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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Use of shape-preserving interpolation methods in surface modeling

In many large-scale scientific computations, it is necessary to use surface models based on information provided at only a finite number of points (rather than determined everywhere via an analytic formula). As an example, an equation of state (EOS) table may provide values of pressure as a function of temperature and density for a particular material. These values, while known quite accurately, are typically known only on a rectangular (but generally quite nonuniform) mesh in (T,d)-space. Thus interpolation methods are necessary to completely determine the EOS surface. The most primitive EOS interpolation scheme is bilinear interpolation. This has the advantages of depending only on local information, so that changes in data remote from a mesh element have no effect on the surface over the element, and of preserving shape information, such as monotonicity. Most scientific calculations, however, require greater smoothness. Standard higher-order interpolation schemes, such as Coons patches or bicubic splines, while providing the requisite smoothness, tend to produce surfaces that are not physically reasonable. This means that the interpolant may have bumps or wiggles that are not supported by the data. The mathematical quantification of ideas such as physically reasonable and visually pleasing is examined.

Ftitsch, F. N.↗
DOE OSTI2019

An isogeometric finite element formulation for phase transitions on deforming surfaces

This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial differential equations (PDEs) that live on an evolving two-dimensional manifold. For the phase transitions, the PDE is the Cahn–Hilliard equation for curved surfaces, which can be derived from surface mass balance in the framework of irreversible thermodynamics. For the surface deformation, the PDE is the (vector-valued) Kirchhoff–Love thin shell equation. Both PDEs can be efficiently discretized using C 1 -continuous interpolations without derivative degrees-of-freedom (dofs). Structured NURBS and unstructured spline spaces with pointwise C 1 -continuity are utilized for these interpolations. The resulting finite element formulation is discretized in time by the generalized-α scheme with adaptive time-stepping, and it is fully linearized within a monolithic Newton–Raphson approach. A curvilinear surface parameterization is used throughout the formulation to admit general surface shapes and deformations. The behavior of the coupled system is illustrated by several numerical examples exhibiting phase transitions on deforming spheres, tori and double-tori.

42 ENGINEERING↗
DOE OSTI2014

WE-G-BRD-07: Investigation of Distal Lung Atelectasis Following Stereotactic Body Radiation Therapy Using Regional Lung Volume Changes Between Pre- and Post- Treatment CT Scans

Purpose: To propose a quantitative method using lung deformations to differentiate between radiation-induced fibrosis and potential airway stenosis with distal atelectasis in patients treated with stereotactic body radiation therapy (SBRT) for lung tumors. Methods: Twenty-four lung patients with large radiation-induced density increases outside the high dose region had their pre- and post-treatment CT scans manually registered. They received SBRT treatments at our institution between 2002 and 2009 in 3 or 5 fractions, to a median total dose of 54Gy (range, 30–60). At least 50 anatomical landmarks inside the lung (airway branches) were paired for the pre- and post-treatment scans to guide the deformable registration of the lung structure, which was then interpolated to the whole lung using splines. Local volume changes between the planning and follow-up scans were calculated using the deformation field Jacobian. Hyperdense regions were classified as atelectatic or fibrotic based on correlations between regional density increases and significant volume contractions compared to the surrounding tissues. Results: Out of 24 patients, only 7 demonstrated a volume contraction that was at least one σ larger than the remaining lung average. Because they did not receive high doses, these shrunk hyperdense regions were likely showing distal atelectasis resulting from radiation-induced airway stenosis rather than conventional fibrosis. On average, the hyperdense regions extended 9.2 cm farther than the GTV contours but not significantly more than 8.6 cm for the other patients (p>0.05), indicating that a large offset between the radiation and hyperdense region centers is not a good surrogate for atelectasis. Conclusion: A method based on the relative comparison of volume changes between different dates was developed to identify potential lung regions experiencing distal atelectasis. Such a tool is essential to study which lung structures need to be avoided to prevent atelectasis and limit lung function loss.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1984

Two-dimensional splines

Noteworthy properties of one-dimensional splines are presented. Stochastic processes, kernel functions, interpolation, and data smoothing were discussed. Theorems and concomitant proofs are provided.

Utreras, F. I.↗
NASA NTRS1974

A simplified package for calculating with splines

This package is designed to solve some of the elementary problems of spline interpretation and least squares fit. The subroutines fall into three basic categories. The first category involves computations with a given spline and/or knot sequence; the second category involves routines which calculate the coefficients of splines which perform a certain task (such as interpolation or least squares fit); and the last category is a banded equation solver for specific linear equations.

Smith, P. W.↗
NASA NTRS1992

Algebraic surface grid generation in three-dimensional space

An interactive program for algebraic generation of structured surface grids in three dimensional space was developed on the IRIS4D series workstations. Interactive tools are available to ease construction of edge curves and surfaces in 3-D space. Addition, removal, or redistribution of points at arbitrary locations on a general 3-D surface or curve is possible. Also, redistribution of surface grid points may be accomplished through use of conventional surface splines or a method called 'surface constrained transfinite interpolation'. This method allows the user to redistribute the grid points on the edges of a surface patch; the effect of the redistribution is then propagated to the remainder of the surface through a transfinite interpolation procedure where the grid points will be constrained to lie on the surface. The program was written to be highly functional and easy to use. A host of utilities are available to ease the grid generation process. Generality of the program allows the creation of single and multizonal surface grids according to the user requirements. The program communicates with the user through popup menus, windows, and the mouse.

Warsi, Saif↗
NASA NTRS1994

Control theory and splines, applied to signature storage

In this report the problem we are going to study is the interpolation of a set of points in the plane with the use of control theory. We will discover how different systems generate different kinds of splines, cubic and exponential, and investigate the effect that the different systems have on the tracking problems. Actually we will see that the important parameters will be the two eigenvalues of the control matrix.

Enqvist, Per↗
DOE OSTI2022

LaplaceInterpolation.jl: A Julia package for fast interpolation on a grid

We implement a linear-time algorithm for interpolation on a regular multidimensional grid in the Julia language. The algorithm is an approximate Laplace interpolation (Press, 1992) when no parameters are given; and when parameters m ∈ Z and ϵ > 0 are set, the interpolant approximates a Matérn kernel, of which radial basis functions and polyharmonic splines are a special case. We implement, in addition, Neumann, Dirichlet (trivial), and average boundary conditions with potentially different aspect ratios in the different dimensions. The interpolant functions in arbitrary dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

SU-E-T-140: Dynamic Wave Arc Trajectory Verification Using KV X-Ray Fluoroscopy

Purpose: Purpose: This study investigates the geometric accuracy of simultaneous Gantry/Ring rotation during Dynamic Wave Arc (DWA) delivery. Methods: The Vero SBRT system consists of a 6MV LINAC mounted on an O-ring gantry that can rotate around the vertical axis (±60°), similar to couch rotation on C-arm gantries. To provide CBCT and fluoroscopy imaging functionalities, two orthogonal kV imaging units are attached to the O-ring at −45°/+45° from the beam axis.Dynamic Wave Arc maximizes Vero's motion capabilities by employing synchronized gantry and ring motion on a complex non-coplanar trajectory in combination with aperture based optimized MLC segments.Four wave arc trajectories (T1-4) were delivered using a cubic phantom with a configuration of five lead beads. O-ring gantry position information was retrieved through continuous dual-source kV X-ray image acquisition during DWA. An in-house algorithm read in the image set, extracted the projected marker positions and determined the angulation through reconstruction of the beam source position. The geometric error was quantified as the distance between the independently detected positions from kV-images and reference trajectory derived from the treatment plan in the Ring-Gantry space. Results: The average displacement between the 3D gantry/ring positions reconstructed from the fluoroscopy images and the reference trajectory was 0.346 mm (SD 0,171) for T1. A mean offset of 0.348 mm (SD 0,182) and 0.357 mm (SD 0.194) was observed for trajectory T2(2segmens) and T3(4segments), respectively. The saw shape T4 presented a mean geometric error of 0.363 (SD 0.156). The overall systematic error of 0.350 was caused by the difference between planned reference trajectory created by linear interpolation between CP, and the machine delivery following a spline curve. Conclusion: An independent geometric QA approach has been developed for DWA delivery verification, successfully applied on diverse trajectories and disclosed that the Vero system is capable of accurately follow complex trajectories.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Autonomous Eco-Driving with Traffic Light and Lead Vehicle Constraints: An Application of Best Constrained Interpolation

Eco-Driving is a critical technology for improving automotive transportation efficiency. It is achieved by modifying the driving trajectory over a particular route to minimize required propulsion energy. Eco-Driving can be approached as an optimal control problem subject to driving constraints such as traffic lights and positions of other vehicles. Best interpolation in a strip is a problem in approximation theory and optimal control. The solution to this problem is a cubic spline. In this research, we demonstrate the connection between Eco-Driving and best interpolation in the strip. By exploiting this connection, we are able to generate optimal Eco-Driving trajectories that could be driven with an autonomous system. Using the simulation tool FASTSim, we can evaluate the trajectories using conventional, hybrid electric, and fully electric vehicle models. Our results quantify the energy efficiency improvements that can be achieved with the proposed approach.

Mahmoud, Yara Hazem↗
DOE OSTI2022

Autonomous Eco-Driving with Traffic Light and Lead Vehicle Constraints: An Application of Best Constrained Interpolation

Eco-Driving is a critical technology for improving automotive transportation efficiency. It is achieved by modifying the driving trajectory over a particular route to minimize required propulsion energy. Eco-Driving can be approached as an optimal control problem subject to driving constraints such as traffic lights and positions of other vehicles. Best interpolation in a strip is a problem in approximation theory and optimal control. The solution to this problem is a cubic spline. In this research, we demonstrate the connection between Eco-Driving and best interpolation in the strip. By exploiting this connection, we are able to generate optimal Eco-Driving trajectories that could be driven with an autonomous system. Using the simulation tool FASTSim, we can evaluate the trajectories using conventional, hybrid electric, and fully electric vehicle models. Our results quantify the energy efficiency improvements that can be achieved with the proposed approach.

Mahmoud, Yara Hazem↗
DOE OSTI2025

Timing based clustering of childhood BMI trajectories reveals differential maturational patterns; Study in the Northern Finland Birth Cohorts 1966 and 1986

Children’s biological age does not always correspond to their chronological age. In the case of BMI trajectories, this can appear as phase variation, which can be seen as shift, stretch, or shrinking between trajectories. With maturation thought of as a process moving towards the final state - adult BMI, we assessed whether children can be divided into latent groups reflecting similar maturational age of BMI. The groups were characterised by early factors and time-related features of the trajectories. We used data from two general population birth cohort studies, Northern Finland Birth Cohorts 1966 and 1986 (NFBC1966 and NFBC1986). Height (n = 6329) and weight (n = 6568) measurements were interpolated in 34 shared time points using B-splines, and BMI values were calculated between 3 months to 16 years. Pairwise phase distances of 2999 females and 3163 males were used as a similarity measure in k-medoids clustering. We identified three clusters of trajectories in females and males (Type 1: females, n = 1566, males, n = 1669; Type 2: females, n = 1028, males, n = 973; Type 3: females, n = 405, males, n = 521). Similar distinct timing patterns were identified in males and females. The clusters did not differ by sex, or early growth determinants studied. Trajectory cluster Type 1 reflected to the shape of what is typically illustrated as the childhood BMI trajectory in literature. However, the other two have not been identified previously. Type 2 pattern was more common in the NFBC1966 suggesting a generational shift in BMI maturational patterns.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2002

Meshless Local Petrov-Galerkin Method for Bending Problems

Recent literature shows extensive research work on meshless or element-free methods as alternatives to the versatile Finite Element Method. One such meshless method is the Meshless Local Petrov-Galerkin (MLPG) method. In this report, the method is developed for bending of beams - C1 problems. A generalized moving least squares (GMLS) interpolation is used to construct the trial functions, and spline and power weight functions are used as the test functions. The method is applied to problems for which exact solutions are available to evaluate its effectiveness. The accuracy of the method is demonstrated for problems with load discontinuities and continuous beam problems. A Petrov-Galerkin implementation of the method is shown to greatly reduce computational time and effort and is thus preferable over the previously developed Galerkin approach. The MLPG method for beam problems yields very accurate deflections and slopes and continuous moment and shear forces without the need for elaborate post-processing techniques.

Phillips, Dawn R.↗
NASA NTRS2019

Fusion of Surface Ceilometer Data and Satellite Cloud Retrievals in 2D Mesh Interpolating Model with Clustering

For accurate cloud ceiling information, a data fusion approach is proposed that utilizes satellite data to extend surface station information to much wider areas. Cloud base height (CBH) retrieved from satellite observations provides for much larger spatial coverage and higher resolution. The direct comparison of GOES-16 CBH with surface station ceiling yields a local bias that has to be corrected for in the initial GOES-16 cloud base information. This sparsely sampled bias correction presents an irregular 2D mesh of control points, which is then interpolated by constructing a continuous smooth field using polyharmonic splines. The influence of remote stations is restricted by grouping the control points into clusters depending on an effective distance. This cluster-based approach allows for constructing separate spline surfaces corresponding to physically different clouds. The obtained continuous bias correction function is then applied to the entire GOES-16 pixel level CBH except for areas far away from surface stations in data sparse regions such as offshore. The described method is currently being tested using daytime-only observations over the central and eastern United States. Overall, this approach has potential to provide more accurate, high spatial resolution cloud ceiling information for the aviation community.

Khlopenkov, Konstantin↗
DOE OSTI2013

Smooth GERBS, orthogonal systems and energy minimization

New results are obtained in three mutually related directions of the rapidly developing theory of generalized expo-rational B-splines (GERBS) [7, 6]: closed-form computability of C{sup ∞}-smooth GERBS in terms of elementary and special functions, Hermite interpolation and least-squares best approximation via smooth GERBS, energy minimizing properties of smooth GERBS similar to those of the classical cubic polynomial B-splines.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1980

Instrumented aircraft verification of clear-air radar detection of low-level wind shear

A technique is described in which the longitudinal wind component at airports, measured by Doppler radar, is put through a Fourier transformation to produce an energy density spectrum. The result is multiplied by the aircraft response characteristics to produce quantitative data on aircraft performance in a wind shear situation. The Doppler radar measurements are made along the intended flight path. Two case studies, along a 3 deg approach path, are described from measurements in two modes: Lagrangian, where predictions were computed one range gate ahead of the plane, and Eulerian, where samples were measured instantaneously along the flight path. Wind data obtained every second were interpolated to fit a numerical model by using a cubic spline. Eulerian data were superior to Lagrangian data in terms of ranging, and nearly equal for wind speeds. Improvements in current 75% accuracy are noted to be possible with shrouded antennas to reduce sidelobes and use of Doppler radar with higher resolution to eliminate effects of small scale disturbances within the pulse volume.

Mccarthy, J.↗
NASA NTRS1973

An automated procedure for computing flutter eigenvalues.

A new, fast and economical automated procedure for implementing the traditional V-g method of flutter solution is described. The procedure requires as input the generalized aerodynamic forces for a range of reduced frequencies obtained from an aerodynamic program. These aerodynamic forces are interpolated with respect to reduced frequency using a newly developed, partially tabulated cubic spline that is both fast in execution and economical in storage. The flutter solution is then obtained using an eigenvalue routine that has been developed to take advantage of the parametric nature of the V-g type of solution. Furthermore, the routine takes care of the fundamental and troublesome problem of properly sorting the output eigenvalues. By solving the root-sorting problem, the interpolation for flutter crossings and automatic plotting are accomplished efficiently. The computational techniques used in this new program are described and some sample results are given.

Desmarais, R. N.↗
NASA NTRS1986

Interactive algebraic grid-generation technique

An algebraic grid generation technique and use of an associated interactive computer program are described. The technique, called the two boundary technique, is based on Hermite cubic interpolation between two fixed, nonintersecting boundaries. The boundaries are referred to as the bottom and top, and they are defined by two ordered sets of points. Left and right side boundaries which intersect the bottom and top boundaries may also be specified by two ordered sets of points. when side boundaries are specified, linear blending functions are used to conform interior interpolation to the side boundaries. Spacing between physical grid coordinates is determined as a function of boundary data and uniformly space computational coordinates. Control functions relating computational coordinates to parametric intermediate variables that affect the distance between grid points are embedded in the interpolation formulas. A versatile control function technique with smooth-cubic-spline functions is presented. The technique works best in an interactive graphics environment where computational displays and user responses are quickly exchanged. An interactive computer program based on the technique and called TBGG (two boundary grid generation) is also described.

Smith, R. E.↗