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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Radar transponder antenna pattern analysis for the space shuttle

In order to improve tracking capability, radar transponder antennas will soon be mounted on the Shuttle solid rocket boosters (SRB). These four antennas, each being identical cavity-backed helices operating at 5.765 GHz, will be mounted near the top of the SRB's, adjacent to the intertank portion of the external tank. The purpose is to calculate the roll-plane pattern (the plane perpendicular to the SRB axes and containing the antennas) in the presence of this complex electromagnetic environment. The large electrical size of this problem mandates an optical (asymptotic) approach. Development of a specific code for this application is beyond the scope of a summer fellowship; thus a general purpose code, the Numerical Electromagnetics Code - Basic Scattering Code, was chosen as the computational tool. This code is based on the modern Geometrical Theory of Diffraction, and allows computation of scattering of bodies composed of canonical problems such as plates and elliptic cylinders. Apertures mounted on a curved surface (the SRB) cannot be accomplished by the code, so an antenna model consisting of wires excited by a method of moments current input was devised that approximated the actual performance of the antennas. The improvised antenna model matched well with measurements taken at the MSFC range. The SRB's, the external tank, and the shuttle nose were modeled as circular cylinders, and the code was able to produce what is thought to be a reasonable roll-plane pattern.

Radcliff, Roger↗
NASA NTRS1977

Variants and extensions of a fast direct numerical cauchy-riemann solver, with illustrative applications

Revised and extended versions of a fast, direct (noniterative) numerical Cauchy-Riemann solver are presented for solving finite difference approximations of first order systems of partial differential equations. Although the difference operators treated are linear and elliptic, one significant application of these extended direct Cauchy-Riemann solvers is in the fast, semidirect (iterative) solution of fluid dynamic problems governed by the nonlinear mixed elliptic-hyperbolic equations of transonic flow. Different versions of the algorithms are derived and the corresponding FORTRAN computer programs for a simple example problem are described and listed. The algorithms are demonstrated to be efficient and accurate.

Martin, E. D.↗
NASA NTRS1996

Smoothers for Optimization Problems

We present a multigrid one-shot algorithm, and a smoothing analysis, for the numerical solution of optimal control problems which are governed by an elliptic PDE. The analysis provides a simple tool to determine a smoothing minimization process which is essential for multigrid application. Numerical results include optimal control of boundary data using different discretization schemes and an optimal shape design problem in 2D with Dirichlet boundary conditions.

Arian, Eyal↗
NASA NTRS1978

Programming effort analysis of the ELLPACK language

ELLPACK is a problem statement language and system for elliptic partial differential equations which is implemented by a FORTRAN preprocessor. ELLPACK's principal purpose is as a tool for the performance evaluation of software. However, it is used here as an example with which to study the programming effort required for problem solving. It is obvious that problem statement languages can reduce programming effort tremendously; the goal is to quantify this somewhat. This is done by analyzing the lengths and effort (as measured by Halstead's software science technique) of various approaches to solving these problems.

Rice, J. R.↗
NASA NTRS1997

Application of the Two-Step Filter to Process Ranging Measurements for Relative Navigation in an Elliptical Orbit

This estimator breaks a nonlinear estimation problem into a set of over determined 'first step' states which are linear in the observations and 'second step' states which are ultimately the states of interest. Linear estimation methods are applied to filter the observations and produce the optimal first step state estimate. The 'second step' states are obtained through iterative nonlinear parameter estimation considering the first step states as observations. It has been shown that this process exactly minimizes the least squares cost function for static problems and provides a better solution than the iterated extended Kalman filter (EKF) for dynamic problems. The two step filter is applied in this paper to process range and range rate measurements between the two spacecraft. Details of the application of the two step estimator to this problem will be given, highlighting the use of a test for ill-conditioned covariance estimates that can result from the first order covariance propagation. A comparison will be made between the performance of the two step filter and the IEKF.

Garrison, James L.↗
NASA NTRS1933

Working charts for the stress analysis of elliptic rings

This report presents charts which reduce the stress analysis of circular and elliptic rings of uniform cross section subjected to balanced systems of concentrated loads from a statically indeterminate problem to a statically determinate one. To demonstrate the use of the charts in the stress analysis of elliptic rings, an illustrative problem is included.

Burke, Walter F↗
NASA NTRS1983

Parallel architectures for iterative methods on adaptive, block structured grids

A parallel computer architecture well suited to the solution of partial differential equations in complicated geometries is proposed. Algorithms for partial differential equations contain a great deal of parallelism. But this parallelism can be difficult to exploit, particularly on complex problems. One approach to extraction of this parallelism is the use of special purpose architectures tuned to a given problem class. The architecture proposed here is tuned to boundary value problems on complex domains. An adaptive elliptic algorithm which maps effectively onto the proposed architecture is considered in detail. Two levels of parallelism are exploited by the proposed architecture. First, by making use of the freedom one has in grid generation, one can construct grids which are locally regular, permitting a one to one mapping of grids to systolic style processor arrays, at least over small regions. All local parallelism can be extracted by this approach. Second, though there may be a regular global structure to the grids constructed, there will be parallelism at this level. One approach to finding and exploiting this parallelism is to use an architecture having a number of processor clusters connected by a switching network. The use of such a network creates a highly flexible architecture which automatically configures to the problem being solved.

Gannon, D.↗
NASA NTRS1985

Two-dimensional modelling of compressive failure in delaminated laminates

An analytical model is developed to assess the compressive strength criticality of near-surface interlaminar defects in laminated composites. The delaminated region is elliptic in shape, separating a thick isotropic plate from a thin orthotropic layer whose material axes coincide with the ellipse axes. The growth conditions and growth behavior of this defect are studied by breaking the overall problem into an elastic stability problem and a fracture problem. Post-buckling solution for the elliptic section is obtained using the Rayleigh-Ritz method while an energy balance criterion based on a self-similar disbond growth governs the fracture. The parameters controlling the growth or arrest of the delamination damage are identified as the fracture energy, disbond depth and elastic properties of the materials from both sides of the delaminating interface. By varying the degree of material anisotropy relative to the loading axis a range in growth behavior was found including stable or unstable crack growth parallel to or normal to the loading axis.

Chai, H.↗
NASA NTRS1996

On DGS Relaxation: The Stokes Problem

Multigrid methods have proven to be efficient methods for solving partial differential equations (especially those of elliptic type). There is also growing experience with multigrid solvers for fluids problems, e.g., the Stokes and Navier-Stokes equations (using both finite element and finite difference discretizations). It is also well known that at the heart of any multigrid method is the smoother. In this work we look at a smoother introduced by Brandt and Dinar (DGS relaxation), and we examine some of its properties and consider some possible modifications to it. It is well known that multigrid performance using DGS relaxation is sensitive to the treatment of boundaries; this issue is addressed.

Meir, A. J.↗
NASA NTRS1989

A computational challenge - Euler solution for ellipses

The Euler equations for flow past an ellipse are solved numerically. A computationally complex problem involving inviscid flow past an elliptical two-dimensional surface at subcritical Mach number and angle of attack is introduced. A lifting solution for any combination of grid and/or angle of attack which is nonsymmetric is obtained.

Pulliam, Thomas H.↗
NASA NTRS1967

[Elliptic Differential Equations]

Reflection laws of systems of elliptic equations, on-line programming to numerically solve nonlinear integral equations, and reduction of electrostriction problem

ON-LINE PROGRAMMING↗
NASA NTRS2007

Optimal Low-Thrust Limited-Power Transfers between Arbitrary Elliptic Coplanar Orbits

In this work, a complete first order analytical solution, which includes the short periodic terms, for the problem of optimal low-thrust limited-power transfers between arbitrary elliptic coplanar orbits in a Newtonian central gravity field is obtained through Hamilton-Jacobi theory and a perturbation method based on Lie series.

daSilvaFernandes, Sandro↗
NASA NTRS1984

Development of a dynamically adaptive grid method for multidimensional problems

An approach to solution adaptive grid generation for use with finite difference techniques, previously demonstrated on model problems in one space dimension, has been extended to multidimensional problems. The method is based on the popular elliptic steady grid generators, but is 'dynamically' adaptive in the sense that a grid is maintained at all times satisfying the steady grid law driven by a solution-dependent source term. Testing has been carried out on Burgers' equation in one and two space dimensions. Results appear encouraging both for inviscid wave propagation cases and viscous boundary layer cases, suggesting that application to practical flow problems is now possible. In the course of the work, obstacles relating to grid correction, smoothing of the solution, and elliptic equation solvers have been largely overcome. Concern remains, however, about grid skewness, boundary layer resolution and the need for implicit integration methods. Also, the method in 3-D is expected to be very demanding of computer resources.

Holcomb, J. E.↗
NASA NTRS1966

Elliptic motion

Newtonian theory, Keplerian law, and two-body problem applied to orbital motion

NEWTON THEORY↗
NASA NTRS1981

Transonic airfoil calculations using solution-adaptive grids

A new algorithm for generating solution-adaptive grids (SAG) about airfoil configurations embedded in transonic flow is presented. The present SAG approach uses only the airfoil surface solution to recluster grid points on the airfoil surface, i.e., the reclustering problem is one dimension smaller than the flow-field calculation problem. Special controls automatically built into the elliptic grid generation procedure are then used to obtain grids with suitable interior behavior. This concept of redistributing grid points greatly simplifies the idea of solution-adaptive grids. Numerical results indicate significant improvements in accuracy for SAG grids relative to standard grids using the same number of points.

Holst, T. L.↗