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NASA NTRS1993

Automatic partitioning of unstructured grids into connected components

This paper presents two partitioning schemes that guarantee connected components given a connected initial grid. Connected components are important for convergence of methods such as domain decomposition or multigrid. For many of the grids tested, the schemes produce partitions as good (in terms of number of cut edges) or better than spectral partitioning and require only modest computational resources. This paper describes the two schemes in detail and presents comparison results from a number of two and three dimensional unstructured grids.

Dagum, Leonardo↗

NASA NTRS1997

Hierarchical Modeling and Robust Synthesis for the Preliminary Design of Large Scale Complex Systems

Large-scale complex systems are characterized by multiple interacting subsystems and the analysis of multiple disciplines. The design and development of such systems inevitably requires the resolution of multiple conflicting objectives. The size of complex systems, however, prohibits the development of comprehensive system models, and thus these systems must be partitioned into their constituent parts. Because simultaneous solution of individual subsystem models is often not manageable iteration is inevitable and often excessive. In this dissertation these issues are addressed through the development of a method for hierarchical robust preliminary design exploration to facilitate concurrent system and subsystem design exploration, for the concurrent generation of robust system and subsystem specifications for the preliminary design of multi-level, multi-objective, large-scale complex systems. This method is developed through the integration and expansion of current design techniques: Hierarchical partitioning and modeling techniques for partitioning large-scale complex systems into more tractable parts, and allowing integration of subproblems for system synthesis; Statistical experimentation and approximation techniques for increasing both the efficiency and the comprehensiveness of preliminary design exploration; and Noise modeling techniques for implementing robust preliminary design when approximate models are employed. Hierarchical partitioning and modeling techniques including intermediate responses, linking variables, and compatibility constraints are incorporated within a hierarchical compromise decision support problem formulation for synthesizing subproblem solutions for a partitioned system. Experimentation and approximation techniques are employed for concurrent investigations and modeling of partitioned subproblems. A modified composite experiment is introduced for fitting better predictive models across the ranges of the factors, and an approach for constructing partitioned response surfaces is developed to reduce the computational expense of experimentation for fitting models in a large number of factors. Noise modeling techniques are compared and recommendations are offered for the implementation of robust design when approximate models are sought. These techniques, approaches, and recommendations are incorporated within the method developed for hierarchical robust preliminary design exploration. This method as well as the associated approaches are illustrated through their application to the preliminary design of a commercial turbofan turbine propulsion system. The case study is developed in collaboration with Allison Engine Company, Rolls Royce Aerospace, and is based on the Allison AE3007 existing engine designed for midsize commercial, regional business jets. For this case study, the turbofan system-level problem is partitioned into engine cycle design and configuration design and a compressor modules integrated for more detailed subsystem-level design exploration, improving system evaluation. The fan and low pressure turbine subsystems are also modeled, but in less detail. Given the defined partitioning, these subproblems are investigated independently and concurrently, and response surface models are constructed to approximate the responses of each. These response models are then incorporated within a commercial turbofan hierarchical compromise decision support problem formulation. Five design scenarios are investigated, and robust solutions are identified. The method and solutions identified are verified by comparison with the AE3007 engine. The solutions obtained are similar to the AE3007 cycle and configuration, but are better with respect to many of the requirements.

Koch, Patrick N.↗

NASA NTRS2009

Partitioning the LIS/OTD Lightning Climatological Dataset into Separate Ground and Cloud Flash Distributions

Presently, it is not well understood how to best model nitrogen oxides (NOx) emissions from lightning because lightning is highly variable. Peak current, channel length, channel altitude, stroke multiplicity, and the number of flashes that occur in a particular region (i.e., flash density) all influence the amount of lightning NOx produced. Moreover, these 5 variables are not the same for ground and cloud flashes; e.g., cloud flashes normally have lower peak currents, higher altitudes, and higher flash densities than ground flashes [see (Koshak, 2009) for additional details]. Because the existing satellite observations of lightning (Fig. 1) from the Lightning Imaging Sensor/Optical Transient Detector (LIS/OTD) do not distinguish between ground and cloud fashes, which produce different amounts of NOx, it is very difficult to accurately account for the regional/global production of lightning NOx. Hence, the ability to partition the LIS/OTD lightning climatology into separate ground and cloud flash distributions would substantially benefit the atmospheric chemistry modeling community. NOx indirectly influences climate because it controls the concentration of ozone and hydroxyl radicals in the atmosphere. The importance of lightning-produced NOx is empasized throughout the scientific literature (see for example, Huntrieser et al. 1998). In fact, lightning is the most important NOx source in the upper troposphere with a global production rate estimated to vary between 2 and 20 Tg (N)yr(sup -1) (Lee et al., 1997), with more recent estimates of about 6 Tg(N)yr(sup -1) (Martin et al., 2007). In order to make accurate predictions, global chemistry/climate models (as well as regional air quality modells) must more accurately account for the effects of lightning NOx. In particular, the NASA Goddard Institute for Space Studies (GISS) Model E (Schmidt et al., 2005) and the GEOS-CHEM global chemical transport model (Bey et al., 2001) would each benefit from a partitioning of the LIS/OTD lightning climatology. In this study, we introduce a new technique for retrieving the ground flash fraction in a set of N lightning observed from space and that occur within a specific latitude/longitude bin. The method is briefly described and applied to CONUS lightning that have already been partitioned into ground and cloud flashes using independent ground-based observations, in order to assess the accuracy of the retrieval method. The retrieval errors are encouragingly small.

Koshak, W. J.↗

NASA NTRS1993

SPH modelling of energy partitioning during impacts on Venus

Impact cratering of the Venusian planetary surface by meteorites was investigated numerically using the Smoothed Particle Hydrodynamics (SPH) method. Venus presently has a dense atmosphere. Vigorous transfer of energy between impacting meteorites, the planetary surface, and the atmosphere is expected during impact events. The investigation concentrated on the effects of the atmosphere on energy partitioning and the flow of ejecta and gas. The SPH method is particularly suitable for studying complex motion, especially because of its ability to be extended to three dimensions. In our simulations, particles representing impactors and targets are initially set to a uniform density, and those of atmosphere are set to be in hydrostatic equilibrium. Target, impactor, and atmosphere are represented by 9800, 80, and 4200 particles, respectively. A Tillotson equation of state for granite is assumed for the target and impactor, and an ideal gas with constant specific heat ratio is used for the atmosphere. Two dimensional axisymmetric geometry was assumed and normal impacts of 10km diameter projectiles with velocities of 5, 10, 20, and 40 km/s, both with and without an atmosphere present were modeled.

Takata, T.↗

NASA NTRS1986

Approximate algorithms for partitioning and assignment problems

The problem of optimally assigning the modules of a parallel/pipelined program over the processors of a multiple computer system under certain restrictions on the interconnection structure of the program as well as the multiple computer system was considered. For a variety of such programs it is possible to find linear time if a partition of the program exists in which the load on any processor is within a certain bound. This method, when combined with a binary search over a finite range, provides an approximate solution to the partitioning problem. The specific problems considered were: a chain structured parallel program over a chain-like computer system, multiple chain-like programs over a host-satellite system, and a tree structured parallel program over a host-satellite system. For a problem with m modules and n processors, the complexity of the algorithm is no worse than O(mnlog(W sub T/epsilon)), where W sub T is the cost of assigning all modules to one processor and epsilon the desired accuracy.

Iqbal, M. A.↗

NASA NTRS2003

The Parameterization of Solid Metal-Liquid Metal Partitioning of Siderophile Elements

The composition of a metallic liquid can significantly affect the partitioning behavior of elements. For example, some experimental solid metal-liquid metal partition coefficients have been shown to increase by three orders of magnitude with increasing S-content of the metallic liquid. Along with S, the presence of other light elements, such as P and C, has also been demonstrated to affect trace element partitioning behavior. Understanding the effects of metallic composition on partitioning behavior is important for modeling the crystallization of magmatic iron meteorites and the chemical effects of planetary differentiation. It is thus useful to have a mathematical expression that parameterizes the partition coefficient as a function of the composition of the metal. Here we present a revised parameterization method, which builds on the theory of the current parameterization of Jones and Malvin and which better handles partitioning in multi-light-element systems.

Chabot, N. L.↗

NASA NTRS1986

Three-dimensional, conservative, Euler computations using patched grid systems and explicit methods

The method of 'zonal approach' (in which the flow field is partitioned into regions with independent grids) for computation of flow over complex geometries, such as aircraft configuration, requires application of a grid-interfacing procedure. A three-dimensional conservative, boundary scheme for patched grids, applicable in generalized coordinates for arbitrary point distributions on a planar zonal surface is presented. The computation technique is derived within the framework of the Osher (1983) upwind scheme, using Euler equations. The three-dimensional interfacing method is applied to the computation of flow about a wing-canard combination using a two-zone, patched grid.

Hessenius, K. A.↗

NASA NTRS1991

A variable multi-step method for transient heat conduction

A variable explicit time integration algorithm is developed for unsteady diffusion problems. The algorithm uses nodal partitioning and allows the nodal groups to be updated with different time steps. The stability of the algorithm is analyzed using energy methods and critical time steps are found in terms of element eigenvalues with no restrictions on element types. Several numerical examples are given to illustrate the accuracy of the method.

Smolinski, Patrick↗

NASA NTRS1994

High-performance parallel analysis of coupled problems for aircraft propulsion

Applications are described of high-performance parallel, computation for the analysis of complete jet engines, considering its multi-discipline coupled problem. The coupled problem involves interaction of structures with gas dynamics, heat conduction and heat transfer in aircraft engines. The methodology issues addressed include: consistent discrete formulation of coupled problems with emphasis on coupling phenomena; effect of partitioning strategies, augmentation and temporal solution procedures; sensitivity of response to problem parameters; and methods for interfacing multiscale discretizations in different single fields. The computer implementation issues addressed include: parallel treatment of coupled systems; domain decomposition and mesh partitioning strategies; data representation in object-oriented form and mapping to hardware driven representation, and tradeoff studies between partitioning schemes and fully coupled treatment.

Felippa, C. A.↗

NASA NTRS2022

Optimizing Lunar Map Partitioning for Multipath Fade Loss Analyses

A methodology is presented pertaining to the run-time optimization of quasi-optical ray-tracing simulations. These shooting-and-bouncing ray methods are used for assessing multipath fade loss in cislunar communication links. Our approach employs partitioning lunar terrain maps in shapes that approximate two-dimensional projections of Fresnel zone cross-sections. This technique drastically reduces computational run-time without causing significant loss of simulation accuracy.

Digital elevation models↗

NASA NTRS1993

FNAS phase partitions

Project NAS8-36955 D.O. #100 initially involved the following tasks: (1) evaluation of various coatings' ability to control wall wetting and surface zeta potential expression; (2) testing various methods to mix and control the demixing of phase systems; and (3) videomicroscopic investigation of cell partition. Three complementary areas were identified for modification and extension of the original contract. They were: (1) identification of new supports for column cell partition; (2) electrokinetic detection of protein adsorption; and (3) emulsion studies related to bioseparations.

Vanalstine, James M.↗

NASA NTRS1987

Mapping between parallel processor structures and programs

This paper reports some ongoing research efforts at Stanford in allocation of parallel processing resources. Both processor structures and program structures have their own characteristics. Resource allocation binds the two structures during program execution. The mapping problem determines what processor structure and program structure may be combined to obtain maximum speedup. Three approaches to this mapping problem are considered. Two important factors, granularity and interaction delay, are also considered. A new hierarchical approach to structure definition is outlined. Effective and efficient tools are necessary for the study of the mapping problem. A fast turn-around simulation environment developed for investigating partition strategies for distributed computations and a computationally efficient method to predict performance of parallel processor structures are described.

Ngai, Tin-Fook↗

NASA NTRS1996

Global Load Balancing with Parallel Mesh Adaption on Distributed-Memory Systems

Dynamic mesh adaption on unstructured grids is a powerful tool for efficiently computing unsteady problems to resolve solution features of interest. Unfortunately, this causes load imbalance among processors on a parallel machine. This paper describes the parallel implementation of a tetrahedral mesh adaption scheme and a new global load balancing method. A heuristic remapping algorithm is presented that assigns partitions to processors such that the redistribution cost is minimized. Results indicate that the parallel performance of the mesh adaption code depends on the nature of the adaption region and show a 35.5X speedup on 64 processors of an SP2 when 35% of the mesh is randomly adapted. For large-scale scientific computations, our load balancing strategy gives almost a sixfold reduction in solver execution times over non-balanced loads. Furthermore, our heuristic remapper yields processor assignments that are less than 3% off the optimal solutions but requires only 1% of the computational time.

Biswas, Rupak↗

NASA NTRS1996

Global Load Balancing with Parallel Mesh Adaption on Distributed-Memory Systems

Dynamic mesh adaptation on unstructured grids is a powerful tool for efficiently computing unsteady problems to resolve solution features of interest. Unfortunately, this causes load inbalances among processors on a parallel machine. This paper described the parallel implementation of a tetrahedral mesh adaption scheme and a new global load balancing method. A heuristic remapping algorithm is presented that assigns partitions to processors such that the redistribution coast is minimized. Results indicate that the parallel performance of the mesh adaption code depends on the nature of the adaption region and show a 35.5X speedup on 64 processors of an SP2 when 35 percent of the mesh is randomly adapted. For large scale scientific computations, our load balancing strategy gives an almost sixfold reduction in solver execution times over non-balanced loads. Furthermore, our heuristic remappier yields processor assignments that are less than 3 percent of the optimal solutions, but requires only 1 percent of the computational time.

Biswas, Rupak↗

NASA NTRS1971

A method of computing periods of cyclic phenomena.

Use of an analysis of Expected Mean Square Deviations to search for periodicities in an observational data sample is described. The statistic for testing the null hypothesis of nonperiodicity is derived from a partitioning of the total sum of squared deviations from the mean. Unlike most existing methods, the present one does not require equally spaced observations. No assumptions are made concerning the statistical nature of spacing intervals. The method is illustrated by numerical examples.

Jurkevich, I.↗

NASA NTRS1973

A direct procedure for partitioning scanning workload in control display system design

Experimental eye scanning measurements were made from simulated instrument approaches in a flight-like cockpit representing a contemporary jet transport. The procedure for predicting the partition of the pilot's scanning workload required for monitoring and controlling a task with status displays and a flight director was simplified. When there is but a single director control display, iteration in the preliminary design computations is eliminated. The preliminary design computations are based on predictions of closed-loop input-correlated errors in displayed variables with respect to the trimmed flight values. Methods for predicting multiloop error coherence, and for correcting the predicted partition of scanning workload when the pilot's scanning remnant contribution is significant are included.

Clement, W. F.↗

NASA NTRS1994

Practical Planning in COLLAGE

COLLAGE is a domain-independent planner that differs from traditional planners in two key ways: (1) it uses a diverse and extendible set of (it action-based) plan constructions methods; and (2) it utilizes a technique called (it localization) to partition the planning problem into smaller (and potentially interacting) sub problems. In this paper, we describe these features and how they are exploited in two different real-world planning domains. The first domain, building construction planning, has served as a framework for us to investigate how localization can improve scalability. The second domain, data analysis planning, benefits from COLLAGE's unique plan construction and representation methods. In addition, we describe extensions that were necessary to tackle these real-world problems.

Lansky, Amy L.↗

NASA NTRS1989

Efficient estimation of diffusion during dendritic solidification

A very efficient finite difference method has been developed to estimate the solute redistribution during solidification with diffusion in the solid. This method is validated by comparing the computed results with the results of an analytical solution derived by Kobayashi (1988) for the assumptions of a constant diffusion coefficient, a constant equilibrium partition ratio, and a parabolic rate of the advancement of the solid/liquid interface. The flexibility of the method is demonstrated by applying it to the dendritic solidification of a Pb-15 wt pct Sn alloy, for which the equilibrium partition ratio and diffusion coefficient vary substantially during solidification. The fraction eutectic at the end of solidification is also obtained by estimating the fraction solid, in greater resolution, where the concentration of solute in the interdendritic liquid reaches the eutectic composition of the alloy.

Yeum, K. S.↗