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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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS1966

Matrix methods and automation in structural engineering

The partial differential equations of motion of shell structures subject to arbitrary loads may be extremely difficult or even impossible to solve. Since the digital computer is now an available tool for the structural engineer, current research has been directed toward methods which involve matrix formulation of large systems of algebraic equations and matrix solutions for discrete elements rather than the solution of the partial differential equations. These methods require rapid and accurate computer solutions. Recognizing the accuracy problems inherent in working with large matrices, a comprehensive survey of available computer programs was performed for large matrix inversion and for eigenvalue and eigenvector solutions under a Research Grant from the National Aeronautics and Space Administration and the techniques are developed in this paper for using these programs most efficiently for structural applications. The contents of the paper include: automation of matrix compilation, methods of very large matrix inversion and solution of simultaneous equation, and techniques for finding eigenvalues and vectors. In addition, a finite element stiffness matrix approach developed at the Denver Research Institute for both plates and shells subject to arbitrary dynamic loads is described as it was instrumented with complete automation on the digital computer.

Anita S West↗
NASA NTRS2008

Energetic Consistency and Coupling of the Mean and Covariance Dynamics

The dynamical state of the ocean and atmosphere is taken to be a large dimensional random vector in a range of large-scale computational applications, including data assimilation, ensemble prediction, sensitivity analysis, and predictability studies. In each of these applications, numerical evolution of the covariance matrix of the random state plays a central role, because this matrix is used to quantify uncertainty in the state of the dynamical system. Since atmospheric and ocean dynamics are nonlinear, there is no closed evolution equation for the covariance matrix, nor for the mean state. Therefore approximate evolution equations must be used. This article studies theoretical properties of the evolution equations for the mean state and covariance matrix that arise in the second-moment closure approximation (third- and higher-order moment discard). This approximation was introduced by EPSTEIN [1969] in an early effort to introduce a stochastic element into deterministic weather forecasting, and was studied further by FLEMING [1971a,b], EPSTEIN and PITCHER [1972], and PITCHER [1977], also in the context of atmospheric predictability. It has since fallen into disuse, with a simpler one being used in current large-scale applications. The theoretical results of this article make a case that this approximation should be reconsidered for use in large-scale applications, however, because the second moment closure equations possess a property of energetic consistency that the approximate equations now in common use do not possess. A number of properties of solutions of the second-moment closure equations that result from this energetic consistency will be established.

Cohn, Stephen E.↗
NASA NTRS1976

Optimal control of spin stabilized spacecraft with telescoping appendages

The control of a spin-stabilized spacecraft consisting of a rigid central hub and one or two movable offset telescoping booms (with end masses) is considered. The equations of rotational motion are linearized about either of two desired final states. A control law for the boom and mass position is sought such that a quadratic cost functional involving the weighted components of angular velocity plus the control is minimized when the final time is unspecified and involves the solution of the matrix Riccati algebraic equation. For three-axis control more than one offset boom (orthogonal to each other) is required. For two-axis control with a single boom offset from a symmetrical hub, an analytic solution is obtained; when this system is used for nutation decay the time constant is one order of magnitude smaller than previously achieved using non-optimal control logic. For the general case results are obtained numerically.

Bainum, P. M.↗
NASA NTRS1976

Optimal control of spin-stabilized spacecraft with telescoping appendages

The control of a spin-stabilized spacecraft consisting of a rigid central hub and one or two movable offset telescoping booms (with end masses) is considered. The equations of rotational motion are linearized about either of two desired final states. A control law for the boom end mass position is sought such that a quadratic cost functional involving the weighted components of angular velocity plus the control is minimized when the final time is unspecified and involves the solution of the matrix Riccati algebraic equation. For three axis control more than one offset boom (orthogonal to each other) is required. For two-axis control with a single boom offset from a symmetrical hub, an analytic solution is obtained; when this system is used for nutation decay the time constant is one order of magnitude smaller than previously achieved using nonoptimal control logic. For the general case results are obtained numerically.

Bainum, P. M.↗
NASA NTRS1973

Review of NASTRAN development relative to efficiency of execution

This paper reviews the development of NASTRAN relative to the efficiency of execution, with particular emphasis on those items which have changed significantly since the original release of NASTRAN. Features discussed include main and secondary storage utilization, matrix packing, matrix assembly, matrix multiplication, matrix decomposition and equation solution. Also a brief look into the future discusses the questions of faster arithmetic units and more effective storage utilization. In some cases the improvements in NASTRAN efficiency have resulted from taking advantage of hardware developments, while in other cases increased efficiency has resulted from improvements in the state of the art for data processing or matrix operations. The modular design of NASTRAN has made it possible to improve the efficiency in many parts of NASTRAN without changing the basic design of the program.

Mccormick, C. W.↗
NASA NTRS1990

Improved solution for system identification equations by Epsilon-Decomposition

Matrix eigenvalue theory is used to examine the source of ill-conditioning in linear algebraic equations. This approach highlights the crucial role played by the zero and near-zero eigenvalues and corresponding eigenvectors of poorly conditioned systems. Insight gained from this approach is used to significantly improve a recently developed solution procedure called Epsilon-Decomposition (E-D). E-D is an efficient alternative to Singular Value Decomposition (SVD) for ill-conditioned systems arising in parameter estimation and system identification studies. The efficiency of the improved E-D over SVD resides in the need to only obtain the zero and near-zero eigenvalues of the coefficient matrix as opposed to all of its eigenvalues and vectors (as required by SVD). Thus, the efficiency of E-D is significant for large matrices with small rank deficiency.

Ojalvo, Irving U.↗
DOE OSTI2025

Fast and Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices with Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

In this work, we present an efficient and scalable algorithm for performing matrix-vector multiplications (matvecs) for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint, and (2) efficient fast Fourier transform–based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80% of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Boundary layer stability calculations

In this paper numerical calculation of the spatial stability of disturbances in the parallel and nonparallel Blasius boundary layers is considered. Chebyshev polynomials are used for discretization. The problem with the boundary condition at infinity is overcome, and the resulting nonlinear matrix eigenvalue problem is attacked directly. The secondary eigenvalue problem for three-dimensional disturbances is shown to be uniformly stable, and particular solutions of this problem generated by the Orr-Sommerfeld equation are shown. A numerical solution of the nonparallel problem is considered using Chebyshev polynomials. The matrix equations are analyzed directly and the problem of uniqueness of the nonparallel correction is settled by careful application of the Fredholm alternative. Nonparallel corrections to the streamwise eigenfunction are shown.

Bridges, Thomas J.↗
NASA NTRS1975

A numerical method for determining the natural vibration characteristics of rotating nonuniform cantilever blades

A method is presented for determining the free vibration characteristics of a rotating blade having nonuniform spanwise properties and cantilever boundary conditions. The equations which govern the coupled flapwise, chordwise, and torsional motion of such a blade are solved using an integrating matrix method. By expressing the equations of motion and matrix notation, utilizing the integrating matrix as an operator, and applying the boundary conditions, the equations are formulated into an eigenvalue problem whose solutions may be determined by conventional methods. Computer results are compared with experimental data.

White, W. F., Jr.↗
DOE OSTI2026

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1984

Radiative transfer theory for active remote sensing of a layer of nonspherical particles

The radiative transfer theory is applied to calculate the scattering by a layer of randomly positioned and oriented nonspherical particles. The scattering amplitude functions of each individual particle are calculated with Waterman's T matrix method, which utilizes vector spherical wave functions for expansion of incident, scattered, and surface fields. The orientation of the particles is described by a probability density function of the Eulerian angles of rotation. A rotation matrix is used to relate the T matrix of the principal frame to that of the natural frame of the particle. The extinction matrix and phase matrix of the radiative transfer equations are expressed in terms of the T matrix elements. The extinction matrix for nonspherical particles is generally nondiagonal. There are only two attenuation rates in a specified direction of propagation. The radiative transfer equations are solved by an iterative method to first order in albedo. Numerical results are illustrated as functions of incidence angle and frequency with applications to active remote sensing.

Tsang, L.↗
DOE OSTI2024

Assessing the Feasibility of Bordered Block Diagonal Reordering in Power System Matrices using Fully Convolutional Network

In electromagnetic transient (EMT) simulations for power systems and inverter-based resources (IBRs), the arrangement of states within the system's linear equations, represented by matrix A in Ax=b, is critical. The state ordering in matrix A can highlight distinct characteristics of the system's graph, and identifying an optimal state ordering is crucial for efficient computation. The choice of state ordering, however, is dependent on the solver used, as each solver may perform optimally with different matrix patterns. With a wide array of matrix reordering algorithms available, selecting the most suitable one becomes challenging without insights into the matrix's ideal configuration. To address this, the paper proposes a fully convolutional network (FCN) to evaluate the reordering potential of the A matrix into a bordered block diagonal (BBD) pattern, which is commonly observed in power system and IBR modeling. The FCN's assessment aims to streamline the solver's operation, which in turn could substantially reduce the computational time required to find a solution.

Xia, Qianxue↗
NASA NTRS1972

Power series evaluation of transition and covariance matrices.

Reexamination power series solutions to the matrix covariance differential equation and the transition differential equation. Truncation error bounds are derived which are computationally attractive and which extend previous results. Polynomial approximations are obtained by exploiting the functional equations satisfied by the transition and covariance matrices. The series-functional equation propagation technique represents a fast and accurate alternative to the numerical integration of the time-invariant transition and covariance equations.

Bierman, G. J.↗
NASA NTRS1973

Analytical method for predicting the pressure distribution about a nacelle at transonic speeds

The formulation and development of a computer analysis for the calculation of streamlines and pressure distributions around two-dimensional (planar and axisymmetric) isolated nacelles at transonic speeds are described. The computerized flow field analysis is designed to predict the transonic flow around long and short high-bypass-ratio fan duct nacelles with inlet flows and with exhaust flows having appropriate aerothermodynamic properties. The flow field boundaries are located as far upstream and downstream as necessary to obtain minimum disturbances at the boundary. The far-field lateral flow field boundary is analytically defined to exactly represent free-flight conditions or solid wind tunnel wall effects. The inviscid solution technique is based on a Streamtube Curvature Analysis. The computer program utilizes an automatic grid refinement procedure and solves the flow field equations with a matrix relaxation technique. The boundary layer displacement effects and the onset of turbulent separation are included, based on the compressible turbulent boundary layer solution method of Stratford and Beavers and on the turbulent separation prediction method of Stratford.

Keith, J. S.↗