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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 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Strategies for vectorizing the sparse matrix vector product on the CRAY XMP, CRAY 2, and CYBER 205

Large, randomly sparse matrix vector products are important in a number of applications in computational chemistry, such as matrix diagonalization and the solution of simultaneous equations. Vectorization of this process is considered for the CRAY XMP, CRAY 2, and CYBER 205, using a matrix of dimension of 20,000 with from 1 percent to 6 percent nonzeros. Efficient scatter/gather capabilities add coding flexibility and yield significant improvements in performance. For the CYBER 205, it is shown that minor changes in the IO can reduce the CPU time by a factor of 50. Similar changes in the CRAY codes make a far smaller improvement.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1994

Diagonalized Lagrangian Robot Dynamics

A diagonal equation for robot dynamics is developed by combining recent mass matrix factorization results with classical Lagrangian mechanics.

working joint moments total joint rotational rates↗
NASA NTRS1972

Orbit improvement from satellite imaging data obtainable from the Mariner/Jupiter/Saturn 1977 missions

Equations of motion are established for a dynamic system in which a spacecraft flies close to and interacts with an outer planet and one or more of its satellites. For the computation of the state and mass partials needed in the orbit corrections, a set of variational equations is derived. These assume a notably compact form through the introduction of a matrix operator D. The above system of differential equations is integrated numerically on a computer.

Aksnes, K.↗
NASA NTRS1999

Strain Rate Dependent Modeling of Polymer Matrix Composites

A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. Strain rate dependent inelastic constitutive equations have been developed to model the polymer matrix, and have been incorporated into a micromechanics approach to analyze polymer matrix composites. The Hashin failure criterion has been implemented within the micromechanics results to predict ply failure strengths. The deformation model has been implemented within LS-DYNA, a commercially available transient dynamic finite element code. The deformation response and ply failure stresses for the representative polymer matrix composite AS4/PEEK have been predicted for a variety of fiber orientations and strain rates. The predicted results compare favorably to experimentally obtained values.

Goldberg, Robert K.↗
DOE OSTI2024

Impact of Reordering on the LU Factorization Performance of Bordered Block-Diagonal Sparse Matrix

Power engineers rely on computer-based simulation tools to assess grid performance and ensure security. At the core of these tools are solvers for sparse linear equations. When transformed into a bordered block-diagonal (BBD) structure, part of the sparse linear equation solving can be parallelized. This work focuses on using the Schur-complement-based method for LU factorization on BBD matrices, specifically, Jacobian matrices from large-scale systems. Our findings show that the natural ordering method outperforms the default ordering method in computational performance for each block of the BBD matrix. This observation is validated using synthetic 25k-bus and 70k-bus cases, showing a speedup of up to 38% when using natural ordering without permutation. Additionally, the impact of the number of partitions is studied, and the result shows that computational performance improves with more, smaller partitions in the BBD matrices.

BBD matrix↗
DOE OSTI2024

HHL algorithm with mapping function and enhanced sampling for model predictive control in microgrids

Here, this paper presents a refined quantum Harrow Hassidim Lloyd (HHL) algorithm for microgrid control. The first novelty of the developed method is that a mapping shift function enables the original HHL algorithm to handle general linear equations with non-singular and indefinite matrix. Second, a method of Matrix Extension for Amplifying Sampling Probabilities of Intended Solution (ME-ASPI) is proposed to design the reformulated linear algebraic equations, allowing for improved sampling efficiency of the quantum tomography in the refined HHL algorithm. Then, we applied the method to solve the model predictive control (MPC) problem in nonlinear dynamical microgrids. Specifically, with the ME-ASPI method, the refined HHL algorithm can effectively obtain the intended partial optimal control inputs for MPC. The optimization of quadratic programming problem in each time step of MPC is transformed into a linear system problem, which is addressed by the proposed quantum solver through using only partial information, with the time complexity improved from $\mathscr{O}(\mathscr{N}^{2.37286})$ classically to $\mathscr{O}(\mathscr{N}^{2} log \mathscr{N}$ x $p$ log $p)$ in quantum. Numerical examples have validated the effectiveness of the refined HHL algorithm with the proposed mapping function and the ME-ASPI method. By leveraging quantum properties, the proposed method provides a hybrid quantum–classical framework for microgrid control. This generic method can also potentially tackle many other challenges in analyzing and controlling general complex engineered systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1981

Research on numerical algorithms for large space structures

Numerical algorithms for analysis and design of large space structures are investigated. The sign algorithm and its application to decoupling of differential equations are presented. The generalized sign algorithm is given and its application to several problems discussed. The Laplace transforms of matrix functions and the diagonalization procedure for a finite element equation are discussed. The diagonalization of matrix polynomials is considered. The quadrature method and Laplace transforms is discussed and the identification of linear systems by the quadrature method investigated.

Denman, E. D.↗
NASA NTRS1995

Finite-element time evolution operator for the anharmonic oscillator

The finite-element approach to lattice field theory is both highly accurate (relative errors approximately 1/N(exp 2), where N is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly preserved at the lattice sites). In this talk I construct matrix elements for dynamical variables and for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian is H = p(exp 2)/2 + lambda q(exp 4)/4. Construction of such matrix elements does not require solving the implicit equations of motion. Low order approximations turn out to be extremely accurate. For example, the matrix element of the time evolution operator in the harmonic oscillator ground state gives a results for the anharmonic oscillator ground state energy accurate to better than 1 percent, while a two-state approximation reduces the error to less than 0.1 percent.

Milton, Kimball A.↗
NASA NTRS2007

Corrigendum: New Form of Kane's Equations of Motion for Constrained Systems

A correction to the previously published article "New Form of Kane's Equations of Motion for Constrained Systems" is presented. Misuse of the transformation matrix between time rates of change of the generalized coordinates and generalized speeds (sometimes called motion variables) resulted in a false conclusion concerning the symmetry of the generalized inertia matrix. The generalized inertia matrix (sometimes referred to as the mass matrix) is in fact symmetric and usually positive definite when one forms nonminimal Kane's equations for holonomic or simple nonholonomic systems, systems subject to nonlinear nonholonomic constraints, and holonomic or simple nonholonomic systems subject to impulsive constraints according to Refs. 1, 2, and 3, respectively. The mass matrix is of course symmetric when one forms minimal equations for holonomic or simple nonholonomic systems using Kane s method as set forth in Ref. 4.

Roithmayr, Carlos M.↗
NASA NTRS2016

Time-Dependent Stress Rupture Strength Degradation of Hi-Nicalon Fiber-Reinforced Silicon Carbide Composites at Intermediate Temperatures

The stress rupture strength of silicon carbide fiber-reinforced silicon carbide composites with a boron nitride fiber coating decreases with time within the intermediate temperature range of 700 to 950 degree Celsius. Various theories have been proposed to explain the cause of the time-dependent stress rupture strength. The objective of this paper is to investigate the relative significance of the various theories for the time-dependent strength of silicon carbide fiber-reinforced silicon carbide composites. This is achieved through the development of a numerically based progressive failure analysis routine and through the application of the routine to simulate the composite stress rupture tests. The progressive failure routine is a time-marching routine with an iterative loop between a probability of fiber survival equation and a force equilibrium equation within each time step. Failure of the composite is assumed to initiate near a matrix crack and the progression of fiber failures occurs by global load sharing. The probability of survival equation is derived from consideration of the strength of ceramic fibers with randomly occurring and slow growing flaws as well as the mechanical interaction between the fibers and matrix near a matrix crack. The force equilibrium equation follows from the global load sharing presumption. The results of progressive failure analyses of the composite tests suggest that the relationship between time and stress-rupture strength is attributed almost entirely to the slow flaw growth within the fibers. Although other mechanisms may be present, they appear to have only a minor influence on the observed time-dependent behavior.

Progressive Failure Analysis↗
NASA NTRS2015

A Numerical Solution Routine for Investigating Oxidation-Induced Strength Degradation Mechanisms in SiC/SiC Composites

The stress rupture strength of silicon carbide fiber-reinforced silicon carbide (SiCSiC) composites with a boron nitride (BN) fiber coating decreases with time within the intermediate temperature range of 700-950 C. Various theories have been proposed to explain the cause of the time dependent stress rupture strength. Some previous authors have suggested that the observed composite strength behavior is due to the inherent time dependent strength of the fibers, which is caused by the slow growth of flaws within the fibers. Flaw growth is supposedly enabled by oxidation of free carbon at the grain boundaries. The objective of this paper is to investigate the relative significance of the various theories for the time-dependent strength of SiCSiC composites. This is achieved through the development of a numerically-based progressive failure analysis routine and through the application of the routine to simulate the composite stress rupture tests. The progressive failure routine is a time marching routine with an iterative loop between a probability of fiber survival equation and a force equilibrium equation within each time step. Failure of the composite is assumed to initiate near a matrix crack and the progression of fiber failures occurs by global load sharing. The probability of survival equation is derived from consideration of the strength of ceramic fibers with randomly occurring and slow growing flaws as well as the mechanical interaction between the fibers and matrix near a matrix crack. The force equilibrium equation follows from the global load sharing presumption. The results of progressive failure analyses of the composite tests suggest that the relationship between time and stress-rupture strength is attributed almost entirely to the slow flaw growth within the fibers. Although other mechanisms may be present, they appear to have only a minor influence on the observed time dependent behavior.

degradation↗
DOE OSTI2020

Fast matrix algebra for Bayesian model calibration

In Bayesian model calibration, evaluation of the likelihood function usually involves finding the inverse and determinant of a covariance matrix. When Markov Chain Monte Carlo (MCMC) methods are used to sample from the posterior, hundreds of thousands of likelihood evaluations may be required. In this paper, we demonstrate that the structure of the covariance matrix can be exploited, leading to substantial time savings in practice. Here, we also derive two simple equations for approximating the inverse of the covariance matrix in this setting, which can be computed in near-quadratic time. The practical implications of these strategies are demonstrated using a simple numerical case study and the "quack" R package. For a covariance matrix with 1000 rows, application of these strategies for a million likelihood evaluations leads to a speedup of roughly 4000 compared to the naive implementation

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

In this study involving advanced fluid flow codes, an incremental iterative formulation (also known as the delta or correction form) together with the well-known spatially-split approximate factorization algorithm, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For smaller 2D problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods are needed for larger 2D and future 3D applications, however, because direct methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioning of the coefficient matrix; this problem can be overcome when these equations are cast in the incremental form. These and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two sample airfoil problems: (1) subsonic low Reynolds number laminar flow; and (2) transonic high Reynolds number turbulent flow.

Taylor, Arthur C., III↗
DOE OSTI2020

A model for discrete fracture-clay rock interaction incorporating electrostatic effects on transport

Abstract A model based on the code CrunchClay is presented for a fracture-clay matrix system that takes electrostatic effects on transport into account. The electrostatic effects on transport include those associated with the development of a diffusion potential as captured by the Nernst-Planck equation, and the formation of a diffuse layer bordering negatively charged clay particles within which partial anion exclusion occurs. The model is based on a dual continuum formulation that accounts for diffuse layer and bulk water pore space, providing a more flexible framework than is found in the classical mean electrostatic potential models. The diffuse layer model is obtained by volume averaging ion concentrations in the Poisson-Boltzmann equation, but also includes the treatment of longitudinal transport within this continuum. The calculation of transport within the bulk and diffuse layer porosity is based on a new formulation for the Nernst-Planck equation that considers averaging of diffusion coefficients and accumulation factors at grid cell interfaces. Equations for function residuals and the associated Jacobian matrix are presented such that the system of nonlinear differential-algebraic equations can be solved with Newton’s method. As an example, we consider a 2D system with a single discrete fracture within which flow and advective transport occurs that is coupled to diffusion in the clay-rich matrix. The simulation results demonstrate the lack of retardation for anions (e.g., 36 Cl − ) of the contaminant plume within the fracture flow system because they are largely excluded from the charged clay rock, while the migration of cations (e.g., 90 Sr ++ ) is more strongly attenuated. The diffusive loss of divalent cations in particular from the fracture is accentuated by their accumulation in the diffuse layer within the clay-rich matrix.

58 GEOSCIENCES↗
DOE OSTI2023

Adjoint DSMC for nonlinear spatially-homogeneous Boltzmann equation with a general collision model

We derive an adjoint method for the Direct Simulation Monte Carlo (DSMC) method for the spatially homogeneous Boltzmann equation with a general collision law. This generalizes our previous results in Caflisch et al., which was restricted to the case of Maxwell molecules, for which the collision rate is constant. The main difficulty in generalizing the previous results is that a rejection sampling step is required in the DSMC algorithm in order to handle the variable collision rate. We find a new term corresponding to the so-called score function in the adjoint equation and a new adjoint Jacobian matrix capturing the dependence of the collision parameter on the velocities. The new formula works for a much more general class of collision models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Predicting the tensile and compressive modulus of electrospun fiber mat‐reinforced hydrogels using the Halpin–Tsai equations

Abstract The reinforcement of mechanically‐weak hydrogels to yield composites with increased stiffness, strength, or toughness is a well‐established approach. In particular, introducing electrospun nanofibers into hydrogels is a common strategy for biomedical applications, as the resulting hierarchical structure mimics biology and allows for control over fiber diameter and alignment and tuning of mechanical properties. However, further study of the link between the constituent materials and the mechanical properties of the composite is uncommon. One potential model to understand the mechanical properties of fiber‐reinforced hydrogels involves the Halpin–Tsai equations, which relate the modulus values of the fibers and hydrogel matrix and the fiber volume fraction, to the modulus of the composite. To assess the application of this model to fiber‐reinforced hydrogels, predicted values were compared with experimental values from mechanical testing of a poly(ethylene glycol) (PEG) matrix reinforced with an electrospun polycaprolactone (PCL) fiber mat. Although the equations described these systems well in tension, providing a facile approach to identify a fiber volume fraction that will achieve a desired modulus, the Halpin–Tsai approach was less successful under compression. This study motivates additional investigation of the role of structural features of hydrogel composites in determining mechanical properties to enable design of materials for specific applications.

Polymer Science↗
NASA NTRS1989

Unified micromechanics of damping for unidirectional fiber reinforced composites

An integrated micromechanics methodology for the prediction of damping capacity in fiber-reinforced polymer matrix unidirectional composites has been developed. Explicit micromechanics equations based on hysteretic damping are presented relating the on-axis damping capacities to the fiber and matrix properties and volume fraction. The damping capacities of unidirectional composites subjected to off-axis loading are synthesized from thermal effect on the damping performance of unidirectional composites due to temperature and moisture variations is also modeled. The damping contributions from interfacial friction between broken fibers and matrix are incorporated. Finally, the temperature rise in continuously vibrating composite plies is estimated. Application examples illustrate the significance of various parameters on the damping performance of unidirectional and off-axis fiber reinforced composites.

Saravanos, D. A.↗