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At least 19 records

A Uniform Subdivision Method for Triangular Bezier Patches

A subdivision method for Bezier triangles is presented that parallels the development of Lane-Riesenfeld for Bezier Curves. The method is developed from the mathematical description of the patch, and the resulting algorithm does not require evaluation of the blending functions. This method subdivides the triangle uniformly so that the lengths of the sides of the subtriangles are uniformly reduced. This method is a member of the class of methods first presented by Goldman, which contain subdivision methods that arise from degenerate subdivision of Bezier tetrahedra. It is shown that a certain method is a natural extension of the Lane-Riesenfeld results for Bezier curves.

Joy, K. I.↗

An Adaptive Unstructured Grid Method by Grid Subdivision, Local Remeshing, and Grid Movement

An unstructured grid adaptation technique has been developed and successfully applied to several three dimensional inviscid flow test cases. The approach is based on a combination of grid subdivision, local remeshing, and grid movement. For solution adaptive grids, the surface triangulation is locally refined by grid subdivision, and the tetrahedral grid in the field is partially remeshed at locations of dominant flow features. A grid redistribution strategy is employed for geometric adaptation of volume grids to moving or deforming surfaces. The method is automatic and fast and is designed for modular coupling with different solvers. Several steady state test cases with different inviscid flow features were tested for grid/solution adaptation. In all cases, the dominant flow features, such as shocks and vortices, were accurately and efficiently predicted with the present approach. A new and robust method of moving tetrahedral "viscous" grids is also presented and demonstrated on a three-dimensional example.

Pirzadeh, Shahyar Z.↗

Optimal Synthesis of Compliant Mechanisms using Subdivision and Commercial FEA (DETC2004-57497)

The field of distributed-compliance mechanisms has seen significant work in developing suitable topology optimization tools for their design. These optimal design tools have grown out of the techniques of structural optimization. This paper will build on the previous work in topology optimization and compliant mechanism design by proposing an alternative design space parameterization through control points and adding another step to the process, that of subdivision. The control points allow a specific design to be represented as a solid model during the optimization process. The process of subdivision creates an additional number of control points that help smooth the surface (for example a C(sup 2) continuous surface depending on the method of subdivision chosen) creating a manufacturable design free of some traditional numerical instabilities. Note that these additional control points do not add to the number of design parameters. This alternative parameterization and description as a solid model effectively and completely separates the design variables from the analysis variables during the optimization procedure. The motivation behind this work is to create an automated design tool from task definition to functional prototype created on a CNC or rapid-prototype machine. This paper will describe the proposed compliant mechanism design process and will demonstrate the procedure on several examples common in the literature.

Hull, Patrick V.↗

Wing tip vortex calculations with an unstructured adaptive-grid Euler solver

A solution-adaptive grid method has been developed for computing tip-vortex flowfields around rectangular wings. This method uses subdivision in order to locally refine the grid in regions with high vorticity. Two different flow solvers are used. Each solves the three-dimensional Euler equations on unstructured grids. Computed results are compared to experimentally measured surface pressures and vortex velocities on a NACA 0015 rectangular wing. Predicted results for surface pressures and integrated lift agree well with the experimental data. The predicted size of the rotational vortex core is larger than the experimentally-measured value and the peak velocities are less. This discrepancy appears to be caused by deficiencies in the inviscid Euler-equation model. This model cannot capture the complex viscous effects at the tip that determine the detailed structure of the resulting vortex. In spite of this limitation, the present Euler unstructured adaptive-grid method demonstrates the ability to convert vortical flows with low numerical diffusion. Applications for modeling helicopter rotor wake systems are discussed.

Strawn, Roger C.↗

Hydrologic models for land-atmosphere retrospective studies of the use of LANDSAT and AVHRR data

The use of a Geographic Information System (GIS) and LANDSAT analysis in conjunction with the Simulator for Water Resources on a Rural Basin (SWRRB) hydrologic model to examine the water balance on the Little Washita River basin is discussed. LANDSAT analysis was used to divide the basin into eight non-contiguous land covers or subareas: rangeland, grazed range, winter wheat, alfalfa/pasture, bare soil, water, woodland, and impervious land (roads, quarry). The use of a geographic information system allowed for the calculation of SWRRB model parameters in each subarea. Four data sets were constructed in order to compare SWRRB estimates of hydrologic processes using two methods of maximum LAI and two methods of watershed subdivision. Maximum LAI was determined from a continental scale map, which provided a value of 4.5 for the entire basin, and from its association with the type of land-cover (eight values). The two methods of watershed subdivision were determined according to drainage subbasin (four) and the eight land-covers. These data sets were used with the SWRRB model to obtain daily hydrologic estimates for 1985. The results of the one year analysis lead to the conclusion that the greater homogeneity of a land-cover subdivision provides better water yield estimates than those based on a drainage properties subdivision.

Duchon, Claude E.↗

A subdivision-stabilized B-spline mixed material point method

Subjected to external loadings, polymeric materials, e.g., biological tissues, hydrogels, and elastomers, may undergo extreme, nearly incompressible, (self-)contact deformations. For numerical modeling employing mesh-based techniques such as the finite element method (FEM), these deformations pose significant challenges due to large distortions in the deformed geometry, accuracy issues stemming from volumetric locking effects, and increased computational cost from complex contact searches. As an alternative to mesh-based methods, the material point method (MPM), a continuum-based particle technique, is gaining attention for its ability to handle extreme distortions and capture no-slip contact without added cost. For nearly incompressible material behaviors, while mixed formulations can address locking effects by treating displacements and pressure as independent fields, they can suffer from numerical instabilities close to the incompressibility limit due to the violation of the inf-sup condition, leading to inaccurate nodal pressure solutions. Here we propose an efficient and stable mixed B-spline material point method with highest achievable regularity for quasi-compressible polymeric materials. Using the two-scale relation of B-splines, we introduce a subdivision-stabilization for the two-field mixed MPM and obtain numerically stable, oscillation-free nodal solutions with equal-order interpolations with optimal regularity. Building on the Eulerian-Lagrangian nature of MPM, a previously-converged solution framework is adopted to mitigate issues related to cell-crossing and numerical fracture artifact present in standard MPM. We assess the stability and accuracy of the developed mixed MPM at large deformations for soft materials through the benchmark Cook’s membrane problem. Additionally, we test the robustness of the proposed MPM by modeling several examples, including the compression and indentation of a circular block into a quasi-compressible substrate and the twisting deformation of a rectangular block. The findings demonstrate the MPM’s capabilities for modeling practical soft material applications.

36 MATERIALS SCIENCE↗

NASA Experimental Program to Stimulate Competitive Research: South Carolina

The use of an appropriate relationship model is critical for reliable prediction of future urban growth. Identification of proper variables and mathematic functions and determination of the weights or coefficients are the key tasks for building such a model. Although the conventional logistic regression model is appropriate for handing land use problems, it appears insufficient to address the issue of interdependency of the predictor variables. This study used an alternative approach to simulation and modeling urban growth using artificial neural networks. It developed an operational neural network model trained using a robust backpropagation method. The model was applied in the Myrtle Beach region of South Carolina, and tested with both global datasets and areal datasets to examine the strength of both regional models and areal models. The results indicate that the neural network model not only has many theoretic advantages over other conventional mathematic models in representing the complex urban systems, but also is practically superior to the logistic model in its capability to predict urban growth with better - accuracy and less variation. The neural network model is particularly effective in terms of successfully identifying urban patterns in the rural areas where the logistic model often falls short. It was also found from the area-based tests that there are significant intra-regional differentiations in urban growth with different rules and rates. This suggests that the global modeling approach, or one model for the entire region, may not be adequate for simulation of a urban growth at the regional scale. Future research should develop methods for identification and subdivision of these areas and use a set of area-based models to address the issues of multi-centered, intra- regionally differentiated urban growth.

Sutton, Michael A.↗

Dividing the Concentrator Target From the Genesis Mission

The Genesis spacecraft, launched in 2001, traveled to a Lagrangian point between the Earth and Sun to collect particles from the solar wind and return them to Earth. However, during the return of the spacecraft in 2004, the parachute failed to open during descent, and the Genesis spacecraft crashed into the Utah desert. Many of the solar wind collectors were broken into smaller pieces, and the field team rapidly collected the capsule and collector pieces for later assessment. On each of the next few days, the team discovered that various collectors had survived intact, including three of four concentrator targets. Within a month, the team had imaged more than 10,000 fragments and packed them for transport to the Astromaterials Acquisition and Curation Office within the ARES Directorate at JSC. Currently, the Genesis samples are curated along with the other extraterrestrial sample collections within ARES. Although they were broken and dirty, the Genesis solar wind collectors still offered the science community the opportunity to better understand our Sun and the solar system as a whole. One of the more highly prized concentrator collectors survived the crash almost completely intact. The Genesis Concentrator was designed to concentrate the solar wind by a factor of at least 20 so that solar oxygen and nitrogen isotopes could be measured. One of these materials was the Diamond-on-Silicon (DoS) concentrator target. Unfortunately, the DoS concentrator broke on impact. Nevertheless, the scientific value of the DoS concentrator target was high. The Genesis Allocation Committee received a request for approximately 1 cm(sup 2) of the DoS specimen taken near the focal point of the concentrator for the analysis of solar wind nitrogen isotopes. The largest fragment, Genesis sample 60000, was designated for this allocation and needed to be precisely cut. The requirement was to subdivide the designated sample in a manner that prevented contamination of the sample and minimized the risk of losing or breaking the precious requested sample fragment. The Genesis curator determined that the use of laser scribing techniques to "cut" a precise line and subsequently cleave the sample (in a controlled break of the sample along that line) was the best method for accomplishing the sample subdivision. However, there were risks, including excess heating of the sample, that could cause some of the implanted solar wind to be lost via thermal diffusion. Accidentally breaking the sample during the handling and cleaving process was an additional risk. Early in fiscal year 2013, to address this delicate, complicated task, the ARES Directorate assembled its top scientists to develop a cutting plan that would ensure success when applied to the actual concentrator target wafer; i.e., to produce an approximately 1 cm(sup 2) piece from the requested area of the wafer. The team, subsequently referred to as the JSC Genesis Tiger Team, spent months researching and testing parameters and techniques related to scribing, cleaving, transporting, handling, and holding (i.e., mounting) the specimen. The investigation required considerable "thinking outside the box," and many, many trials using nonflight wafer analogs. After all preliminary testing, the following method was adopted as the final cutting plan. It was used in two final end-to-end practice runs before being used on the actual flight target wafer. The wafer was oriented on the laser cutting stage with the 100 and 010 directions of the wafer parallel to the corresponding X and Y directions of the cutting stage. The laser was programed to scribe 31 lines of the appropriate length along the Y stage direction. The programed scribe lines were separated by 5 micron in the X direction. The laser parameters were set as follows: (1) The laser power was 0.5 watts; (2) each line consisted of 50 passes, with the Z position being advanced 5 micron per pass; and (3) 30 s would elapse before the next line was scribed to allow for wafer cool down from any possible heating via the laser. The ablated material that "stuck" in the "scribe-cut" was removed from the "cut" using an ultrasonic micro-tool. After all the ablated silicon was removed from the wafer, the wafer was repositioned in exactly the same orientation on the laser stage. The laser was focused using the bottom of the wafer channel, and the 31-line scribing pattern described above was reprogrammed using the Z position of the groove bottom as the starting Z value instead of the top wafer surface, which was used previously. Upon completion of the second set of scribes, the ultrasonic micro-tool was again used to clean out the cut. The wafer was remounted on the stage in exactly the same orientation as before. The laser was again focused on the bottom of the groove. This time, however, the laser was.programed to scribe only one line down the exact center of the channel. The final scribe line consisted of 100 passes with a Z advance of 5 micron per pass and with the laser power set at 0.5 watts. As mentioned above, the final cutting plan was practiced in two end-to-end trials using non-flight, triangular-shaped silicon wafers similar in size and orientation to the actual DOS 60000 target sample. The actual scribing of the triangular-shaped wafers required scribing two lines and cleaving (i.e. scribe-cleave, then scribe-cleave) to obtain the piece requested for allocation. Early in December 2012, after many months of experiments and practicing and perfecting the techniques and procedures, the team successfully subdivided the Genesis DoS 60000 target sample, one of the most scientifically important samples from the Genesis mission (figure 2). On December 17, 2012, the allocated piece of concentrator target sample was delivered to the requesting principal investigator.The cutting plan developed for the subdivision of this sample will be used as the model for subdividing future requested Genesis flight wafers (appropriately modified for different wafer types).

Lauer, H. V., Jr.↗

A Solution Adaptive Technique Using Tetrahedral Unstructured Grids

An adaptive unstructured grid refinement technique has been developed and successfully applied to several three dimensional inviscid flow test cases. The method is based on a combination of surface mesh subdivision and local remeshing of the volume grid Simple functions of flow quantities are employed to detect dominant features of the flowfield The method is designed for modular coupling with various error/feature analyzers and flow solvers. Several steady-state, inviscid flow test cases are presented to demonstrate the applicability of the method for solving practical three-dimensional problems. In all cases, accurate solutions featuring complex, nonlinear flow phenomena such as shock waves and vortices have been generated automatically and efficiently.

Pirzadeh, Shahyar Z.↗

Yet another method for triangulation and contouring for automated cartography

An algorithm is presented for hierarchical subdivision of a set of three-dimensional surface observations. The data structure used for obtaining the desired triangulation is also singularly appropriate for extracting contours. Some examples are presented, and the results obtained are compared with those given by Delaunay triangulation. The data points selected by the algorithm provide a better approximation to the desired surface than do randomly selected points.

De Floriani, L.↗

Topology Synthesis of Structures Using Parameter Relaxation and Geometric Refinement

Typically, structural topology optimization problems undergo relaxation of certain design parameters to allow the existence of intermediate variable optimum topologies. Relaxation permits the use of a variety of gradient-based search techniques and has been shown to guarantee the existence of optimal solutions and eliminate mesh dependencies. This Technical Publication (TP) will demonstrate the application of relaxation to a control point discretization of the design workspace for the structural topology optimization process. The control point parameterization with subdivision has been offered as an alternative to the traditional method of discretized finite element design domain. The principle of relaxation demonstrates the increased utility of the control point parameterization. One of the significant results of the relaxation process offered in this TP is that direct manufacturability of the optimized design will be maintained without the need for designer intervention or translation. In addition, it will be shown that relaxation of certain parameters may extend the range of problems that can be addressed; e.g., in permitting limited out-of-plane motion to be included in a path generation problem.

Hull, P. V.↗

Construction of higher order accurate vortex and particle methods

The standard point vortex method has recently been shown to be of high order of accuracy for problems on the whole plane, when using a uniform initial subdivision for assigning the vorticity to the points. If obstacles are present in the flow, this high order deteriorates to first or second order. New vortex methods are introduced which are of arbitrary accuracy (under regularity assumptions) regardless of the presence of bodies and the uniformity of the initial subdivision.

Nicolaides, R. A.↗

Lunar terrain mapping and relative-roughness analysis

Terrain maps of the equatorial zone were prepared at scales of 1:2,000,000 and 1:1,000,000 to classify lunar terrain with respect to roughness and to provide a basis for selecting sites for Surveyor and Apollo landings, as well as for Ranger and Lunar Orbiter photographs. Lunar terrain was described by qualitative and quantitative methods and divided into four fundamental classes: maria, terrae, craters, and linear features. Some 35 subdivisions were defined and mapped throughout the equatorial zone, and, in addition, most of the map units were illustrated by photographs. The terrain types were analyzed quantitatively to characterize and order their relative roughness characteristics. For some morphologically homogeneous mare areas, relative roughness can be extrapolated to the large scales from measurements at small scales.

Rowan, L. C.↗

A survey of unclassified axial-flow-compressor literature

A survey of unclassified axial-flow-compressor literature is presented in the form of brief reviews of the methods, results, and conclusions of selected reports. The reports are organized into several main categories with subdivisions, and frequent references are made within the individual reviews to pertinent material elsewhere in the survey.

Herzig, Howard Z↗

Aircraft accidents : method of analysis

This report on a method of analysis of aircraft accidents has been prepared by a special committee on the nomenclature, subdivision, and classification of aircraft accidents organized by the National Advisory Committee for Aeronautics in response to a request dated February 18, 1928, from the Air Coordination Committee consisting of the Assistant Secretaries for Aeronautics in the Departments of War, Navy, and Commerce. The work was undertaken in recognition of the difficulty of drawing correct conclusions from efforts to analyze and compare reports of aircraft accidents prepared by different organizations using different classifications and definitions. The air coordination committee's request was made "in order that practices used may henceforth conform to a standard and be universally comparable." the purpose of the special committee therefore was to prepare a basis for the classification and comparison of aircraft accidents, both civil and military. (author)

Source record↗

CG-Kit: Code Generation Toolkit for performant and maintainable variants of source code applied to Flash-X hydrodynamics simulations

CG-Kit is a new Code Generation tool-Kit that we have developed as a part of the solution for portability and maintainability for multiphysics computing applications. The development of CG-Kit is rooted in the urgent need created by the shifting landscape of high-performance computing platforms and the algorithmic complexities of a particular large-scale multiphysics application: Flash-X. To efficiently use computing resources on a heterogeneous node, an application must have a map of computation to resources and a mechanism to move the data and computation to the resources according to the map. Most existing performance portability solutions are focussed on abstracting the expression of computations so that a unified source code can be specialized to run on different resources. However, such an approach is insufficient for a code like Flash-X, which has a multitude of code components that can be assembled in various permutations and combinations to form different instances of applications. Similar challenges apply to any code that has composability, where a single specified way of apportioning work among devices may not be optimal. Additionally, use cases arise where the optimal control flow of computation may differ for different devices while the underlying numerics remain identical. This combination leads to unique challenges including handling an existing large code base in Fortran and/or C/C++, subdivision of code into a great variety of units supporting a wide range of physics and numerical methods, different parallelization techniques for distributed and shared memory systems and accelerator devices, and heterogeneity of computing platforms requiring coexisting variants of parallel algorithms. All of these challenges demand that scientific software developers apply existing knowledge about domain applications, algorithms, and computing platforms to determine custom abstractions and granularity for code generation. There is a critical lack of tools to tackle those problems. CG-Kit is designed to fill this gap by providing a user with the ability to express their desired control flow and computation-to-resource map in the form a pseudocode-like recipe. It consists of standalone tools that can be combined into highly specific and, we argue, highly effective portability and maintainability toolchains. Here we present the design of our new tools: parametrized source trees, control flow graphs, and recipes. The tools are implemented in Python. They are agnostic to the programming language of the source code targeted for code generation. In conclusion, we demonstrate the capabilities of the toolkit with two examples, first, multithreaded variants of the basic AXPY operation, and second, variants of parallel algorithms within a hydrodynamics solver, called Spark, from Flash-X that operates on block-structured adaptive meshes.

Algorithmic portability↗

Motion planning of mobile multi-limb robotic systems subject to force and friction constraints

A method is presented to generate motions for a class of multilimb robotic systems enabling them to apply large static forces over large ranges of motion without saturating actuator effort limits, system-environment friction constraints, kinematic joint limits, or geometric workspace obstacles. The approach, termed the force-workspace (FW) approach, maps these constraints into the system C-space to form constraint obstacles using a recursive subdivision process. To generate motions along which actuator efforts can be specified without violating system constraints, paths are planned that avoid these constraint obstacles. The method permits the shape of the paths to be controlled using any configuration-dependent performance criterion. The FW approach was applied to a proposed three-limb planar climbing robot whose task is to climb upwards between two vertical walls by pushing outwards to generate frictional support. Motions were planned automatically within the system FW, enabling it to lift itself upwards using two limbs at a time, and a gait was planned to enable it to switch limbs and climb continuously.

Madhani, Akhil↗

Ontology-Driven Information Integration

Ontology-driven information integration (ODII) is a method of computerized, automated sharing of information among specialists who have expertise in different domains and who are members of subdivisions of a large, complex enterprise (e.g., an engineering project, a government agency, or a business). In ODII, one uses rigorous mathematical techniques to develop computational models of engineering and/or business information and processes. These models are then used to develop software tools that support the reliable processing and exchange of information among the subdivisions of this enterprise or between this enterprise and other enterprises.

Tissot, Florence↗