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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Data traffic reduction schemes for Cholesky factorization on asynchronous multiprocessor systems

Communication requirements of Cholesky factorization of dense and sparse symmetric, positive definite matrices are analyzed. The communication requirement is characterized by the data traffic generated on multiprocessor systems with local and shared memory. Lower bound proofs are given to show that when the load is uniformly distributed the data traffic associated with factoring an n x n dense matrix using n to the alpha power (alpha less than or equal 2) processors is omega(n to the 2 + alpha/2 power). For n x n sparse matrices representing a square root of n x square root of n regular grid graph the data traffic is shown to be omega(n to the 1 + alpha/2 power), alpha less than or equal 1. Partitioning schemes that are variations of block assignment scheme are described and it is shown that the data traffic generated by these schemes are asymptotically optimal. The schemes allow efficient use of up to O(n to the 2nd power) processors in the dense case and up to O(n) processors in the sparse case before the total data traffic reaches the maximum value of O(n to the 3rd power) and O(n to the 3/2 power), respectively. It is shown that the block based partitioning schemes allow a better utilization of the data accessed from shared memory and thus reduce the data traffic than those based on column-wise wrap around assignment schemes.

Naik, Vijay K.↗
NASA NTRS1984

Algorithms for solving large sparse systems of simultaneous linear equations on vector processors

Very efficient algorithms for solving large sparse systems of simultaneous linear equations have been developed for serial processing computers. These involve a reordering of matrix rows and columns in order to obtain a near triangular pattern of nonzero elements. Then an LU factorization is developed to represent the matrix inverse in terms of a sequence of elementary Gaussian eliminations, or pivots. In this paper it is shown how these algorithms are adapted for efficient implementation on vector processors. Results obtained on the CYBER 200 Model 205 are presented for a series of large test problems which show the comparative advantages of the triangularization and vector processing algorithms.

David, R. E.↗
NASA NTRS1994

Rarefied solids

One important limit to creating low density materials is the objects' own weight. As a solid or colloidal matrix becomes more rarefied, gravity acts destructively to compress its suporting skeleton. We describe experimental results and propose a model which matches the low gravity behavior of rarefied or fractal solids. On parabolic airplane flights, we sought to demonstrate a key component of producing higher surface area fractals. Flight paths were selected to give a range of gravity levels: 0.01 g/g(sub 0) (low), 0.16 g(sub 0) (Lunar), 0.33 g/g(sub 0) (Martian), 1 g/g(sub 0) (Earth) and 1.8 g/g(sub 0) (high) (where g(sub 0) = 980 cm/sq s). Results using the model material of hydrophobic silica indicated that stable agglomeration of such tenuous objects can increase markedly in reduced gravity. Optical characterization revealed that fractal dimension changed directly with varying gravity. As measured by fractal dimension, effective surface area and roughness increased by 40% in low gravity. This finding supports the conclusion that relieving internal weight stresses on delicate aggregates can enhance their overall size (by two orders of magnitude) and internal surface area. We conclude that gravitational restructuring limits the overall size and void content of low-density solids. These sparse colloidal regimes may present new and technologically attractive physics, ranging from improved insulators, liquid-like tension in a 'solid' matrix, and characteristically low conductivities for sound and (8 to 14 micrometers wavelength) infrared radiation.

Noever, D. A.↗
NASA NTRS1985

Multiprocessor sparse L/U decomposition with controlled fill-in

Generation of the maximal compatibles of pivot elements for a class of small sparse matrices is studied. The algorithm involves a binary tree search and has a complexity exponential in the order of the matrix. Different strategies for selection of a set of compatible pivots based on the Markowitz criterion are investigated. The competing issues of parallelism and fill-in generation are studied and results are provided. A technque for obtaining an ordered compatible set directly from the ordered incompatible table is given. This technique generates a set of compatible pivots with the property of generating few fills. A new hueristic algorithm is then proposed that combines the idea of an ordered compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. Finally, an elimination set to reduce the matrix is selected. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices are presented and analyzed.

Alaghband, G.↗
NASA NTRS2019

Electromagnetic Scattering by Discrete Random Media. III: The Vector Radiative Transfer Equation

A vector radiative transfer equation with an additional source term typical of dense media is obtained. The analysis includes (i) the derivation of an integral equation for the correlation matrix of the exciting field coefficients accounting for the correlation between the particles, (ii) the derivation of an integral representation for the specific coherency dyadicin terms of this matrix, and (iii) the simplification of the integral equation for the correlation matrix and of the integral representation for the specific coherency dyadic by employing a series of approximations which are characteristic of sparse media.

Adrian Doicu↗
NASA NTRS2002

Bench top interferometric test bed for LISA

Adaptive optics systems with Shack-Hartmann wavefront sensors require reconstruction of the atmospheric phase error from slope measurements, with every sensor in the array being used in the computation of each actuator command. This fully populated reconstruction matrix can result in a significant computational burden for adaptive optics systems with large numbers of actuators. A method for generating sparse wavefront reconstruction matrices for adaptive optics is proposed. The method exploits the relevance of nearby slope measurements for control of an individual actuator, and relies upon the limited extent of the influence function for a zonal deformable mirror. Relying only on nearby sensor information can significantly reduce the calculation time for wavefront reconstruction. In addition, a hierarchic controller is proposed to recover some of the global wavefront information. The performance of these sparse wavefront reconstruction matrices was evaluated in simulation, and tested on the Palomar Adaptive Optics System. This paper will present some initial results from the simulations and experiments.

LISA↗
NASA NTRS1985

Iterative solution of large, sparse linear systems on a static data flow architecture - Performance studies

The applicability of static data flow architectures to the iterative solution of sparse linear systems of equations is investigated. An analytic performance model of a static data flow computation is developed. This model includes both spatial parallelism, concurrent execution in multiple PE's, and pipelining, the streaming of data from array memories through the PE's. The performance model is used to analyze a row partitioned iterative algorithm for solving sparse linear systems of algebraic equations. Based on this analysis, design parameters for the static data flow architecture as a function of matrix sparsity and dimension are proposed.

Reed, D. A.↗
NASA NTRS1995

A Hybrid Finite Element Method for Axisymmetric Waveguide fed Horns

A new method for finding radiation patterns and the reflection coefficients associated with an axisymmetric waveguide fed horn is presented. The approach is based on a hybrid finite element method (FEM) wherein the electromagnetic fields in the FEM region are coupled to the fields outside by two surface integral equations. Because of the local nature of the FEM, this formalism allows for the presence of inhomogeneities to be included in the problem domain. The matrix equation which results from the application of this method is shown to be complex-symmetric. It is, furthermore, diagonally dominant and sparse. Comparisons of calculated and measured data for two different horns show good agreement.

Hybrid↗
NASA NTRS1982

Out-of-Core Solutions of Complex Sparse Linear Equations

ETCLIB is library of subroutines for obtaining out-of-core solutions of complex sparse linear equations. Routines apply to dense and sparse matrices too large to be stored in core. Useful for solving any set of linear equations, but particularly useful in cases where coefficient matrix has no special properties that guarantee convergence with any of interative processes. The only assumption made is that coefficient matrix is not singular.

Yip, E. L.↗
NASA NTRS1985

A General-applications Direct Global Matrix Algorithm for Rapid Seismo-acoustic Wavefield Computations

A new matrix method for rapid wave propagation modeling in generalized stratified media, which has recently been applied to numerical simulations in diverse areas of underwater acoustics, solid earth seismology, and nondestructive ultrasonic scattering is explained and illustrated. A portion of recent efforts jointly undertaken at NATOSACLANT and NORDA Numerical Modeling groups in developing, implementing, and testing a new fast general-applications wave propagation algorithm, SAFARI, formulated at SACLANT is summarized. The present general-applications SAFARI program uses a Direct Global Matrix Approach to multilayer Green's function calculation. A rapid and unconditionally stable solution is readily obtained via simple Gaussian ellimination on the resulting sparsely banded block system, precisely analogous to that arising in the Finite Element Method. The resulting gains in accuracy and computational speed allow consideration of much larger multilayered air/ocean/Earth/engineering material media models, for many more source-receiver configurations than previously possible. The validity and versatility of the SAFARI-DGM method is demonstrated by reviewing three practical examples of engineering interest, drawn from ocean acoustics, engineering seismology and ultrasonic scattering.

Schmidt, H.↗
NASA NTRS1989

Solving sparse triangular linear systems on parallel computers

This paper describes and compares three parallel algorithms for solving sparse triangular systems of equations. These methods involve some preprocessing overhead and are primarily of interest in solving many systems with the same coefficient matrix. The first approach is to use a fixed blocksize and form the inverse of the diagonal blocks. The second approach is to use a variable blocksize and reorder the unknowns so that the diagonal blocks are diagonal matrices. The latter technique is called level scheduling because of how it is represented in the adjacency graph, and both row-wise and jagged diagonal storage for the off-diagonal blocks are considered. These techniques are analyzed for general parallel computers and experiments are presented for the eight-processor Alliant FX/8.

Anderson, Edward↗
NASA NTRS2011

Efficient Kriging Algorithms

More efficient versions of an interpolation method, called kriging, have been introduced in order to reduce its traditionally high computational cost. Written in C++, these approaches were tested on both synthetic and real data. Kriging is a best unbiased linear estimator and suitable for interpolation of scattered data points. Kriging has long been used in the geostatistic and mining communities, but is now being researched for use in the image fusion of remotely sensed data. This allows a combination of data from various locations to be used to fill in any missing data from any single location. To arrive at the faster algorithms, sparse SYMMLQ iterative solver, covariance tapering, Fast Multipole Methods (FMM), and nearest neighbor searching techniques were used. These implementations were used when the coefficient matrix in the linear system is symmetric, but not necessarily positive-definite.

Memarsadeghi, Nargess↗
NASA NTRS2000

Quantitative image analysis of laminin immunoreactivity in skin basement membrane irradiated with 1 GeV/nucleon iron particles

We previously reported that laminin immunoreactivity in mouse mammary epithelium is altered shortly after whole-body irradiation with 0.8 Gy from 600 MeV/nucleon iron ions but is unaffected after exposure to sparsely ionizing radiation. This observation led us to propose that the effect could be due to protein damage from the high ionization density of the ion tracks. If so, we predicted that it would be evident soon after radiation exposure in basement membranes of other tissues and would depend on ion fluence. To test this hypothesis, we used immunofluorescence, confocal laser scanning microscopy, and image segmentation techniques to quantify changes in the basement membrane of mouse skin epidermis. At 1 h after exposure to 1 GeV/nucleon iron ions with doses from 0.03 to 1.6 Gy, neither the visual appearance nor the mean pixel intensity of laminin in the basement membrane of mouse dorsal skin epidermis was altered compared to sham-irradiated tissue. This result does not support the hypothesis that particle traversal directly affects laminin protein integrity. However, the mean pixel intensity of laminin immunoreactivity was significantly decreased in epidermal basement membrane at 48 and 96 h after exposure to 0.8 Gy 1 GeV/nucleon iron ions. We confirmed this effect with two additional antibodies raised against affinity-purified laminin 1 and the E3 fragment of the long-arm of laminin 1. In contrast, collagen type IV, another component of the basement membrane, was unaffected. Our studies demonstrate quantitatively that densely ionizing radiation elicits changes in skin microenvironments distinct from those induced by sparsely ionizing radiation. Such effects may might contribute to the carcinogenic potential of densely ionizing radiation by altering cellular signaling cascades mediated by cell-extracellular matrix interactions.

Non-NASA Center↗
NASA NTRS1990

Application of symbolic computations to the constitutive modeling of structural materials

In applications involving elevated temperatures, the derivation of mathematical expressions (constitutive equations) describing the material behavior can be quite time consuming, involved and error-prone. Therefore intelligent application of symbolic systems to faciliate this tedious process can be of significant benefit. Presented here is a problem oriented, self contained symbolic expert system, named SDICE, which is capable of efficiently deriving potential based constitutive models in analytical form. This package, running under DOE MACSYMA, has the following features: (1) potential differentiation (chain rule), (2) tensor computations (utilizing index notation) including both algebraic and calculus; (3) efficient solution of sparse systems of equations; (4) automatic expression substitution and simplification; (5) back substitution of invariant and tensorial relations; (6) the ability to form the Jacobian and Hessian matrix; and (7) a relational data base. Limited aspects of invariant theory were also incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet pre-defined order and simplify expressions so as to limit expression growth. Results are displayed, when applicable, utilizing index notation. SDICE was designed to aid and complement the human constitutive model developer. A number of examples are utilized to illustrate the various features contained within SDICE. It is expected that this symbolic package can and will provide a significant incentive to the development of new constitutive theories.

Arnold, Steven M.↗
NASA NTRS1986

Preconditioning matrices for Chebyshev derivative operators

The problem of preconditioning the matrices arising from pseudo-spectral Chebyshev approximations of first order operators is considered in both one and two dimensions. In one dimension a preconditioner represented by a full matrix which leads to preconditioned eigenvalues that are real, positive, and lie between 1 and pi/2, is already available. Since there are cases in which it is not computationally convenient to work with such a preconditioner, a large number of preconditioners were studied which were more sparse (in particular three and four diagonal matrices). The eigenvalues of such preconditioned matrices are compared. The results were applied to the problem of finding the steady state solution to an equation of the type u sub t = u sub x + f, where the Chebyshev collocation is used for the spatial variable and time discretization is performed by the Richardson method. In two dimensions different preconditioners are proposed for the matrix which arises from the pseudo-spectral discretization of the steady state problem. Results are given for the CPU time and the number of iterations using a Richardson iteration method for the unpreconditioned and preconditioned cases.

Rothman, Ernest E.↗
NASA NTRS1997

A Portable MPI Implementation of the SPAI Preconditioner in ISIS++

A parallel MPI implementation of the Sparse Approximate Inverse (SPAI) preconditioner is described. SPAI has proven to be a highly effective preconditioner, and is inherently parallel because it computes columns (or rows) of the preconditioning matrix independently. However, there are several problems that must be addressed for an efficient MPI implementation: load balance, latency hiding, and the need for one-sided communication. The effectiveness, efficiency, and scaling behavior of our implementation will be shown for different platforms.

Barnard, Stephen T.↗