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All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Surface Generation and Cartesian Mesh Support

This document serves as the final report for the grant titled Surface Generation and Cartesian Mesh Support . This completed work was in algorithmic research into automatically generating surface triangulations from CAD geometries. NASA's OVERFLOW and Cart3D simulation packages use surface triangulations as an underlying geometry description and the ability to automatically generate these from CAD files (without translation) substantially reduces both the wall-clock time and expertise required to get geometry out of CAD and into mesh generation. This surface meshing was exercised greatly during the Shuttle investigation during the last year with success. The secondary efforts performed in this grant involve work on a visualization system cut-cell handling for Cartesian Meshes with embedded boundaries.

Haimes, Robert↗
NASA NTRS2004

Watertight Anisotropic Surface Meshing Using Quadrilateral Patches

This paper presents a simple technique for generating anisotropic surface triangulations using unstructured quadrilaterals when the CAD entity can be mapped to a logical rectangle. Watertightness and geometric quality measures are maintained and are consistent with the CAPRI default tessellator. These triangulations can match user specified criteria for chord-height tolerance, neighbor triangle dihedral angle, and maximum triangle side length. This discrete representation has hooks back to the owning geometry and therefore can be used in conjunction with these entities to allow for easy enhancement or modification of the tessellation suitable for grid generation or other downstream applications.

Haimes, Robert↗
NASA NTRS1999

Brain segmentation and the generation of cortical surfaces

This paper describes methods for white matter segmentation in brain images and the generation of cortical surfaces from the segmentations. We have developed a system that allows a user to start with a brain volume, obtained by modalities such as MRI or cryosection, and constructs a complete digital representation of the cortical surface. The methodology consists of three basic components: local parametric modeling and Bayesian segmentation; surface generation and local quadratic coordinate fitting; and surface editing. Segmentations are computed by parametrically fitting known density functions to the histogram of the image using the expectation maximization algorithm [DLR77]. The parametric fits are obtained locally rather than globally over the whole volume to overcome local variations in gray levels. To represent the boundary of the gray and white matter we use triangulated meshes generated using isosurface generation algorithms [GH95]. A complete system of local parametric quadratic charts [JWM+95] is superimposed on the triangulated graph to facilitate smoothing and geodesic curve tracking. Algorithms for surface editing include extraction of the largest closed surface. Results for several macaque brains are presented comparing automated and hand surface generation. Copyright 1999 Academic Press.

NASA Discipline Neuroscience↗
NASA NTRS2006

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Nemec, Marian↗
NASA NTRS2006

Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry

A DJOINT solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (e.g., geometric parameters that control the shape). Classic aerodynamic applications of gradient-based optimization include the design of cruise configurations for transonic and supersonic flow, as well as the design of high-lift systems. are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric computer-aided design (CAD). In previous work on Cartesian adjoint solvers, Melvin et al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the two-dimensional Euler equations using a ghost-cell method to enforce the wall boundary conditions. In Refs. 18 and 19, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm were the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The accuracy of the gradient computation was verified using several three-dimensional test cases, which included design variables such as the free stream parameters and the planform shape of an isolated wing. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Factors under consideration include the computation of mesh sensitivities that provide a reliable approximation of the objective function gradient, as well as the computation of surface shape sensitivities based on a direct-CAD interface. We present detailed gradient verification studies and then focus on a shape optimization problem for an Apollo-like reentry vehicle. The goal of the optimization is to enhance the lift-to-drag ratio of the capsule by modifying the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design.

Nemec, Marian↗
NASA NTRS2011

The Development of the Puerto Rico Lightning Detection Network for Meteorological Research

A land-based Puerto Rico Lightning Detection Network (PR-LDN) dedicated to the academic research of meteorological phenomena has being developed. Five Boltek StormTracker PCI-Receivers with LTS-2 Timestamp Cards with GPS and lightning detectors were integrated to Pentium III PC-workstations running the CentOS linux operating system. The Boltek detector linux driver was compiled under CentOS, modified, and thoroughly tested. These PC-workstations with integrated lightning detectors were installed at five of the University of Puerto Rico (UPR) campuses distributed around the island of PR. The PC-workstations are left on permanently in order to monitor lightning activity at all times. Each is networked to their campus network-backbone permitting quasi-instantaneous data transfer to a central server at the UPR-Bayam n campus. Information generated by each lightning detector is managed by a C-program developed by us called the LDN-client. The LDN-client maintains an open connection to the central server operating the LDN-server program where data is sent real-time for analysis and archival. The LDN-client also manages the storing of data on the PC-workstation hard disk. The LDN-server software (also an in-house effort) analyses the data from each client and performs event triangulations. Time-of-arrival (TOA) and related hybrid algorithms, lightning-type and event discriminating routines are also implemented in the LDN-server software. We also have developed software to visually monitor lightning events in real-time from all clients and the triangulated events. We are currently monitoring and studying the spatial, temporal, and type distribution of lightning strikes associated with electrical storms and tropical cyclones in the vicinity of Puerto Rico.

Legault, Marc D.↗
NASA NTRS2017

JIGSAW-GEO (1.0): Locally Orthogonal Staggered Unstructured Grid Generation for General Circulation Modelling on the Sphere

An algorithm for the generation of non-uniform, locally orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered VoronoiDelaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a priori bounds on element size and shape. Grid quality is further improved through the application of hill-climbing-type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid-type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution-type studies is discussed in detail.

geophysical fluid dynamics↗
NASA NTRS2018

MoonBEAM: A Beyond Earth-Orbit Gamma-Ray Burst Detector for Multi-Messenger Astronomy

Moon Burst Energetics All-sky Monitor (MoonBEAM) is a CubeSat concept of deploying gamma-ray detectors in cislunar space to increase gamma-ray burst detections and improve localization precision with the timing triangulation technique. A gamma-ray instrument in cislunar orbit will have greatly reduced sky blockage compared to instruments in low Earth orbit. Working in conjunction with another instrument in low Earth orbit, MoonBEAM can also help constrain the arrival direction of the wavefront to an annulus on the sky by utilizing the light arrival times between the different orbits. This method has been demonstrated by the Interplanetary Gamma- Ray Burst Timing Network. However, delays in data downlink for instruments outside the Tracking and Data Relay Satellite network prevent rapid follow-up observations. We present here a gamma-ray CubeSat concept in Earth-Moon L3 halo orbit that is capable of faster response and provide a timing baseline for localization improvement. Such an instrument would aid in the gravitational wave follow-up observations in other wavelengths to identify the gamma-ray burst afterglow and kilonova emission. Reducing the region of interest makes identifying afterglows much faster, allowing for rapid on-source observations and monitoring of the rise and decay times. It will also prevent source confusion between two transients and enable robust association. A gamma-ray detection could also increase the confidence of a simultaneous but marginal gravitational wave signal, extending the detection horizon. MoonBEAM is a 12U CubeSat concept of deploying gamma-ray detectors in cislunar space to increase gamma-ray burst detections and improve localization precision with the timing triangulation technique. Such an instrument would probe the extreme processes in cosmic collision of compact objects and facilitate multi-messenger time-domain astronomy to explore the end of stellar life cycles and black hole formations.

gamma-ray Cubesat↗
NASA NTRS2013

The Interplanetary Network Supplement to the Fermi Gbm Catalog of Cosmic Gamma-Ray Bursts

We present Interplanetary Network (IPN) data for the gamma-ray bursts in the first Fermi Gamma-Ray BurstMonitor (GBM) catalog. Of the 491 bursts in that catalog, covering 2008 July 12 to 2010 July 11, 427 wereobserved by at least one other instrument in the nine-spacecraft IPN. Of the 427, the localizations of 149 could beimproved by arrival time analysis (or triangulation). For any given burst observed by the GBM and one otherdistant spacecraft, triangulation gives an annulus of possible arrival directions whose half-width varies betweenabout 0. 4 and 32, depending on the intensity, time history, and arrival direction of the burst, as well as the distancebetween the spacecraft. We find that the IPN localizations intersect the 1 GBM error circles in only 52 of thecases, if no systematic uncertainty is assumed for the latter. If a 6 systematic uncertainty is assumed and added inquadrature, the two localization samples agree about 87 of the time, as would be expected. If we then multiply theresulting error radii by a factor of three, the two samples agree in slightly over 98 of the cases, providing a goodestimate of the GBM 3 error radius. The IPN 3 error boxes have areas between about 1 arcmin2 and 110 deg2,and are, on the average, a factor of 180 smaller than the corresponding GBM localizations. We identify two burstsin the IPNGBM sample that did not appear in the GBM catalog. In one case, the GBM triggered on a terrestrialgamma flash, and in the other, its origin was given as uncertain. We also discuss the sensitivity and calibration ofthe IPN.

INTERPLANET↗
NASA NTRSDate not supplied

Distributed Visual Sensing and Fusion for Advanced Air Mobility

Surveillance solutions for Advanced and Urban Air Mobility frameworks are a key factor to enable safe operations of highly automated aircraft in the civil airspace. To design solutions suitable for all types of aircraft, non-cooperative sensors can be used, though many challenges arise when the small dimensions of the vehicles and their proximity to the ground during low-altitude missions are considered. A distributed sensing concept can be efficiently applied to address these challenges by exploiting multiple sensors within a surveillance network. This paper proposes a strategy to fuse the information collected by three ground-fixed cameras within a network of multiple distributed sensors and is tested with during experimental flight tests. The solution exploits standalone tracking estimates of each camera within a fusion center that performs triangulation and three-dimensional tracking. This approach is tested in a scenario involving two small UAVs flying at low altitude. The paper deals with the challenges of associating the two objects from independent and unrelated tracks to achieve robust triangulation, which produces meter-level mean errors with respect to GNSS-based ground truth.

Federica Vitiello↗
DOE OSTI2024

T RI M E ++: Multi-threaded triangular meshing in two dimensions

We present T RI M E ++, a multi-threaded software library designed for generating two-dimensional meshes for intricate geometric shapes using the Delaunay triangulation. Multi-threaded parallel computing is implemented throughout the meshing procedure, making it suitable for fast generation of large-scale meshes. Three iterative meshing algorithms are implemented: the DistMesh algorithm, the centroidal Voronoi diagram meshing, and a hybrid of the two. We compare the performance of the three meshing methods in T RI M E ++, and show that the hybrid method retains the advantages of the other two. The software library achieves significant parallel speedup when generating large-scale meshes containing between 10 4 to 10 7 points. T RI M E ++ can handle complicated geometries and generates adaptive meshes of high quality.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Data-driven Event Identification in the U.S. Power Systems Based on 2D-OLPP and RUSBoosting Trees

Accurate event identification is an essential part of situation awareness ability for power system operators. Therefore, this work proposes an integrated event identification algorithm for power systems. First, to obtain and filter suitable inputs for event identification, an event detection trigger based on the rate of change of frequency (RoCoF) is presented. Then, the wave arrival time difference-based triangulation method considering the anisotropy of wave propagation speed is utilized to estimate the location of the detected event. Next, the two-dimensional orthogonal locality preserving projection (2D-OLPP)-based method, which is suitable for multiple types of measured data, is employed to achieve higher effectiveness in extracting the event features compared with traditional one-dimensional projection and principle component analysis (PCA). Finally, the random undersampling boosted (RUSBoosted) trees-based classifier, which can mitigate the data sample imbalance issue, is utilized to identify the type of the detected event. Furthermore, the proposed approach is demonstrated using the actual measurement data of U.S. power systems from FNET/GridEye. Comparison results show that the proposed event identification algorithm can achieve better performance than existing approaches.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1966

Results from geometric methods.

Satellite triangulation based on simultaneous observations from two stations defining space orientation of plane

SPACE ORIENTATION↗
NASA NTRS2010

Stereoscopic Analysis of STEREO/SECCHI Data for CME Trajectory Determination

The Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI) coronagraphs on the twin Solar TErrestrial RElations Observatory (STEREO) spacecraft provide simultaneous views of the corona and coronal mass ejections from two view points. Here, we analyze simultaneous image pairs using the technique of tie-pointing and triangulation (T&T) to determine the three-dimensional trajectory of seven coronal mass ejections (CMEs). The bright leading edge of a CME seen in coronagraph images results from line-of-sight integration through the CME front; the two STEREO coronagraphs see different apparent leading edges, leading to a systematic error in its three-dimensional reconstruction. We analyze this systematic error using a simple geometric model of a CME front. We validate the technique and analysis by comparing T&T trajectory determinations for seven CMEs with trajectories determined by Thernisien et al. (2009) using a forward modeling technique not susceptible to this systematic effect.

CORONAGRAPHS↗
NASA NTRS2015

Multi-Resolution Unstructured Grid-Generation for Geophysical Applications on the Sphere

An algorithm for the generation of non-uniform unstructured grids on ellipsoidal geometries is described. This technique is designed to generate high quality triangular and polygonal meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric and ocean simulation, and numerical weather predication. Using a recently developed Frontal-Delaunay-refinement technique, a method for the construction of high-quality unstructured ellipsoidal Delaunay triangulations is introduced. A dual polygonal grid, derived from the associated Voronoi diagram, is also optionally generated as a by-product. Compared to existing techniques, it is shown that the Frontal-Delaunay approach typically produces grids with near-optimal element quality and smooth grading characteristics, while imposing relatively low computational expense. Initial results are presented for a selection of uniform and non-uniform ellipsoidal grids appropriate for large-scale geophysical applications. The use of user-defined mesh-sizing functions to generate smoothly graded, non-uniform grids is discussed.

Weather↗