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DOE OSTI2023

A Comparison of Void-finding Algorithms Using Crossing Numbers

We study how well void-finding algorithms identify cosmic void regions and whether we can quantitatively and qualitatively compare the voids they find with dynamical information from the underlying matter distribution. Using the ORIGAMI algorithm to determine the number of dimensions along which dark matter particles have undergone shell crossing (crossing number) in N-body simulations from the AbacusSummit simulation suite, we identify dark matter particles that have undergone no shell crossing as belonging to voids. We then find voids in the corresponding halo distribution using two different void-finding algorithms: VoidFinder and V 2 , a ZOBOV-based algorithm. The resulting void catalogs are compared to the distribution of dark matter particles to examine how their crossing numbers depend on void proximity. While both algorithms' voids have a similar distribution of crossing numbers near their centers, we find that beyond 0.25 times the effective void radius, voids found by VoidFinder exhibit a stronger preference for particles with low crossing numbers than those found by V 2 . We examine two possible methods of mitigating this difference in efficacy between the algorithms. While we are able to partially mitigate the ineffectiveness of V 2 by using the distance from the void edge as a measure of centrality, we conclude that VoidFinder more reliably identifies dynamically distinct regions of low crossing number.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1973

Function space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs

Two existing function space algorithms, Davidon and projected gradient, are modified so that they may handle directly control variable inequality constraints. A third quasi-Newton type algorithm developed by C. G. Broyden is extended to optimal control problems. The Broyden algorithm is further modified so that it also may handle directly control variable inequality constraints. These methods along with a pure gradient and two conjugate gradient algorithms are simulated on three relatively simple yet representative bounded control problems, two of which have singular subarcs. Overall the Broyden algorithm was found to be superior. The most notable result of the study was the clear superiority of the Broyden and Davidon algorithms in producing a sharp interior control subarc.

Edge, E. R.↗

NASA NTRS1975

A boundary finding algorithm and its applications

An algorithm for locating gray level and/or texture edges in digitized pictures is presented. The algorithm is based on the concept of hypothesis testing. The digitized picture is first subdivided into subsets of picture elements, e.g., 2 x 2 arrays. The algorithm then compares the first- and second-order statistics of adjacent subsets; adjacent subsets having similar first- and/or second-order statistics are merged into blobs. By continuing this process, the entire picture is segmented into blobs such that the picture elements within each blob have similar characteristics. The boundaries between the blobs comprise the boundaries. The algorithm always generates closed boundaries. The algorithm was developed for multispectral imagery of the earth's surface. Application of this algorithm to various image processing techniques such as efficient coding, information extraction (terrain classification), and pattern recognition (feature selection) are included.

Gupta, J. N.↗

NASA NTRS1977

Performance tests of signature extension algorithms

Comparative tests were performed on seven signature extension algorithms to evaluate their effectiveness in correcting for changes in atmospheric haze and sun angle in a LANDSAT scene. Four of the algorithms were cluster matching, and two were maximum likelihood algorithms. The seventh algorithm determined the haze level in both training and recognition segments and used a set of tables calculated from an atmospheric model to determine the affine transformation that corrects the training signatures for changes in sun angle and haze level. Three of the algorithms were tested on a simulated data set, and all of the algorithms were tested on consecutive-day data.

Abotteen, R. A.↗

NASA NTRS1979

Faster fourier transformation: The algorithm of S. Winograd

The new DFT algorithm of S. Winograd is developed and presented in detail. This is an algorithm which uses about 1/5 of the number of multiplications used by the Cooley-Tukey algorithm and is applicable to any order which is a product of relatively prime factors from the following list: 2,3,4,5,7,8,9,16. The algorithm is presented in terms of a series of tableaus which are convenient, compact, graphical representations of the sequence of arithmetic operations in the corresponding parts of the algorithm. Using these in conjunction with included Tables makes it relatively easy to apply the algorithm and evaluate its performance.

Zohar, S.↗

NASA NTRS1981

Algorithm for vertical ozone profile determination for the Nimbus-4 BUV data set

A description is provided of the algorithm used by the Ozone Processing Team at NASA to process seven years of Backscatter Ultraviolet (BUV) ozone profile data. The algorithm is a modification of the original retrieval algorithm developed by Mateer (1972) to process some of the early data from the BUV experiment. Principal changes made are in the first guess selection scheme, the use of all wavelengths in the inversion, and the weighting of the various wavelengths according to the errors in the radiance estimation. It is found that the described BUV ozone profile algorithm is an extremely efficient algorithm for retrieving large amounts of satellite data. The algorithm makes full use of all the available information from the measured radiances including the longer wavelength radiances which previously had not been used.

Bhartia, P. K.↗

NASA NTRS1985

A Comparison of Three Curve Intersection Algorithms

An empirical comparison is made between three algorithms for computing the points of intersection of two planar Bezier curves. The algorithms compared are: the well known Bezier subdivision algorithm, which is discussed in Lane 80; a subdivision algorithm based on interval analysis due to Koparkar and Mudur; and an algorithm due to Sederberg, Anderson and Goldman which reduces the problem to one of finding the roots of a univariate polynomial. The details of these three algorithms are presented in their respective references.

Sederberg, T. W.↗

NASA NTRS1986

The algorithms for rational spline interpolation of surfaces

Two algorithms for interpolating surfaces with spline functions containing tension parameters are discussed. Both algorithms are based on the tensor products of univariate rational spline functions. The simpler algorithm uses a single tension parameter for the entire surface. This algorithm is generalized to use separate tension parameters for each rectangular subregion. The new algorithm allows for local control of tension on the interpolating surface. Both algorithms are illustrated and the results are compared with the results of bicubic spline and bilinear interpolation of terrain elevation data.

Schiess, J. R.↗

NASA NTRS1986

A lateral guidance algorithm to reduce the post-aerobraking burn requirements for a lift-modulated orbital transfer vehicle

A lateral guidance algorithm which controls the location of the line of intersection between the actual and desired orbital planes (the hinge line) is developed for the aerobraking phase of a lift-modulated orbital transfer vehicle. The on-board targeting algorithm associated with this lateral guidance algorithm is simple and concise which is very desirable since computation time and space are limited on an on-board flight computer. A variational equation which describes the movement of the hinge line is derived. Simple relationships between the plane error, the desired hinge line position, the position out-of-plane error, and the velocity out-of-plane error are found. A computer simulation is developed to test the lateral guidance algorithm for a variety of operating conditions. The algorithm does reduce the total burn magnitude needed to achieve the desired orbit by allowing the plane correction and perigee-raising burn to be combined in a single maneuver. The algorithm performs well under vacuum perigee dispersions, pot-hole density disturbance, and thick atmospheres. The results for many different operating conditions are presented.

Herman, G. C.↗

NASA NTRS1987

Development and application of unified algorithms for problems in computational science

A framework is presented for developing computationally unified numerical algorithms for solving nonlinear equations that arise in modeling various problems in mathematical physics. The concept of computational unification is an attempt to encompass efficient solution procedures for computing various nonlinear phenomena that may occur in a given problem. For example, in Computational Fluid Dynamics (CFD), a unified algorithm will be one that allows for solutions to subsonic (elliptic), transonic (mixed elliptic-hyperbolic), and supersonic (hyperbolic) flows for both steady and unsteady problems. The objectives are: development of superior unified algorithms emphasizing accuracy and efficiency aspects; development of codes based on selected algorithms leading to validation; application of mature codes to realistic problems; and extension/application of CFD-based algorithms to problems in other areas of mathematical physics. The ultimate objective is to achieve integration of multidisciplinary technologies to enhance synergism in the design process through computational simulation. Specific unified algorithms for a hierarchy of gas dynamics equations and their applications to two other areas: electromagnetic scattering, and laser-materials interaction accounting for melting.

Shankar, Vijaya↗

NASA NTRS1987

A parallel simulated annealing algorithm for standard cell placement on a hypercube computer

A parallel version of a simulated annealing algorithm is presented which is targeted to run on a hypercube computer. A strategy for mapping the cells in a two dimensional area of a chip onto processors in an n-dimensional hypercube is proposed such that both small and large distance moves can be applied. Two types of moves are allowed: cell exchanges and cell displacements. The computation of the cost function in parallel among all the processors in the hypercube is described along with a distributed data structure that needs to be stored in the hypercube to support parallel cost evaluation. A novel tree broadcasting strategy is used extensively in the algorithm for updating cell locations in the parallel environment. Studies on the performance of the algorithm on example industrial circuits show that it is faster and gives better final placement results than the uniprocessor simulated annealing algorithms. An improved uniprocessor algorithm is proposed which is based on the improved results obtained from parallelization of the simulated annealing algorithm.

Jones, Mark Howard↗

NASA NTRS1985

Three-dimensional algorithms for grid restructuring in Free-Lagrangian calculations

Grid restructuring algorithms which lower the price of three-dimensional Free-Lagrange calculations are presented. The algorithms are first given for the case of planar triangulated surfaces embedded in and spanning a three-dimensional region. The tetrahedra generated by this technique form a Delaunay mesh if the interplane spacing is comparable to the resolution within the planes. The algorithm can therefore be used for efficient determinations of Voronoi connections for initial grids. Modifications of the algorithm for the case of closely spaced surfaces are demonstrated in the context of restructuring algorithms which can accommodate colliding surfaces. Then, the restriction to planar surfaces is removed and regular surfaces are examined. The basic algorithm is the same, with an additional operation to project the vertices of one surface onto another. Finally, vertices on the surface are allowed to migrate anywhere in space.

Fritts, M.↗

NASA NTRS1987

A microwave radiometer weather-correcting sea ice algorithm

A new algorithm for estimating the proportions of the multiyear and first-year sea ice types under variable atmospheric and sea surface conditions is presented, which uses all six channels of the SMMR. The algorithm is specifically tuned to derive sea ice parameters while accepting error in the auxiliary parameters of surface temperature, ocean surface wind speed, atmospheric water vapor, and cloud liquid water content. Not only does the algorithm naturally correct for changes in these weather conditions, but it retrieves sea ice parameters to the extent that gross errors in atmospheric conditions propagate only small errors into the sea ice retrievals. A preliminary evaluation indicates that the weather-correcting algorithm provides a better data product than the 'UMass-AES' algorithm, whose quality has been cross checked with independent surface observations. The algorithm performs best when the sea ice concentration is less than 20 percent.

Walters, J. M.↗

NASA NTRS1987

Algorithms and programming tools for image processing on the MPP:3

This is the third and final report on the work done for NASA Grant 5-403 on Algorithms and Programming Tools for Image Processing on the MPP:3. All the work done for this grant is summarized in the introduction. Work done since August 1986 is reported in detail. Research for this grant falls under the following headings: (1) fundamental algorithms for the MPP; (2) programming utilities for the MPP; (3) the Parallel Pascal Development System; and (4) performance analysis. In this report, the results of two efforts are reported: region growing, and performance analysis of important characteristic algorithms. In each case, timing results from MPP implementations are included. A paper is included in which parallel algorithms for region growing on the MPP is discussed. These algorithms permit different sized regions to be merged in parallel. Details on the implementation and peformance of several important MPP algorithms are given. These include a number of standard permutations, the FFT, convolution, arbitrary data mappings, image warping, and pyramid operations, all of which have been implemented on the MPP. The permutation and image warping functions have been included in the standard development system library.

Reeves, Anthony P.↗

NASA NTRS1987

Unsteady transonic algorithm improvements for realistic aircraft applications

Improvements to a time-accurate approximate factorization (AF) algorithm were implemented for steady and unsteady transonic analysis of realistic aircraft configurations. These algorithm improvements were made to the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code developed at the Langley Research Center. The code permits the aeroelastic analysis of complete aircraft in the flutter critical transonic speed range. The AF algorithm of the CAP-TSD code solves the unsteady transonic small-disturbance equation. The algorithm improvements include: an Engquist-Osher (E-O) type-dependent switch to more accurately and efficiently treat regions of supersonic flow; extension of the E-O switch for second-order spatial accuracy in these regions; nonreflecting far field boundary conditions for more accurate unsteady applications; and several modifications which accelerate convergence to steady-state. Calculations are presented for several configurations including the General Dynamics one-ninth scale F-16C aircraft model to evaluate the algorithm modifications. The modifications have significantly improved the stability of the AF algorithm and hence the reliability of the CAP-TSD code in general.

Batina, John T.↗

NASA NTRS1987

Vectorizable implicit algorithms for the flux-difference split, three-dimensional Navier-Stokes equations

The computational efficiency of four vectorizable implicit algorithms is assessed when applied to calculate steady-state solutions to the three-dimensional, incompressible Navier-Stokes equations in general coordinates. Two of these algorithms are characterized as hybrid schemes; that is, they combine some approximate factorization in two coordinate directions with relaxation in the remaining spatial direction. The other two algorithms utilize an approximate factorization approach which yields two-factor algorithms for three-dimensional systems. All four algorithms are implemented in identical high-resolution upwind schemes for the flux-difference split Navier-Stokes equations. These highly nonlinear schemes are obtained by extending an implicit Total Variation Diminishing (TVD) scheme recently developed for linear one-dimensional systems of hyperbolic conservation laws to the three-dimensional Navier-Stokes equations. The computation of vortical flow over a sharp-edged, thin delta wing has been chosen as a common numerical test case. The convergence of the algorithms is discussed and the accuracy of the computed flow-field results is assessed. The validity of the present results are demonstrated by a comparison with experimental data.

Hartwich, P. M.↗

NASA NTRS1989

Systolic VLSI array for implementing the Kalman filter algorithm

A method and apparatus for processing signals representative of a complex matrix/vector equation. More particularly, signals representing an orderly sequence of the combined matrix and vector equation, known as a Kalman filter algorithm, are processed in real time in accordance with the principles of this invention. The Kalman filter algorithm is rearranged into a Faddeeva algorithm, which is a matrix-only algorithm that is modified to represent both the matrix and vector portions of the Kalman filter algorithm. The modified Faddeeva algorithm is embodied into electrical signals which are applied as inputs to a systolic array processor. The processor performs triangulation and nullification on the input signals, and delivers an output signal which is a real-time solution to the input signals.

Jaw J Chang↗

NASA NTRS1989

Group implicit concurrent algorithms in nonlinear structural dynamics

During the 70's and 80's, considerable effort was devoted to developing efficient and reliable time stepping procedures for transient structural analysis. Mathematically, the equations governing this type of problems are generally stiff, i.e., they exhibit a wide spectrum in the linear range. The algorithms best suited to this type of applications are those which accurately integrate the low frequency content of the response without necessitating the resolution of the high frequency modes. This means that the algorithms must be unconditionally stable, which in turn rules out explicit integration. The most exciting possibility in the algorithms development area in recent years has been the advent of parallel computers with multiprocessing capabilities. So, this work is mainly concerned with the development of parallel algorithms in the area of structural dynamics. A primary objective is to devise unconditionally stable and accurate time stepping procedures which lend themselves to an efficient implementation in concurrent machines. Some features of the new computer architecture are summarized. A brief survey of current efforts in the area is presented. A new class of concurrent procedures, or Group Implicit algorithms is introduced and analyzed. The numerical simulation shows that GI algorithms hold considerable promise for application in coarse grain as well as medium grain parallel computers.

Ortiz, M.↗