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Results for “eigenvalue method”

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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Two-Stage Reduction Of Dynamical Models

No longer necessary to solve eigenvalue problems of high order. Component-mode projection-and-assembly model-reduction (COMPARE) method provides approximation of dynamics of vibrations of complicated, multiple flexible bodies by use of mathematical models of reduced order. Incorporates component-mode synthesis (CMS) method and enhanced projection-and-assembly (EP&A) method, described in "Enhanced Method of Reduction of Dynamical Models" (NPO-18402), providing for somewhat simplified two-stage process in which order of applicable mathematical models reduced. Reduced-order models used to design algorithms of control systems to suppress vibrations or otherwise control structure.

Lee, Allan Y.↗
NASA NTRS2015

Advanced Background Subtraction Applied to Aeroacoustic Wind Tunnel Testing

An advanced form of background subtraction is presented and applied to aeroacoustic wind tunnel data. A variant of this method has seen use in other fields such as climatology and medical imaging. The technique, based on an eigenvalue decomposition of the background noise cross-spectral matrix, is robust against situations where isolated background auto-spectral levels are measured to be higher than levels of combined source and background signals. It also provides an alternate estimate of the cross-spectrum, which previously might have poor definition for low signal-to-noise ratio measurements. Simulated results indicate similar performance to conventional background subtraction when the subtracted spectra are weaker than the true contaminating background levels. Superior performance is observed when the subtracted spectra are stronger than the true contaminating background levels. Experimental results show limited success in recovering signal behavior for data where conventional background subtraction fails. They also demonstrate the new subtraction technique's ability to maintain a proper coherence relationship in the modified cross-spectral matrix. Beam-forming and de-convolution results indicate the method can successfully separate sources. Results also show a reduced need for the use of diagonal removal in phased array processing, at least for the limited data sets considered.

Bahr, Christopher J.↗
NASA NTRS1990

Numerical methods for hypersonic boundary layer stability

Four different schemes for solving compressible boundary layer stability equations are developed and compared, considering both the temporal and spatial stability for a global eigenvalue spectrum and a local eigenvalue search. The discretizations considered encompass: (1) a second-order-staggered finite-difference scheme; (2) a fourth-order accurate, two-point compact scheme; (3) a single-domain Chebychev spectral collocation scheme; and (4) a multidomain spectral collocation scheme. As Mach number increases, the performance of the single-domain collocation scheme deteriorates due to the outward movement of the critical layer; a multidomain spectral method is accordingly designed to furnish superior resolution of the critical layer.

Malik, M. R.↗
NASA NTRS1991

Methods for evaluating the predictive accuracy of structural dynamic models

Modeling uncertainty is defined in terms of the difference between predicted and measured eigenvalues and eigenvectors. Data compiled from 22 sets of analysis/test results was used to create statistical databases for large truss-type space structures and both pretest and posttest models of conventional satellite-type space structures. Modeling uncertainty is propagated through the model to produce intervals of uncertainty on frequency response functions, both amplitude and phase. This methodology was used successfully to evaluate the predictive accuracy of several structures, including the NASA CSI Evolutionary Structure tested at Langley Research Center. Test measurements for this structure were within + one-sigma intervals of predicted accuracy for the most part, demonstrating the validity of the methodology and computer code.

Hasselman, Timothy K.↗
NASA NTRS2017

Subspace-based Background Subtraction Applied to Aeroacoustic Wind Tunnel Testing

A subspace-based form of background subtraction is presented and applied to aeroacoustic wind tunnel data. A variant of this method has seen use in other fields such as climatology and medical imaging. The technique is based on an eigenvalue decomposition of the background noise cross-spectral matrix. Simulated results indicate similar performance to conventional background subtraction when the subtracted spectra are weaker than the true contaminating background levels. Superior performance is observed when the subtracted spectra are stronger than the true contaminating background levels, and when background data do not match between measurements. Experimental results show limited success in recovering signal behavior for data in which conventional background subtraction fails. The results also demonstrate the subspace subtraction technique's ability to maintain a physical coherence relationship in the modified cross-spectral matrix. Deconvolution results from microphone phased array data indicate that array integration methods are largely insensitive to subtraction type, and that background subtraction with appropriate background data is an effective alternative to diagonal removal.

deconvolution↗
NASA NTRS1999

Practical Aspects of Stabilized FEM Discretizations of Nonlinear Conservation Law Systems with Convex Extension

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the Galerkin least-squares (GLS) and the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the POE system. Central to the development of the simplified GLS and DG methods is the Degenerative Scaling Theorem which characterizes right symmetrizes of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobean matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler, Navier-Stokes, and magnetohydrodynamic (MHD) equations. Linear and nonlinear energy stability is proven for the simplified GLS and DG methods. Spatial convergence properties of the simplified GLS and DO methods are numerical evaluated via the computation of Ringleb flow on a sequence of successively refined triangulations. Finally, we consider a posteriori error estimates for the GLS and DG demoralization assuming error functionals related to the integrated lift and drag of a body. Sample calculations in 20 are shown to validate the theory and implementation.

Barth, Timothy↗
NASA NTRS1977

NASTRAN hydroelastic modal studies. Volume 3: NASTRAN 3-D hydroelastic analysis and MESHGEN user's manuals

The method used to formulate the fluid/structure equations is described in the updates to the NASTRAN Theoretical Manual. The basis for defining the fluid are three dimensional finite elements connected to fluid grid points defining the Eulerian pressure at a point fixed in space. The use of a pressure single degree of freedom at each point rather than three displacements allows a finer mesh of elements with a reasonable matrix order. In the formulation of the fluid/structure system the interior fluid degrees of freedom are transformed and removed from the solution matrices. The eigenvalues of the combination are extracted from small, fully dense, symmetric mass and stiffness matrices, efficiently processed with the Givens method. The solution matrices are defined by the free surface displacements and the reduced structure coordinates.

Source record↗
DOE OSTI2024

Numerical eigen-spectrum slicing, accurate orthogonal eigen-basis, and mixed-precision eigenvalue refinement using OpenMP data-dependent tasks and accelerator offload

Performing a variety of numerical computations efficiently and, at the same time, in a portable fashion requires both an overarching design followed by a number of implementation strategies. All of these are exemplified below as we present transitioning the PLASMA numerical library from relying on dependence-driven large tasks to achieving utilization of fine grain tasking and offload to hardware accelerators while keeping its core dependence sets: OpenMP source code pragmas and runtime for most system-level functionality and basic low-level numerical kernels provided directly by hardware vendors or open source projects with vendor contributions. We also present new algorithmic methods and their efficient parallel implementations including fine grained tasking for eigen-spectrum slicing and offload for mixed-precision eigenvalue refinement. We provide performance, scaling, and numerical results showing sizable gains over the available solutions from either the open source and vendor-provided packages.

Luszczek, Piotr↗
DOE OSTI2025

Relativistic core–valence-separated equation-of-motion coupled-cluster singles and doubles method: Efficient implementation and benchmark calculations

An efficient implementation for the relativistic exact two-component core–valence-separated equation-of-motion coupled-cluster singles and doubles (X2C-CVS-EOM-CCSD) method is reported. The explicit exclusion of pure valence excitations in the EOM-CCSD excited-state eigenvalue equations significantly improves the efficiency for calculations of core-excited states. Benchmark relativistic CVS-EOM-CC calculations with systematic inclusion of relativistic, correlation, and basis-set effects are shown to provide highly accurate results for core ionized and excited states involving heavy atoms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1976

Natural modes of oscillation of rotating flexible structures about nontrivial equilibrium

This paper is concerned with the vibrational characteristics of rotating flexible structures in the neighborhood of steady rotation. It is assumed that the structure undergoes deformations during the steady rotation, so that the equilibrium is nontrivial. The object of the paper is to formulate the eigenvalue problem associated with small oscillations of the structure about the nontrivial equilibrium and to develop efficient methods to compute the system natural frequencies and modal vectors. A numerical example showing the procedure for the calculation of spacecraft modes is presented.

Meirovitch, L.↗
NASA NTRS1981

Instability of non-zonal baroclinic flows - Multiple-scale analysis

The linear instability of a non-zonal flow can be reduced to an eigenvalue-eigenfunction problem, governed by a nonseparable partial differential equation (Niehaus, 1980). Approximate solutions, found by the method of multiple scales, are derived here and compared with earlier results found using a spectral method. The amplitude maxima are correctly located. The zonal variations of local wavenumber and of amplitude are qualitatively correct, but not sufficiently extreme. Because the method is oversensitive to local conditions, and less sensitive to global constraints, this comparison provides theoretical limits to the possibility of parameterizing transient eddies in terms of the local time mean state of the atmosphere. The method can be extended easily to flows with more realistic vertical structure.

Niehaus, M. C. W.↗
NASA NTRS1985

Three-dimensional baroclinic instability of a Hadley cell for small Richardson number

A three-dimensional, linear stability analysis of a baroclinic flow for Richardson number, Ri, of order unity is presented. The model considered is a thin horizontal, rotating fluid layer which is subjected to horizontal and vertical temperature gradients. The basic state is a Hadley cell which is a solution of the complete set of governing, nonlinear equations and contains both Ekman and thermal boundary layers adjacent to the rigid boundaries; it is given in a closed form. The stability analysis is also based on the complete set of equations; and perturbation possessing zonal, meridional, and vertical structures were considered. Numerical methods were developed for the stability problem which results in a stiff, eighth-order, ordinary differential eigenvalue problem. The previous work on three-dimensional baroclinic instability for small Ri was extended to a more realistic model involving the Prandtl number, sigma, and the Ekman number, E, and to finite growth rates and a wider range of the zonal wavenumber.

Antar, B. N.↗
NASA NTRSDate not supplied

Exploring Quantum State Preparation Using Tensor Networks and Sparse Wavefunction Simulations

The variational quantum eigenvalue solver is a powerful hybrid quantum-classical approach that has been suggested as a candidate method to run on near-term quantum hardware for computing ground state electronic energies of molecular systems. However, even for small molecules, the number of variational parameters and qubits required to minimize the electronic energy is beyond the reach of current quantum computers except for small basis sets. We explore a new paradigm for state preparation where we test how much of the optimization can be approximately prepared with classical computers to reduce the number of optimization steps performed using a quantum device. By adapting a recent algorithm for the factorized form of the UCC ansatz, we can study molecular electronic structure problems with up to 64 qubits. In addition, we also test a related approach of using tensor networks to optimize quantum circuits in order to benchmark various lattice models. We present results using these approaches and discuss strategies for incorporating these ideas into variational algorithms involving near-term quantum computers. Our results help demonstrate the strength of the UCC ansatz and address pressing questions about optimal initial parameterizations and circuit construction.

quantum computing↗
NASA NTRS2010

Analysis of Instabilities in Non-Axisymmetric Hypersonic Boundary Layers Over Cones

Hypersonic flows over circular cones constitute one of the most important generic configurations for fundamental aerodynamic and aerothermodynamic studies. In this paper, numerical computations are carried out for Mach 6 flows over a 7-degree half-angle cone with two different flow incidence angles and a compression cone with a large concave curvature. Instability wave and transition-related flow physics are investigated using a series of advanced stability methods ranging from conventional linear stability theory (LST) and a higher-fidelity linear and nonlinear parabolized stability equations (PSE), to the 2D eigenvalue analysis based on partial differential equations. Computed N factor distribution pertinent to various instability mechanisms over the cone surface provides initial assessments of possible transition fronts and a guide to corresponding disturbance characteristics such as frequency and azimuthal wave numbers. It is also shown that strong secondary instability that eventually leads to transition to turbulence can be simulated very efficiently using a combination of advanced stability methods described above.

Li, Fei↗
NASA NTRS1993

An efficient procedure for cascade aeroelastic stability determination using nonlinear, time-marching aerodynamic solvers

A numerical eigenvalue problem formulation and a practical calculation procedure for exact eigenvalues and corresponding eigenvectors are developed and applied to a nonlinear, two-dimensional, time-marching full potential solver for cascade aeroelastic stability analysis. This procedure is based on the Lanczos recursive method and it directly calculates stability information about a nonlinear steady state. It is compared to conventional approaches in the frequency and time domains developed earlier and is found to be 100-10.000 times more computationally efficient. Eigenvalue constellations and the flutter results for flow through a cascade SR5 propfan airfoil are presented.

Mahajan, Aparajit J.↗
NASA NTRS1984

A survey of payload integration methods

Several full-scale and short-cut methods for analyzing a booster/payload system are presented. Two full-scale techniques are considered: (1) a technique that uses a restrained payload together with a free-booster model, the latter being augmented with residual mass and stiffness correction and (2) a technique that uses a restrained payload and booster model. Both techniques determine the 'modal modes', which require the solution of a system eigenvalue problem; the loads usually are then determined via an acceleration approach. A brief description is given of a number of short-cut methods which are of special interest to Shuttle payload design: structural modification, base drive, and interface impedance methods. Directions for further research and development are suggested.

Engels, R. C.↗
NASA NTRS1989

A novel implementation of method of optimality criterion in synthesizing spacecraft structures with natural frequency constraints

In the design of spacecraft structures, fine tuning the structure to achieve minimum weight with natural frequency constraints is a time consuming process. Here, a novel implementation of the method of optimality criterion (OC) is developed. In this new implementation of OC, the free vibration analysis results are used to compute the eigenvalue sensitivity data required for the formulation. Specifically, the modal elemental strain and kinetic energies are used. Additionally, normalized design parameters are introduced as a second level linking that allows design variables of different values to be linked together. With the use of this novel formulation, synthesis of structures with natural frequency constraint can be carried out manually using modal analysis results. Design examples are presented to illustrate this novel implementation of the optimality criterion method.

Wang, Bo Ping↗