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In this paper a new factorization technique for computation of inverse of mass matrix, and the operational space mass matrix, as arising in implementation of the operational space control scheme, is presented.
Spectral collocation methods have proven to be efficient discretization schemes for many aerodynamic and fluid mechanic problems. The high order accuracy and resolution shown by these methods allows one to obtain engineering accuracy solutions on coarse meshes, or alternatively, to obtain solutions with very small error. One drawback to these techniques was the requirement that a complicated physical domain must map into a simple computational domain for discretization. This mapping must be smooth if the high order accuracy and expontential convergence rates associated with spectral methods are to be preserved. Additionally even smooth stretching transformations can decrease the accuracy of a spectral method, if the stretching is severe. A further difficulty with spectral methods was in their implementation on parallel processing computers, where efficient spectral algorithms were lacking. The above restrictions are overcome by splitting the domain into regions, each of which preserve the advantages of spectral collocation, and allow the ratio of the mesh spacing between regions to be several orders of magnitude higher than allowable in a single domain. Such stretchings would be required to resolve the thin viscous region in an external aerodynamic problem. Adjoining regions are interfaced by enforcing a global flux balance which preserves high-order continuity of the solution, regardless of the type of the equations being solved.
Recent advances in computer technology that are likely to impact computational mechanics are reviewed. The technical needs for computational mechanics technology are outlined. The major features of new and projected computing systems, including supersystems, parallel processing machines, special-purpose computing hardware, and small systems are described. Advances in programming environments, numerical algorithms, and computational strategies for new computing systems are reviewed, and a novel partitioning strategy is outlined for maximizing the degree of parallelism on multiprocessor computers with a shared memory.
Moore’s “law” was the observation that the number of transistors in an integrated circuit doubled approximately every two years. This trend has distinctly failed to hold in recent years. The death of Moore’s law has left researchers and practitioners in the computational sciences searching for technologies to provide the speedups formerly supported by Moore’s law. Previously overlooked chip architectures and other computing technologies are now receiving more development resources. Critically, these technologies are gaining more mature software support, opening their adoption by researchers in algorithms and applications. In this article, we review some of these computing technologies, their relationship with various algorithms and applications, and their potential benefits (or pitfalls). We close with recommendations for future work by the process systems engineering community specifically.
A large class of scientific computational problems can be characterized as a sequence of steps where a significant amount of computation occurs each step, but the work performed at each step is not necessarily identical. Two good examples of this type of computation are: (1) regridding methods which change the problem discretization during the course of the computation, and (2) methods for solving sparse triangular systems of linear equations. Recent work has investigated a means of mapping such computations onto parallel processors; the method defines a family of static mappings with differing degrees of importance placed on the conflicting goals of good load balance and low communication/synchronization overhead. The performance tradeoffs are controllable by adjusting the parameters of the mapping method. To achieve good performance it may be necessary to dynamically change these parameters at run-time, but such changes can impose additional costs. If the computation's behavior can be determined prior to its execution, it can be possible to construct an optimal parameter schedule using a low-order-polynomial-time dynamic programming algorithm. Since the latter can be expensive, the performance is studied of the effect of a linear-time scheduling heuristic on one of the model problems, and it is shown to be effective and nearly optimal.
The application of advanced computer architecture and software to a broad range of electromagnetic problems had allowed more accurate simulations of electrically larger and more complex components and systems...This paper overviews solutions to Maxwell's equations implicitly defined through systems of linear equations.
These architectures are based on methods of vector processing and the discrete-Fourier-transform/inverse-discrete- Fourier-transform (DFT-IDFT) overlap-and-save method, combined with time-block separation of digital filters into frequency-domain subfilters implemented by use of sub-convolutions. The parallel-processing method implemented in these architectures enables the use of relatively small DFT-IDFT pairs, while filter tap lengths are theoretically unlimited. The size of a DFT-IDFT pair is determined by the desired reduction in processing rate, rather than on the order of the filter that one seeks to implement. The emphasis in this report is on those aspects of the underlying theory and design rules that promote computational efficiency, parallel processing at reduced data rates, and simplification of the designs of very-large-scale integrated (VLSI) circuits needed to implement high-order filters and correlators.
This viewgraph presentation provides information on the technical aspects of debugging computer code that has been automatically converted for use in a parallel computing system. Shared memory parallelization and distributed memory parallelization entail separate and distinct challenges for a debugging program. A prototype system has been developed which integrates various tools for the debugging of automatically parallelized programs including the CAPTools Database which provides variable definition information across subroutines as well as array distribution information.
The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. Recently, Freund and Nachtigal have proposed a novel BCG type approach, the quasi-minimal residual method (QMR), which overcomes the problems of BCG. Here, an implementation is presented of QMR based on an s-step version of the nonsymmetric look-ahead Lanczos algorithm. The main feature of the s-step Lanczos algorithm is that, in general, all inner products, except for one, can be computed in parallel at the end of each block; this is unlike the other standard Lanczos process where inner products are generated sequentially. The resulting implementation of QMR is particularly attractive on massively parallel SIMD architectures, such as the Connection Machine.
A computer program implements parallel- processing algorithms for cor relating images of terrain acquired by stereoscopic pairs of digital stereo cameras on an exploratory robotic vehicle (e.g., a Mars rove r). Such correlations are used to create three-dimensional computatio nal models of the terrain for navigation. In this program, the scene viewed by the cameras is segmented into subimages. Each subimage is assigned to one of a number of central processing units (CPUs) opera ting simultaneously.
The structural analysis methods research has several goals. One goal is to develop analysis methods that are general. This goal of generality leads naturally to finite-element methods, but the research will also include other structural analysis methods. Another goal is that the methods be amenable to error analysis; that is, given a physical problem and a mathematical model of that problem, an analyst would like to know the probable error in predicting a given response quantity. The ultimate objective is to specify the error tolerances and to use automated logic to adjust the mathematical model or solution strategy to obtain that accuracy. A third goal is to develop structural analysis methods that can exploit parallel processing computers. The structural analysis methods research will focus initially on three types of problems: local/global nonlinear stress analysis, nonlinear transient dynamics, and tire modeling.
A discussion is presented on the coupling of computational analysis and experiment. It is believed that this coupling is critical in developing new aerodynamic insights. Additionally, new methods for analyzing and interpreting data are discussed. These methods need to be developed in small-scale research studies and then applied to large-scale technology programs. The specific objectives of this program are threefold: (1) provide definitive data sets for the assessment of numerical simulations to the Navier-Stokes equations; (2) incorporate advanced instrumentation to measure the spatial and temporal structure of fluid flows; and (3) develop true parallelism between computational and experimental research using the 'scientific workstation' concept. The discussion is presented in viewgraph form.
This article introduces an interactive parallel programming environment (IPPE) that simplifies the generation and execution of parallel programs. One of the tasks of the environment is to generate message-passing parallel programs for homogeneous and heterogeneous computing platforms. The parallel programs are represented by using visual objects. This is accomplished with the help of a graphical programming editor that is implemented in Java and enables portability to a wide variety of computer platforms. In contrast to other graphical programming systems, reusable parts of the programs can be stored in a program library to support rapid prototyping. In addition, runtime performance data on different computing platforms is collected in a database. A selection process determines dynamically the software and the hardware platform to be used to solve the problem in minimal wall-clock time. The environment is currently being tested on a Grand Challenge problem, the NASA four-dimensional data assimilation system.
A subsumption planner using a parallel distributed computational paradigm based on the subsumption architecture for control of real-world capable robots is described. Virtual sensor state space is used as a planning tool to visualize the robot's anticipated effect on its environment. Decision sequences are generated based on the environmental situation expected at the time the robot must commit to a decision. Between decision points, the robot performs in a preprogrammed manner. A rudimentary, domain-specific partial world model contains enough information to extrapolate the end results of the rote behavior between decision points. A collective network of predictors operates in parallel with the reactive network forming a recurrrent network which generates plans as a hierarchy. Details of a plan segment are generated only when its execution is imminent. The use of the subsumption planner is demonstrated by a simple maze navigation problem.
The major emphasis of the current effort is in the development and validation of an efficient parallel machine computational model, based on the FDNS code, to analyze the fluid dynamics of a wide variety of liquid jet configurations for general liquid rocket engine injection system applications. This model includes physical models for droplet atomization, breakup/coalescence, evaporation, turbulence mixing and gas-phase combustion. Benchmark validation cases for liquid rocket engine chamber combustion conditions will be performed for model validation purpose. Test cases may include shear coaxial, swirl coaxial and impinging injection systems with combinations LOXIH2 or LOXISP-1 propellant injector elements used in rocket engine designs. As a final goal of this project, a well tested parallel CFD performance methodology together with a user's operation description in a final technical report will be reported at the end of the proposed research effort.
The goal of our research on flame spread across pools of liquid fuel remains the quantitative identification of the mechanisms that control the rate and nature of flame spread when the initial temperature of the liquid pool is below the fuel's flash point temperature. As described in, four microgravity (mu-g) sounding rocket flights examined the effect of forced opposed airflow over a 2.5 cm deep x 2 cm wide x 30 cm long pool of 1-butanol. Among many unexpected findings, it was observed that the flame spread is much slower and steadier than in 1g where flame spread has a pulsating character. Our numerical model, restricted to two dimensions, had predicted faster, pulsating flame spread in mu-g. In a test designed to achieve a more 2-D experiment, our investigation of a shallow, wide pool (2 mm deep x 78 mm wide x 30 cm long) was unsuccessful in mu-g, due to an unexpectedly long time required to fill the tray. As such, the most recent Spread Across Liquids (SAL) sounding rocket experiment had two principal objectives: 1) determine if pulsating flame spread in deep fuel trays would occur under the conditions that a state-of-the-art computational combustion code and short-duration drop tower tests predict; and 2) determine if a long, rectangular, shallow fuel tray could achieve a visibly flat liquid surface across the whole tray without spillage in the mu-g time allotted. If the second objective was met, the shallow tray was to be ignited to determine the nature of flame spread in mu-g for this geometry. For the first time in the experiment series, two fuel trays - one deep (30 cm long x 2 cm wide x 25 mm deep) and one shallow (same length and width, but 2 mm deep)-- were flown. By doing two independent experiments in a single flight, a significant cost savings was realized. In parallel, the computational objective was to modify the code to improve agreement with earlier results. This last objective was achieved by modifying the fuel mass diffusivity and adding a parameter to correct for radiative and lateral heat loss.
A fast, accurate Choleski method for the solution of symmetric systems of linear equations is presented. This direct method is based on a variable-band storage scheme and takes advantage of column heights to reduce the number of operations in the Choleski factorization. The method employs parallel computation in the outermost DO-loop and vector computation via the 'loop unrolling' technique in the innermost DO-loop. The method avoids computations with zeros outside the column heights, and as an option, zeros inside the band. The close relationship between Choleski and Gauss elimination methods is examined. The minor changes required to convert the Choleski code to a Gauss code to solve non-positive-definite symmetric systems of equations are identified. The results for two large-scale structural analyses performed on supercomputers, demonstrate the accuracy and speed of the method.
A fast, accurate Choleski method for the solution of symmetric systems of linear equations is presented. This direct method is based on a variable-band storage scheme and takes advantage of column heights to reduce the number of operations in the Choleski factorization. The method employs parallel computation in the outermost DO-loop and vector computation via the loop unrolling technique in the innermost DO-loop. The method avoids computations with zeros outside the column heights, and as an option, zeros inside the band. The close relationship between Choleski and Gauss elimination methods is examined. The minor changes required to convert the Choleski code to a Gauss code to solve non-positive-definite symmetric systems of equations are identified. The results for two large scale structural analyses performed on supercomputers, demonstrate the accuracy and speed of the method.