier- Stokes equations using an explicit fourth-order accurate numerical scheme, it incorporates a compressible form of Smagorinsky s model for the subgrid-scale turbulence, and it uses generalized curvilinear coordinates to allow analysis of a wide range of geometries. The code runs in parallel on shared memory multiprocessor computers and is written in Fortran 90 with dynamic memory allocation. A sample result for a Mach-1.4 round jet is presented in the figure. Instantaneous Mach number contours in several cross-planes downstream of the nozzle exit are shown, illustrating how an LES captures the large unsteady three-dimensional turbulent structures present in the jet.
Subspace and Lanczos iterations have been developed, well documented, and widely accepted as efficient methods for obtaining p-lowest eigen-pair solutions of large-scale, practical engineering problems. The focus of this paper is to incorporate recent developments in vectorized sparse technologies in conjunction with Subspace and Lanczos iterative algorithms for computational enhancements. Numerical performance, in terms of accuracy and efficiency of the proposed sparse strategies for Subspace and Lanczos algorithm, is demonstrated by solving for the lowest frequencies and mode shapes of structural problems on the IBM-R6000/590 and SunSparc 20 workstations.
This paper examines the feasibility of using massively-parallel and vector-processing supercomputers to solve large-scale optimal control problems for human movement. Specifically, we compare the computational expense of determining the optimal controls for the single support phase of walking using a conventional serial machine (a Silicon Graphics Personal Iris 4D25 workstation), a MIMD parallel machine (an Intel iPSC/860 comprising 128 processors), and a parallel-vector-processing machine (a Cray Y-MP 8/864). With the human body modeled as a 14 degree-of-freedom linkage actuated by 46 musculotendinous units, computation of the optimal controls for walking could take up to 3 months of CPU time on the Iris. Both the Cray Y-MP and the Intel iPSC/860 are able to reduce this time to practical levels. The optimal control solution for walking can be found with about 77 hours of CPU time on the Cray, and with about 88 hours of CPU time on the Intel. Although the overall speeds of the Cray and the Intel were found to be similar, the unique capabilities of each machine are best suited to different parts of the optimal control algorithm used. The Intel performed best in the calculation of the derivatives of the performance criterion and the constraints. In contrast, the Cray performed best during parameter optimization of the controls. These results suggest that the ideal computer architecture for solving very large-scale optimal control problems is a hybrid system in which a vector-processing machine is integrated into the communication network of a MIMD parallel machine.
A concurrent processing algorithm is developed for materially nonlinear stability analysis of imperfect columns with biaxial partial rotational end restraints. The algorithm for solving the governing nonlinear ordinary differential equations is implemented on a multiprocessor computer called the 'Finite Element Machine', developed at the NASA Langley Research Center. Numerical results are obtained on up to nine concurrent processors. A substantial computational gain is achieved in using the parallel processing approach.
More than twenty five years have elapsed since it was recognized that a rather general class of structural design optimization tasks could be properly posed as an inequality constrained minimization problem. It is suggested that, independent of primary discipline area, it will be useful to think about: (1) posing design problems in terms of an objective function and inequality constraints; (2) generating design oriented approximate analysis methods (giving special attention to behavior sensitivity analysis); (3) distinguishing between decisions that lead to an analysis model and those that lead to a design model; (4) finding ways to generate a sequence of approximate design optimization problems that capture the essential characteristics of the primary problem, while still having an explicit algebraic form that is matched to one or more of the established optimization algorithms; (5) examining the potential of optimum design sensitivity analysis to facilitate quantitative trade-off studies as well as participation in multilevel design activities. It should be kept in mind that multilevel methods are inherently well suited to a parallel mode of operation in computer terms or to a division of labor between task groups in organizational terms. Based on structural experience with multilevel methods general guidelines are suggested.
In picture processing an important problem is to identify two digital pictures of the same scene taken under different lighting conditions. This kind of problem can be found in remote sensing, satellite signal processing and the related areas. The identification can be done by transforming the gray levels so that the gray level histograms of the two pictures are closely matched. The transformation problem can be solved by using the packing method. Researchers propose a VLSI architecture consisting of m x n processing elements with extensive parallel and pipelining computation capabilities to speed up the transformation with the time complexity 0(max(m,n)), where m and n are the numbers of the gray levels of the input picture and the reference picture respectively. If using uniprocessor and a dynamic programming algorithm, the time complexity will be 0(m(3)xn). The algorithm partition problem, as an important issue in VLSI design, is discussed. Verification of the proposed architecture is also given.
The detection and diagnosis of failures in physical systems characterized by continuous-time operation are studied. A quantitative diagnostic methodology has been developed that utilizes the mathematical model of the physical system. On the basis of the latter, diagnostic models are derived each of which comprises a set of orthogonal parity equations. To improve the robustness of the algorithm, several models may be used in parallel, providing potentially incomplete and/or conflicting inferences. Dempster's rule of combination is used to integrate evidence from the different models. The basic probability measures are assigned utilizing quantitative information extracted from the mathematical model and from online computation performed therewith.
Design of the processor element for general purpose massively parallel supercomputing arrays is highly complex and cost ineffective. To overcome this, the architecture and organization of the functional units of the processor element should be such as to suit the diverse computational structures and simplify mapping of complex communication structures of different classes of algorithms. This demands that the computation and communication structures of different class of algorithms be unified. While unifying the different communication structures is a difficult process, analysis of a wide class of algorithms reveals that their computation structures can be expressed in terms of basic IP,IP,OP,CM,R,SM, and MAA operations. The execution of these operations is unified on the PAcube macro-cell array. Based on this PAcube macro-cell array, we present a novel processor element called the GIPOP processor, which has dedicated functional units to perform the above operations. The architecture and organization of these functional units are such to satisfy the two important criteria mentioned above. The structure of the macro-cell and the unification process has led to a very regular and simpler design of the GIPOP processor. The production cost of the GIPOP processor is drastically reduced as it is designed on high performance mask programmable PAcube arrays.
Computation of the flow field inside a space shuttle main engine (SSME) requires the application of state of the art computational fluid dynamic (CFD) technology. Several computer codes are under development to solve 3-D flow through the hot gas manifold. Some algorithms were designed to solve the unsteady compressible Navier-Stokes equations, either by implicit or explicit factorization methods, using several hundred or thousands of time steps to reach a steady state solution. A new iterative algorithm is being developed for the solution of the implicit finite element equations without assembling global matrices. It is an efficient iteration scheme based on a modified nonlinear Gauss-Seidel iteration with symmetric sweeps. The algorithm is analyzed for a model equation and is shown to be unconditionally stable. Results from a series of test problems are presented. The finite element code was tested for couette flow, which is flow under a pressure gradient between two parallel plates in relative motion. Another problem that was solved is viscous laminar flow over a flat plate. The general 3-D finite element code was used to compute the flow in an axisymmetric turnaround duct at low Mach numbers.
This paper considers an algebraic preconditioning algorithm for hyperbolic-elliptic fluid flow problems. The algorithm is based on a parallel non-overlapping Schur complement domain-decomposition technique for triangulated domains. In the Schur complement technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. This suggests a reordering of triangulation vertices which separates subdomain and interface solution unknowns. The reordering induces a natural 2 x 2 block partitioning of the discretization matrix. Exact LU factorization of this block system yields a Schur complement matrix which couples subdomains and the interface together. The remaining sections of this paper present a family of approximate techniques for both constructing and applying the Schur complement as a domain-decomposition preconditioner. The approximate Schur complement serves as an algebraic coarse space operator, thus avoiding the known difficulties associated with the direct formation of a coarse space discretization. In developing Schur complement approximations, particular attention has been given to improving sequential and parallel efficiency of implementations without significantly degrading the quality of the preconditioner. A computer code based on these developments has been tested on the IBM SP2 using MPI message passing protocol. A number of 2-D calculations are presented for both scalar advection-diffusion equations as well as the Euler equations governing compressible fluid flow to demonstrate performance of the preconditioning algorithm.