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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Finite elements and the method of conjugate gradients on a concurrent processor

An algorithm for the iterative solution of finite element problems on a concurrent processor is presented. The method of conjugate gradients is used to solve the system of matrix equations, which is distributed among the processors of a MIMD computer according to an element-based spatial decomposition. This algorithm is implemented in a two-dimensional elastostatics program on the Caltech Hypercube concurrent processor. The results of tests on up to 32 processors show nearly linear concurrent speedup, with efficiencies over 90 percent for sufficiently large problems.

Lyzenga, G. A.↗
NASA NTRS1987

Growth process of gamma'-particles in a liquid-quenched Ni-15 at percent Al alloy

The growth of gamma-prime particles in a supersaturated Ni-15 at% Al alloy prepared by the liquid-quench method was studied using a magnetic mass balance, transmission electron microscopy, and field ion microscopy. Three stages in the precipitation and growth of these particles are demonstrated. In the first phase, the gamma-prime phase was produced by nucleation of spinodal decomposition of the alloy. In the second stage, spherical gamma-prime particles were arranged at random in the matrix with the size independent of aging time. Then, the Al concentration in the matrix decreased with the -1/3 power of the aging time. These results suggest that the degree of ordering increases with aging time. In the third stage, the particles were coarsened with aging time. They were arranged in the matrix (100) zone and were cubic, with the cube face lying on (100). The interfacial free energy was 28.4 mJ/sq m at 873 K and 22.4 mJ/sq m at 973 K.

Tachikake, A.↗
NASA NTRS1998

A Parallel Non-Overlapping Domain-Decomposition Algorithm for Compressible Fluid Flow Problems on Triangulated Domains

This paper considers an algebraic preconditioning algorithm for hyperbolic-elliptic fluid flow problems. The algorithm is based on a parallel non-overlapping Schur complement domain-decomposition technique for triangulated domains. In the Schur complement technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. This suggests a reordering of triangulation vertices which separates subdomain and interface solution unknowns. The reordering induces a natural 2 x 2 block partitioning of the discretization matrix. Exact LU factorization of this block system yields a Schur complement matrix which couples subdomains and the interface together. The remaining sections of this paper present a family of approximate techniques for both constructing and applying the Schur complement as a domain-decomposition preconditioner. The approximate Schur complement serves as an algebraic coarse space operator, thus avoiding the known difficulties associated with the direct formation of a coarse space discretization. In developing Schur complement approximations, particular attention has been given to improving sequential and parallel efficiency of implementations without significantly degrading the quality of the preconditioner. A computer code based on these developments has been tested on the IBM SP2 using MPI message passing protocol. A number of 2-D calculations are presented for both scalar advection-diffusion equations as well as the Euler equations governing compressible fluid flow to demonstrate performance of the preconditioning algorithm.

Barth, Timothy J.↗
NASA NTRS2009

Origins of Magnetite Nanocrystals in Martian Meteorite ALH84001

The Martian meteorite ALH84001 preserves evidence of interaction with aqueous fluids while on Mars in the form of microscopic carbonate disks. These carbonate disks are believed to have precipitated 3.9 Ga ago at beginning of the Noachian epoch on Mars during which both the oldest extant Martian surfaces were formed, and perhaps the earliest global oceans. Intimately associated within and throughout these carbonate disks are nanocrystal magnetites (Fe3O4) with unusual chemical and physical properties, whose origins have become the source of considerable debate. One group of hypotheses argues that these magnetites are the product of partial thermal decomposition of the host carbonate. Alternatively, the origins of mag- netite and carbonate may be unrelated; that is, from the perspective of the carbonate the magnetite is allochthonous. For example, the magnetites might have already been present in the aqueous fluids from which the carbonates were believed to have been deposited. We have sought to resolve between these hypotheses through the detailed characterized of the compo- sitional and structural relationships of the carbonate disks and associated magnetites with the orthopyroxene matrix in which they are embedded. Extensive use of focused ion beam milling techniques has been utilized for sample preparation. We then compared our observations with those from experimental thermal decomposition studies of sideritic carbonates under a range of plausible geological heating scenarios. We conclude that the vast majority of the nanocrystal magnetites present in the car- bonate disks could not have formed by any of the currently proposed thermal decomposition scenarios. Instead, we find there is considerable evidence in support of an alternative allochthonous origin for the magnetite unrelated to any shock or thermal processing of the carbonates.

Thomas-Keprta, Kathie L.↗
NASA NTRS1993

Application of the target decomposition theorem to a polarimetric random media model

With advances in polarimetric radar measurements of land surfaces, the need for understanding the underlying scattering mechanisms and dominant target features has become the focus of many studies. In particular, the maximum use of the polarimetric information to identify and/or separate parameters related to the surface features such as vegetation thickness, structure, water content, and soil surface characteristics will enhance the possibility of using polarimetric radars for monitoring the earth's surface from space. In this paper, Cloude's decomposition theorem is applied to a polarimetric random media model to simulate the radar measurements of vegetated canopies. The vegetated canopies are modeled as a three layer discrete random medium with leaves and branches in the first layer, tree trunks in the second layer, and a half space of homogeneous ground with rough interface as the bottom layer. The distorted born approximation (DBA) has been used to compute full Mueller matrix of the canopy, using canonical dielectric objects such as thin discs and cylinders as leaves, branches, and trunks, respectively. The Mueller matrix and the derived covariance matrix contain information on the second order statistics of radar signals at various polarizations from the canopy. To decompose the covariance matrix to its constituent targets, the eigenvalues and eigenvectors of the covariance matrix are computed in terms of the physical parameters of the canopy. In addition, each eigenvector explicitly shows the scattering mechanisms such as odd and even reflections in the canopy. Cloude's decomposition theorem is applied using the Pauli spin matrices as a basis and an expression for the degree of disorder or the entropy for the vegetated surface is found. Then, the physical parameters estimated from in situ measurements are used in the random media to obtain realistic covariance matrices. As a result, the sensitivity of the eigenvalue spectrums and the coefficients resulting from the target decomposition theorem to the physical parameters of the canopy are examined and the possible use of Cloude's theorem to estimate vegetation and soil parameters is discussed.

Saatchi, Sasan S.↗
NASA NTRS1983

Asymptotic unbounded root loci - Formulas and computation

A new geometric way of computing the asymptotic behavior of unbounded root loci of a strictly proper linear time-invariant control system as loop gain goes to infinity is presented. Properties of certain restricted linear maps and nested restrictions of linear maps are developed, and formulas are obtained for the leading coefficient of the asymptotic values of the unbounded multivariable root loci are obtained in terms of eigenvalues of those maps. Published results and a certain simple null structure assumption are used to relate these asymptotic values to the structure at infinity of the Smith-McMillan form of the open loop transfer function. Explicit matrix formulas for the more abstract derived formulas are given and additional geometric insights are developed with orthogonal projections and singular value decomposition. Formulas for the pivots of the unbounded root loci are calculated and shown to have the same form as the coefficients of the unbounded asymptotic root loci.

Sastry, S. S.↗
NASA NTRS1986

Use of laboratory simulated pyrolysis in tracing the history of sedimentary organic matter

Results from laboratory simulated pyrolyses experiments show that in addition to depth of burial, preservation of kerogen, and hence any morphologic structure in it, is also dependent on the mineral matrix with which it is associated. In the presence of clay minerals, and especially under dry conditions, extractable lipids released during kerogen decomposition are more rapidly destroyed than in the presence of calcite or chert matrices. The result is production of gas, polar bitumen and pyrobitumen and destruction of biomarkers. During such an early reorganization of the kerogen, the biomarker constituents can be destroyed, or unrecognizably altered. The above process of organic residues maturation appears to be inhibited in the presence of water and is significantly reduced where kerogen is hosted in limestones, dolomites or cherts. These minerals have been characteristically found to be the most reliable in yielding morphological fossils and small quantities of extractable bitumen in Archean and Proterozoic rocks. To understand the validity of chemical and morphological fossils, in the early geologic record, it will be necessary to understand the process of kerogen in sedimentary rocks. To test the role of various minerals on the preservation process, kerogen extracted from a variety of rocks has been heated together with montmorillonite, illite and calcite. The kinetics of the process has been monitored and the products quantitatively identified.

Kaplan, I. R.↗
NASA NTRS1987

Robust eigensystem assignment for flexible structures

An improved method is developed for eigenvalues and eigenvectors placement of a closed-loop control system using either state or output feedback. The method basically consists of three steps. First, the singular value of QR decomposition is used to generate an orthonormal basis that spans admissible eigenvector space corresponding to each assigned eigenvalue. Secondly, given a unitary matrix, the eigenvector set which best approximates the given matrix in the least-square sense and still satisfy eigenvalue cosntraints is determined. Thirdly, a unitary matrix is sought to minimize the error between the unitary matrix and the assignable eigenvector matrix. For use as the desired eigenvector set, two matrices, namely, the open-loop eigenvector matrix and its closest unitary matrix are proposed. The latter matrix generally encourages both minimum conditioning and control gains. In addition, the algorithm is formulated in real arithmetic for efficient implementation. To illustrate the basic concepts, numerical examples are included.

Juang, Jer-Nan↗
NASA NTRS1989

An interpretation and solution of ill-conditioned linear equations

Data insufficiency, poorly conditioned matrices and singularities in equations occur regularly in complex optimization, correlation, and interdisciplinary model studies. This work concerns itself with two methods of obtaining certain physically realistic solutions to ill-conditioned or singular algebraic systems of linear equations arising from such studies. Two efficient computational solution procedures that generally lead to locally unique solutions are presented when there is insufficient data to completely define the model, or a least-squares error formulation of this system results in an ill-conditioned system of equations. If it is assumed that a reasonable estimate of the uncertain data is available in both cases cited above, then we shall show how to obtain realistic solutions efficiently, in spite of the insufficiency of independent data. The proposed methods of solution are more efficient than singular-value decomposition for dealing with such systems, since they do not require solutions for all the non-zero eigenvalues of the coefficient matrix.

Ojalvo, I. U.↗
NASA NTRS2012

The Role of (Delta)C-13 in the Search for Reduced Organics on the Surface of Mars

The capabilities of the Sample Analysis at Mars (SAM) instrument suite on the Mars Science Laboratory (MSL) to detect trace amounts of organic carbon compounds are unprecedented, and MSL may be the first mission to reveal the presence of organic carbon on Mars. The search for reduced organic carbon on Mars is inextricably tied to: a) the preservation potential of the environment from which we take a solid sample, and b) the evolved gas analysis (EGA) techniques used by SAM to release volatiles from this solid sample. Several prospective targets have been identified for sample analysis at Gale Crater. Stratigraphic sequences of phyllosilicates and sulfates at Gale are thought to represent a period of global climate transition from a moderate pH lacustrine environment to an evaporitic environment, both of which could sequester organic carbon (Thomson et al. 2011). The sediment mound in Gale Crater contains a range of lithologies suggesting changes in redox conditions, and evidence of both lacustrine and fluvial depositional processes, which may have transported organic carbon from the layer in which it formed and resulted in its preservation elsewhere within the crater (Anderson and Bell, 2010). Inverted channel fills suggest erosion resistant material that could serve to preserve organics originally deposited in a low energy aqueous environment. The lithology sampled will affect not only the preservation of organics, but also our ability to detect organics during our evolved gas analysis, based on the sample matrix. For example, reduced organics may be trapped in the mineral structure, and thermal evolution of these organics will occur during thermal decomposition of the host mineral. If organics are occluded in minerals that have very high thermal decomposition temperatures, they may be, in effect, "too well preserved," and difficult to detect during EGA. Alternatively, the possible presence of perchlorate, or other strong oxidants in surface regolith, may result in destruction of structural information identifying organic molecules before reaching the QMS on SAM via oxidation to C02 during heating. If this is the case, the stable carbon isotopic composition (delta 13C) of the C02 evolved and measured by the Tunable Laser Spectrometer (TLS) on SAM may help identify the presence of organics. On Earth, biological activity can cause large fractionations of 13C/12C, which can preserved in sedimentary deposits and distinguish the organic products of biotic processes from inorganic atmospheric and geological reservoirs. It is plausible that similar fractionations could occur on Mars and be preserved in reduced organic matter in sediments. Bulk delta 13C measurements alone may not reveal a signature of trace organic carbon that may be present along with inorganic carbon. If both organic and inorganic carbon compounds are present, it may be possible to detect the organic carbon by comparing the 013C of pyrolysis and combustion experiments. The TLS on SAM is capable of obtaining high precision measurements of delta13C from C02 evolved during pyrolysis and combustion of solid regolith samples. Because carbonates are expected to be present at abundances of 0.1-1 % in Martian soil, and organics in the ppb range (Webster and Mahaffy, 2011), analog samples must represent this mix of reduced organic carbon and carbonate. The work presented here will examine the use of delta13C of C02 produced during combustion of bulk Mars analog samples as a proxy for detection of reduced organic carbon.

Stern, J. C.↗
NASA NTRS2010

Probabilistic Round Trip Contamination Analysis of a Mars Sample Acquisition and Handling Process Using Markovian Decompositions

A method for evaluating the probability of a Viable Earth Microorganism (VEM) contaminating a sample during the sample acquisition and handling (SAH) process of a potential future Mars Sample Return mission is developed. A scenario where multiple core samples would be acquired using a rotary percussive coring tool, deployed from an arm on a MER class rover is analyzed. The analysis is conducted in a structured way by decomposing sample acquisition and handling process into a series of discrete time steps, and breaking the physical system into a set of relevant components. At each discrete time step, two key functions are defined: The probability of a VEM being released from each component, and the transport matrix, which represents the probability of VEM transport from one component to another. By defining the expected the number of VEMs on each component at the start of the sampling process, these decompositions allow the expected number of VEMs on each component at each sampling step to be represented as a Markov chain. This formalism provides a rigorous mathematical framework in which to analyze the probability of a VEM entering the sample chain, as well as making the analysis tractable by breaking the process down into small analyzable steps.

Hudson, Nicolas↗
NASA NTRS1988

Eigenstructure assignment for the control of highly augmented aircraft

Eigenstructure assignment is utilized to design flight control laws for aircraft with many control effectors. It is shown that a previous eigenstructure design for the flight propulsion control coupling (FPCC) aircraft lateral dynamics with three control surfaces exhibits a lack of stability robustness because the control distribution matrix is nearly rank-deficient. A method is mapped back, reducing the control space to two dimensions by using the singular value decomposition. After the design is complete, the controller is mapped back to the original three-dimensional control space. This design approach yields a controller with both smaller gains and improved multivariable stability margins at the aircraft inputs. An interesting characteristics of the control mapping, as applied to the given example, is that the most effective inputs have the larger gains while the less effective inputs have smaller gains.

Sobel, Kenneth M.↗
NASA NTRS1993

Preconditioned domain decomposition scheme for three-dimensional aerodynamic sensitivity analysis

A preconditioned domain decomposition scheme is introduced for the solution of the 3D aerodynamic sensitivity equation. This scheme uses the iterative GMRES procedure to solve the effective sensitivity equation of the boundary-interface cells in the sensitivity analysis domain-decomposition scheme. Excluding the dense matrices and the effect of cross terms between boundary-interfaces is found to produce an efficient preconditioning matrix.

Eleshaky, Mohammed E.↗
NASA NTRS1995

Development of Fast Algorithms Using Recursion, Nesting and Iterations for Computational Electromagnetics

In the first phase of our work, we have concentrated on laying the foundation to develop fast algorithms, including the use of recursive structure like the recursive aggregate interaction matrix algorithm (RAIMA), the nested equivalence principle algorithm (NEPAL), the ray-propagation fast multipole algorithm (RPFMA), and the multi-level fast multipole algorithm (MLFMA). We have also investigated the use of curvilinear patches to build a basic method of moments code where these acceleration techniques can be used later. In the second phase, which is mainly reported on here, we have concentrated on implementing three-dimensional NEPAL on a massively parallel machine, the Connection Machine CM-5, and have been able to obtain some 3D scattering results. In order to understand the parallelization of codes on the Connection Machine, we have also studied the parallelization of 3D finite-difference time-domain (FDTD) code with PML material absorbing boundary condition (ABC). We found that simple algorithms like the FDTD with material ABC can be parallelized very well allowing us to solve within a minute a problem of over a million nodes. In addition, we have studied the use of the fast multipole method and the ray-propagation fast multipole algorithm to expedite matrix-vector multiplication in a conjugate-gradient solution to integral equations of scattering. We find that these methods are faster than LU decomposition for one incident angle, but are slower than LU decomposition when many incident angles are needed as in the monostatic RCS calculations.

Chew, W. C.↗
NASA NTRS1983

Accuracy and resolution of Earth Radiation Budget Estimates

A numerical filter inversion technique that reduces wide-angle satellite measurements to top-of-the-atmosphere radiant exitances has been proposed for the Earth Radiation Budget Experiment (ERBE). The matrix formulation of this technique is presented, and the design of the numerical filter is discussed. The filter is smoothed with a singular value decomposition. The inversion process is simulated by generating synthetic measurements from a 24 degree spherical harmonic radiation field derived from Nimbus 6 ERB data. The numerical filter is applied to these measurements after they are corrupted with instrument error. The results are curves of expected error versus resolution area.

Green, R. N.↗
NASA NTRS2010

Decomposition Algorithm for Global Reachability on a Time-Varying Graph

A decomposition algorithm has been developed for global reachability analysis on a space-time grid. By exploiting the upper block-triangular structure, the planning problem is decomposed into smaller subproblems, which is much more scalable than the original approach. Recent studies have proposed the use of a hot-air (Montgolfier) balloon for possible exploration of Titan and Venus because these bodies have thick haze or cloud layers that limit the science return from an orbiter, and the atmospheres would provide enough buoyancy for balloons. One of the important questions that needs to be addressed is what surface locations the balloon can reach from an initial location, and how long it would take. This is referred to as the global reachability problem, where the paths from starting locations to all possible target locations must be computed. The balloon could be driven with its own actuation, but its actuation capability is fairly limited. It would be more efficient to take advantage of the wind field and ride the wind that is much stronger than what the actuator could produce. It is possible to pose the path planning problem as a graph search problem on a directed graph by discretizing the spacetime world and the vehicle actuation. The decomposition algorithm provides reachability analysis of a time-varying graph. Because the balloon only moves in the positive direction in time, the adjacency matrix of the graph can be represented with an upper block-triangular matrix, and this upper block-triangular structure can be exploited to decompose a large graph search problem. The new approach consumes a much smaller amount of memory, which also helps speed up the overall computation when the computing resource has a limited physical memory compared to the problem size.

Kuwata, Yoshiaki↗
NASA NTRS2002

Decomposition-Based Failure Mode Identification Method for Risk-Free Design of Large Systems

When designing products, it is crucial to assure failure and risk-free operation in the intended operating environment. Failures are typically studied and eliminated as much as possible during the early stages of design. The few failures that go undetected result in unacceptable damage and losses in high-risk applications where public safety is of concern. Published NASA and NTSB accident reports point to a variety of components identified as sources of failures in the reported cases. In previous work, data from these reports were processed and placed in matrix form for all the system components and failure modes encountered, and then manipulated using matrix methods to determine similarities between the different components and failure modes. In this paper, these matrices are represented in the form of a linear combination of failures modes, mathematically formed using Principal Components Analysis (PCA) decomposition. The PCA decomposition results in a low-dimensionality representation of all failure modes and components of interest, represented in a transformed coordinate system. Such a representation opens the way for efficient pattern analysis and prediction of failure modes with highest potential risks on the final product, rather than making decisions based on the large space of component and failure mode data. The mathematics of the proposed method are explained first using a simple example problem. The method is then applied to component failure data gathered from helicopter, accident reports to demonstrate its potential.

Tumer, Irem Y.↗
NASA NTRS1974

Derivatives of eigenvalues and eigenvectors for a general matrix

Expressions are obtained for the derivatives of the eigenvalues and eigenvectors which are expressions of only one left-hand and one right-hand eigenvector. The approach described makes use of a Choleski decomposition or some other decomposition method. The method may be extended to find any order of derivative of the eigenvalue and eigenvector. The expressions obtained for finding the derivatives of eigenvalues and eigenvectors for nonself-adjoint systems may be applied to self-adjoint systems.

Rudisill, C. S.↗