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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Theoretical effect of modifications to the upper surface of two NACA airfoils using smooth polynomial additional thickness distributions which emphasize leading edge profile and which vary linearly at the trailing edge

An investigation was conducted on a CDC 7600 digital computer to determine the effects of additional thickness distributions to the upper surface of airfoils. The additional thickness distribution had the form of a continuous mathematical function which disappears at both the leading edge and the trailing edge. Results were obtained at a Mach number of 0.2 with an angle of attack of 6 deg. All calculations employed the full potential flow equations for two dimensional flow. The relaxation method of Jameson was used for solution of the potential flow equations. It is shown that increasing the thickness and variations in shape increases the lift and the adverse pitching moment coefficients.

Hague, D. S.↗
NASA NTRS1979

The accurate solution of Poisson's equation by expansion in Chebyshev polynomials

A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways - by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.

Haidvogel, D. B.↗
NASA NTRS1980

On the application of a fast polynomial transform and the Chinese remainder theorem to compute a two-dimensional convolution

A fast algorithm is developed to compute two dimensional convolutions of an array of d sub 1 X d sub 2 complex number points, where d sub 2 = 2(M) and d sub 1 = 2(m-r+) for some 1 or = r or = m. This algorithm requires fewer multiplications and about the same number of additions as the conventional fast fourier transform method for computing the two dimensional convolution. It also has the advantage that the operation of transposing the matrix of data can be avoided.

Truong, T. K.↗
NASA NTRS1981

Recursive algorithms for two-dimensional smoothing using bicubic hermite polynomial

It is noted that in the past, smoothing splines originated from approximation theory have been successfully applied to data filtering and image smoothing problems. Even though the nonrecursive technique of smoothing splines gives an optimal solution, the amount of computation increases rapidly with the size of the two-dimensional data. A derivation is presented here of quarter-plane filtering algorithms that provide smoothed estimates of function values and their derivatives by fitting two-dimensional smoothing splines in a recursive manner. The derivation procedure sheds light on specific problems encountered in two-dimensional filtering problems. What is more, the amount of computation for this recursive processor increases only linearly with the size of the two-dimensional data. Because of certain approximations introduced in its derivation, this recursive processor becomes suboptimal.

Kim, C. S.↗
NASA NTRS1982

Application of a polynomial spline in higher-order accurate viscous-flow computations

A quartic spline, S(4,2), is proposed which overcomes some of the difficulties associated with the use of splines S(5,3) and S(3,1) and provides fourth-order accurate results with relatively few grid points. The accuracy of spline S(4,2) is comparable to or better than that of the fourth-order box scheme and the compact differencing scheme. The use of spline S(4,2) is suggested as a possible way of obtaining fourth-order accurate solutions to Navier-Stokes equations.

Turner, M. G.↗
NASA NTRS1987

The binary weight distribution of the extended (2 sup m, 2 sup m-4) code of Reed-Solomon code over GF(2 sup m) with generator polynomial (x-alpha sup 2) (x-alpha sup 3)

Consider an (n,k) linear code with symbols from GF(2 sup m). If each code symbol is represented by a binary m-tuple using a certain basis for GF(2 sup m), a binary (nm,km) linear code called a binary image of the original code is obtained. A lower bound is presented on the minimum weight enumerator for a binary image of the extended (2 sup m, 2 sup m -4) code of Reed-Solomon code over GF(2 sup m) with generator polynomical (x - alpha)(x- alpha squared)(x - alpha cubed) and its dual code, where alpha is a primitive element in GF(2 sup m).

Lin, Shu↗
NASA NTRS1991

A fast algorithm for control and estimation using a polynomial state-space structure

One of the major problems associated with the control of flexible structures is the estimation of system states. Since the parameters of the structures are not constant under varying loads and conditions, conventional fixed parameter state estimators can not be used to effectively estimate the states of the system. One alternative is to use a state estimator which adapts to the condition of the system. One such estimator is the Kalman filter. This filter is a time varying recursive digital filter which is based upon a model of the system being measured. This filter adapts the model according to the output of the system. Previously, the Kalman filter has only been used in an off-line capacity due to the computational time required for implementation. With recent advances in computer technology, it is becoming a viable tool for use in the on-line environment. A distributed Kalman filter implementation is described for fast estimation of the state of a flexible arm. A key issue, is the sensor structure and initial work on a distributed sensor that could be used with the Kalman filter is presented.

Shults, James R.↗
NASA NTRS1990

Implicit application of polynomial filters in a k-step Arnoldi method

The Arnoldi process is a well known technique for approximating a few eigenvalues and corresponding eigenvectors of a general square matrix. Numerical difficulties such as loss of orthogonality and assessment of the numerical quality of the approximations as well as a potential for unbounded growth in storage have limited the applicability of the method. These issues are addressed by fixing the number of steps in the Arnoldi process at a prescribed value k and then treating the residual vector as a function of the initial Arnoldi vector. This starting vector is then updated through an iterative scheme that is designed to force convergence of the residual to zero. The iterative scheme is shown to be a truncation of the standard implicitly shifted QR-iteration for dense problems and it avoids the need to explicitly restart the Arnoldi sequence. The main emphasis of this paper is on the derivation and analysis of this scheme. However, there are obvious ways to exploit parallelism through the matrix-vector operations that comprise the majority of the work in the algorithm. Preliminary computational results are given for a few problems on some parallel and vector computers.

Sorensen, D. C.↗
NASA NTRS1992

The explicit computation of integration algorithms and first integrals for ordinary differential equations with polynomials coefficients using trees

This note is concerned with the explicit symbolic computation of expressions involving differential operators and their actions on functions. The derivation of specialized numerical algorithms, the explicit symbolic computation of integrals of motion, and the explicit computation of normal forms for nonlinear systems all require such computations. More precisely, if R = k(x(sub 1),...,x(sub N)), where k = R or C, F denotes a differential operator with coefficients from R, and g member of R, we describe data structures and algorithms for efficiently computing g. The basic idea is to impose a multiplicative structure on the vector space with basis the set of finite rooted trees and whose nodes are labeled with the coefficients of the differential operators. Cancellations of two trees with r + 1 nodes translates into cancellation of O(N(exp r)) expressions involving the coefficient functions and their derivatives.

Crouch, P. E.↗