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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 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Linear Static Structural and Vibration Analysis on High-Performance Computers

Parallel computers offer the opportunity to significantly reduce the computation time necessary to analyze large-scale aerospace structures. This paper presents algorithms developed for and implemented on a massively-parallel computers hereafter referred to as Scalable High Performance Computers (SHPC) for the most computationally intensive tasks involved in structural analysis, namely, generation and assembly of system matrices, solution of systems of equations and calculation of the eigenvalues and eigenvectors. Results on SHPC are presented for large-scale structural problems (i.e. Models of high speed civil transport). The goal of this research is to develop new efficient technique which extend structural analysis to SHPC and make large-scale structural analyses tractable.

Baddourah, Majdi↗
DOE OSTI2026

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗
DOE OSTI2018

On the Theory of Elastic Scattering of Particles

The problem of elastic scattering of particles has been considered by the potential quantization method. The properties of the eigenfunctions ϕ{sub ν}{sup (+)}(r) and eigenvalues α{sub ν}{sup (+)} of this method for states with positive energies (continuous spectrum) have been studied. Under the assumption of the completeness of the set {ϕ_ν"("+")(r)}, the problem has been solved by expanding the desired wavefunction in this set. The proposed approach reproduces known results in all considered limiting cases. At the same time, it gives a more detailed description of the scattering amplitude than the standard phase theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

The asymptotic behaviour of the scattering matrix in a neighbourhood of the endpoints of a spectral gap

The behaviour of the scattering matrix is investigated as the spectral parameter approaches an endpoint of a spectral gap of a quantum waveguide from the inside or the outside. The waveguide has two sleeves, one is cylindrical and the other periodic. When the spectral parameter traverses the spectral gap, the scattering matrix is reshaped because the number of waves inside and outside the gap is different. Notwithstanding, the smaller scattering matrix (in size) is transformed continuously into an identical block in the bigger scattering matrix and, in addition, the latter takes block diagonal form in the limit at the endpoint of the gap, that is, at the spectral threshold. The unexpected phenomena are related to the other block. It is shown that in the limit this block can only take certain values at the threshold, and taking one or other of these values depends on the structure of the continuous spectrum and also on the structure of the subspace of 'almost standing' waves at the threshold, which are solutions of the homogeneous problem that transfer no energy to infinity. A criterion for the existence of such solutions links the dimension of this subspace to the multiplicity of the eigenvalue −1 of the threshold scattering matrix. Asymptotic formulae are obtained, which show, in particular, that the phenomenon of anomalous scattering of high-amplitude waves at near-threshold frequencies, discovered by Weinstein in a special acoustic problem, also occurs in periodic waveguides. Bibliography: 38 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1977

CAVE: A computer code for two-dimensional transient heating analysis of conceptual thermal protection systems for hypersonic vehicles

A digital computer code CAVE (Conduction Analysis Via Eigenvalues), which finds application in the analysis of two dimensional transient heating of hypersonic vehicles is described. The CAVE is written in FORTRAN 4 and is operational on both IBM 360-67 and CDC 6600 computers. The method of solution is a hybrid analytical numerical technique that is inherently stable permitting large time steps even with the best of conductors having the finest of mesh size. The aerodynamic heating boundary conditions are calculated by the code based on the input flight trajectory or can optionally be calculated external to the code and then entered as input data. The code computes the network conduction and convection links, as well as capacitance values, given basic geometrical and mesh sizes, for four generations (leading edges, cooled panels, X-24C structure and slabs). Input and output formats are presented and explained. Sample problems are included. A brief summary of the hybrid analytical-numerical technique, which utilizes eigenvalues (thermal frequencies) and eigenvectors (thermal mode vectors) is given along with aerodynamic heating equations that have been incorporated in the code and flow charts.

Rathjen, K. A.↗
DOE OSTI2018

Variance Estimation in Monte Carlo Eigenvalue Simulations Using Spectral Analysis Method

Monte Carlo (MC) simulation is widely used to solve the eigenvalue form of the Boltzmann transport equation that mathematically represents the neutron transport process through complex multiplying (fissionable) systems. Monte Carlo eigenvalue simulation starts with an assumed fission source distribution and uses the fission sites from the previous iteration (cycle) as the starting source in the current iteration. Important system parameters (MC tallies) such as fuel pin-power distribution are estimated over several cycles after the convergence of the fission source distribution to a stationary distribution. However, the MC fission source iteration algorithm that uses fission source sites from the previous cycle introduces a cycle-to-cycle correlation. Monte Carlo simulations that do not account for the cycle-to-cycle correlation systematically underestimate the variance of the estimated system parameters (sample mean). This paper presents the relationship between the spectral density in the frequency domain at frequency zero and the variance of the sample mean. This paper introduces a novel method in the frequency domain for the MC variance estimation. For the three test problems used in this paper, researchers have observed that the new method results in an improvement of more than one order of magnitude to the standard deviation of the sample mean. The new method also compares favorably with the previously introduced batch, bootstrap, and covariance-adjusted methods when applied to the three test problems investigated in this paper. This new method does not require modification of the MC eigenvalue algorithm (power iteration), is code agnostic, and is therefore easy to use when implementing in any existing MC code. In conclusion, the new estimate can be calculated without saving tally results of all active/stationary cycles.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1977

Robustness of linear quadratic state feedback designs in the presence of system uncertainty

The paper deals with the problem of expressing the robustness (stability) property of a linear quadratic state feedback (LQSF) design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices so that the closed-loop system remains stable. Nonlinear time-varying and linear time-invariant perturbations are considered. The only computation required in obtaining a measure of the robustness of an LQSF design is to determine the eigenvalues of two symmetric matrices determined when solving the algebraic Riccati equation corresponding to the LQSF design problem. Results are applied to a complex dynamic system consisting of the flare control of a STOL aircraft. The design of the flare control is formulated as an LQSF tracking problem.

Patel, R. V.↗
DOE OSTI2020

Multigroup Constant Calculation with Static α-Eigenvalue Monte Carlo for Time-Dependent Neutron Transport Simulations

Herein, multigroup constants for deterministic methods that preserve the time-dependent physics of the neutron transport equations are derived. Alternative multigroup constant weighting spectra are discussed: (1) the fundamental k-eigenfunction, (2) the fundamental α-eigenfunction, and (3) a composite of several α-modes. To generate the fundamental α-eigenfunction for calculating the multigroup constants, a static fundamental α-eigenvalue method is implemented into the open source Monte Carlo code OpenMC. Several static and kinetic problems are devised to verify the implementations and to investigate the relative performance of the alternative multigroup constant weighting spectra. Results emphasize that as a multigroup constant weighting spectrum, the fundamental α-eigenfunction offers physical characteristics that make it advantageous (in producing accurate solutions) over the typically used fundamental k-eigenfunction.

42 ENGINEERING↗
DOE OSTI2016

Stochastic Schrödinger evolution over piecewise enlarged filtrations

This paper constructs a nonlinear filtering framework that admits appearances of new information processes at random times by introducing piecewise enlargements of filtrations and proposes a new energy-based Schrodinger evolution expressed as a stochastic differential equation on a complex Hilbert space. Each information process is modeled as the sum of a random variable taking the eigenvalues of a Hamiltonian and an independent Brownian bridge noise. It is shown that under a piecewise enlarged filtration, the wave function is a jump-diffusion process until it collapses at some terminal time. In between discontinuities, the dynamics of the state vector are governed by different Wiener processes and diffusion coefficients. This motivates the introduction of an inclusive chain of Kolmogorov probability spaces or a *-isomorphic chain of commutative von Neumann probability spaces, on which the quantum system evolves differently based on the number of active information processes. The expectation of the Hamiltonian at a given state is the solution of a second-order nonlinear differential equation determined by one of the possible regimes that the quantum system belongs to. It is shown that the collapse rate is a submartingale with positive jumps and the Shannon entropy process is a supermartingale with expected negative jumps when passing to higher-order probability spaces. The framework is extended to the case when the Hamiltonian is modeled as a function of a set of commutative operators, where each operator is associated with a different piecewise enlarged filtration.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1978

Use of asymptotic methods in vibration analysis

The derivation of dynamic differential equations, suitable for studying the vibrations of rotating, curved, slender structures was examined, and the Hamiltonian procedure was advocated for this purpose. Various reductions of the full system are displayed, which govern the vibrating troposkien when various order of magnitude restrictions are placed on important parameters. Possible advantages of the WKB asymptotic method for solving these classes of problems are discussed. A special case of this method is used illustratively to calculate eigenvalues and eigenfunctions for a flat turbine blade with small flexural stiffness.

Ashley, H.↗
NASA NTRS1980

Multivariable identification using centralized fixed modes

A procedure to determine a state space model of a multivariable system (lambda inputs, m outputs) is presented. The model is suitable for control studies and uses single input, single output (SISO) system data in the identification procedure. The procedure can be defined in three distinct steps. First, the system's lambda x m SISO transfer functions are identified by using any standard or known identification technique for SISO systems. One objective of this step is to identify SISO transfer functions with as few distinct modes as possible between any two functions. Second, the time domain realization of each SISO transfer function is obtained in a straightforward manner and combined into a total multivariable realization. This total realization, in all probability, has more state variables than are required to define system response. In the third step, these excess or redundant states are removed by using minimal realization theory. The remaining states are related to system centralized fixed modes. Eigenvalue-eigenvector techniques were recently reported that yield a computationally feasible solution to the problem posed in step three. The procedure is applied to QCSEE data to demonstrate its feasibility.

Merrill, W. C.↗
NASA NTRS1989

On the calculation of derivatives of eigenvalues and eigenvectors in the simultaneous design and control of structures

Independent Modal Space Control (IMSC) is a technique that is often used for the control of large order structural systems. The pertinent optimization problem in the simultaneous design and control of structures is a min - min problem that minimizes with respect to the structural design variables, the minimum value of the performance index with respect to the control forces obtained using the IMSC technique. The minimization process requires derivatives of eigenvalues and eigenvectors with respect to the design variables. These derivatives can be computed by a rather involved analytical procedure or a relatively simple finite difference procedure. The computer cost effectiveness of these two procedures for the derivative calculations is examined.

Mesquita, Luis↗
NASA NTRS1992

Convexity property of the one-sided multivariable stability margin

In evaluating the stability robustness of multivariable control systems having one-sided parameter uncertainty, a problem that naturally arises is the minimization over diagonal matrices D of the greatest eigenvalue of (e sup D Ae sup -D + (e sup D Ae sup -D)*)/2. The minimization is proved to be convex, thus guaranteeing that every local minimum is also a global minimum and, in theory, guaranteeing the global convergence of generalized gradient nonlinear programming algorithms for computing the minimizing D.

Tekawy, Jonathan A.↗
DOE OSTI2018

GSTS-Uzawa method for a class of complex singular saddle point problems

In this paper, we propose GSTS–Uzawa method for solving a class of complex singular saddle point problems based on generalized skew-Hermitian triangular splitting (GSTS) iteration method and classical Uzawa method. We research on its semi-convergence properties and the eigenvalues distributions of its preconditioned matrix. The resulting GSTS–Uzawa preconditioner is used to precondition Krylov subspace methods such as the restarted generalized minimal residual (GMRES) method for solving the equivalent formulation of the complex singular saddle point problems. The theoretical results and effectiveness of the GSTS–Uzawa method are supported by a numerical example.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Elimination of spurious eigenvalues in the Chebyshev tau spectral method

A very simple modification is presented for the Chebyshev tau method which can eliminate spurious eigenvalues, proceeding from a consideration of the vorticity-streamfunction reformulation of the Chebyshev tau method and the Chebyshev-Galerkin method, which have no spurious modes. Consideration of a model problem indicates that these two approaches are equivalent, and that they reduce to the present modification of the tau method. This modified tau method also eliminates spurious eigenvalues from the Orr-Sommerfeld equation.

Mcfadden, G. B.↗
NASA NTRS1997

On the Possibility of Ill-Conditioned Covariance Matrices in the First-Order Two-Step Estimator

The first-order two-step nonlinear estimator, when applied to a problem of orbital navigation, is found to occasionally produce first step covariance matrices with very low eigenvalues at certain trajectory points. This anomaly is the result of the linear approximation to the first step covariance propagation. The study of this anomaly begins with expressing the propagation of the first and second step covariance matrices in terms of a single matrix. This matrix is shown to have a rank equal to the difference between the number of first step states and the number of second step states. Furthermore, under some simplifying assumptions, it is found that the basis of the column space of this matrix remains fixed once the filter has removed the large initial state error. A test matrix containing the basis of this column space and the partial derivative matrix relating first and second step states is derived. This square test matrix, which has dimensions equal to the number of first step states, numerically drops rank at the same locations that the first step covariance does. It is formulated in terms of a set of constant vectors (the basis) and a matrix which can be computed from a reference trajectory (the partial derivative matrix). A simple example problem involving dynamics which are described by two states and a range measurement illustrate the cause of this anomaly and the application of the aforementioned numerical test in more detail.

Garrison, James L.↗
NASA NTRS2016

Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review

A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di erential equations (ODEs) is undertaken. The goal of this review is to summarize the characteristics, assess the potential, and then design several nearly optimal, general purpose, DIRK-type methods. Over 20 important aspects of DIRKtype methods are reviewed. A design study is then conducted on DIRK-type methods having from two to seven implicit stages. From this, 15 schemes are selected for general purpose application. Testing of the 15 chosen methods is done on three singular perturbation problems. Based on the review of method characteristics, these methods focus on having a stage order of two, sti accuracy, L-stability, high quality embedded and dense-output methods, small magnitudes of the algebraic stability matrix eigenvalues, small values of aii, and small or vanishing values of the internal stability function for large eigenvalues of the Jacobian. Among the 15 new methods, ESDIRK4(3)6L[2]SA is recommended as a good default method for solving sti problems at moderate error tolerances.

Kennedy, Christopher A.↗
DOE OSTI2021

Structural stability and artificial buckling modes in topology optimization

Abstract This paper demonstrates how a strain energy transition approach can be used to remove artificial buckling modes that often occur in stability constrained topology optimization problems. To simulate the structural response, a nonlinear large deformation hyperelastic simulation is performed, wherein the fundamental load path is traversed using Newton’s method and the critical buckling load levels are estimated by an eigenvalue analysis. The goal of the optimization is to minimize displacement, subject to constraints on the lowest critical buckling loads and maximum volume. The topology optimization problem is regularized via the Helmholtz PDE-filter and the method of moving asymptotes is used to update the design. The stability and sensitivity analyses are outlined in detail. The effectiveness of the energy transition scheme is demonstrated in numerical examples.

Dalklint, Anna (ORCID:0000000346195205)↗