Search NASA⌕ Search

SEARCH · Search NASA

Results for “Approximation methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 955 records · Page 53
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Method for estimating optimal spectral and energy parameters of laser irradiation in photodynamic therapy of biological tissue

We have solved the problem of layer-by-layer laser-light dosimetry in biological tissues and of selecting an individual therapeutic dose in laser therapy. A method is proposed for real-time monitoring of the radiation density in tissue layers in vivo, concentrations of its endogenous (natural) and exogenous (specially administered) chromophores, as well as in-depth distributions of the spectrum of light action on these chromophores. As the background information use is made of the spectrum of diffuse light reflected from a patient's tissue, measured by a fibre-optic spectrophotometer. The measured spectrum is quantitatively analysed by the method of approximating functions for fluxes of light multiply scattered in tissue and by a semi-analytical method for calculating the in-depth distribution of the light flux in a multi-layered medium. We have shown the possibility of employing the developed method for monitoring photosensitizer and oxyhaemoglobin concentrations in tissue, light power absorbed by chromophores in tissue layers at different depths and laser-induced changes in the tissue morphology (vascular volume content and ratios of various forms of haemoglobin) during photodynamic therapy. (biophotonics)

60 APPLIED LIFE SCIENCES↗
NASA NTRS1992

Computer program for calculating and fitting thermodynamic functions

A computer program is described which (1) calculates thermodynamic functions (heat capacity, enthalpy, entropy, and free energy) for several optional forms of the partition function, (2) fits these functions to empirical equations by means of a least-squares fit, and (3) calculates, as a function of temperture, heats of formation and equilibrium constants. The program provides several methods for calculating ideal gas properties. For monatomic gases, three methods are given which differ in the technique used for truncating the partition function. For diatomic and polyatomic molecules, five methods are given which differ in the corrections to the rigid-rotator harmonic-oscillator approximation. A method for estimating thermodynamic functions for some species is also given.

Mcbride, Bonnie J.↗
NASA NTRS1992

Development of a fractional-step method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the velocity. This choice is equivalent to using the contravariant velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with the consistent approximations of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

Rosenfeld, Moshe↗
DOE OSTI2022

Constructing approximately diagonal quantum gates

We study a method of producing approximately diagonal 1-qubit gates. For each positive integer, the method provides a sequence of gates that are defined iteratively from a fixed diagonal gate and an arbitrary gate. These sequences are conjectured to converge to diagonal gates doubly exponentially fast and are verified for small integers. We systemically study this conjecture and prove several important partial results. Some techniques are developed to pave the way for a final resolution of the conjecture. The sequences provided here have applications in quantum search algorithms, quantum circuit compilation, generation of leakage-free entangled gates in topological quantum computing, etc.

Computer Science↗
DOE OSTI2021

Optimal design of acoustic metamaterial cloaks under uncertainty

In this work, we consider the problem of optimal design of an acoustic cloak under uncertainty and develop scalable approximation and optimization methods to solve this problem. The design variable is taken as an infinite-dimensional spatially-varying field that represents the material property, while an additive infinite-dimensional random field represents the variability of the material property or the manufacturing error. Discretization of this optimal design problem results in high-dimensional design variables and uncertain parameters. To solve this problem, we develop a computational approach based on a Taylor approximation and an approximate Newton method for optimization, which is based on a Hessian derived at the mean of the random field. We show our approach is scalable with respect to the dimension of both the design variables and uncertain parameters, in the sense that the necessary number of acoustic wave propagations is essentially independent of these dimensions, for numerical experiments with up to one million design variables and half a million uncertain parameters. Additionally, we demonstrate that, using our computational approach, an optimal design of the acoustic cloak that is robust to material uncertainty is achieved in a tractable manner. The optimal design under uncertainty problem is posed and solved for the classical circular obstacle surrounded by a ring-shaped cloaking region, subjected to both a single-direction single-frequency incident wave and multiple-direction multiple-frequency incident waves. Finally, we apply the method to a deterministic large-scale optimal cloaking problem with complex geometry, to demonstrate that the approximate Newton method’s Hessian computation is viable for large, complex problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1973

Digital approximation of continuous-data control systems by point-by-point state comparison

This paper presents a point-by-point state comparison method of approximating a continuous-data system by a sampled-data system. The problem is to attempt the matching of the states of the two systems at the sampling instants. A partial matching has to be conducted if the systems have more states than controls. A weighting matrix is used to regulate the partial matching and weights placed on each state. The digital approximation is affected by use of forward gain E(T) and feedback gain G(T) in the sampled-data system. It is shown that, in general, these gains can be approximated by truncated Taylor series expansions. An illustrative example is given using the one-axis dynamics of the Skylab satellite.

Kuo, B. C.↗
DOE OSTI2017

A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes

Implicit–Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity-of-interest for approximations obtained from multi-stage IMEX schemes. This is done by first defining a finite element method that is nodally equivalent to an IMEX scheme, then using typical methods for adjoint-based error estimation. Furthermore, the use of a nodally equivalent finite element method allows a decomposition of the error into multiple components, each describing the effect of a different portion of the method on the total error in a quantity-of-interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

An efficient method to propagate model uncertainty when inverting seismic data for time domain seismic moment tensors

SUMMARY We present a computationally efficient method to approximately propagate uncertainty when linearly inverting seismic data for point source, time variable moment tensor components. The method is based on the assumption that the data residual, given by the difference between the observed seismic data and the data predicated by a linear inversion, contains the effects of both data and model uncertainty. Our method uses a distribution of data residuals, added directly to the data, in a pseudo-Monte Carlo scheme. Using the assumption that the data residual is a stochastic process, we use the well-known Karhunen–Loève (KL) theorem to construct a distribution of data residuals, where the required basis functions are constructed using Fourier series. The Fourier series are scaled by a product of a random variable and the real-valued spectral amplitudes of the original data residual’s spectrum. Thus, the Fourier series and spectral amplitudes are eigenfunction-eigenvalue pairs used in the KL-based construction of data residual distribution. Using tests with synthetic data, we show that our method compares closely with a Finite Difference Monte Carlo (FDMC) method that we presented previously. More importantly, the method presented here is computationally several orders of magnitude faster than our previous FDMC method, and requires no a priori assumptions of model and/or data uncertainty.

Poppeliers, Christian (ORCID:0000000159526849)↗
NASA NTRS2004

A Numerical Investigation of the Extinction of Low Strain Rate Diffusion Flames by an Agent in Microgravity

Our goal has been to investigate the influence of both dilution and radiation on the extinction process of nonpremixed flames at low strain rates. Simulations have been performed by using a counterflow code and three radiation models have been included in it, namely, the optically thin, the narrowband, and discrete ordinate models. The counterflow flame code OPPDIFF was modified to account for heat transfer losses by radiation from the hot gases. The discrete ordinate method (DOM) approximation was first suggested by Chandrasekhar for solving problems in interstellar atmospheres. Carlson and Lathrop developed the method for solving multi-dimensional problem in neutron transport. Only recently has the method received attention in the field of heat transfer. Due to the applicability of the discrete ordinate method for thermal radiation problems involving flames, the narrowband code RADCAL was modified to calculate the radiative properties of the gases. A non-premixed counterflow flame was simulated with the discrete ordinate method for radiative emissions. In comparison with two other models, it was found that the heat losses were comparable with the optically thin and simple narrowband model. The optically thin model had the highest heat losses followed by the DOM model and the narrow-band model.

Puri, Ishwar K.↗
DOE OSTI2019

Investigation of assumptions and approximations in the virtual fields method for a viscoplastic material model

The Virtual Fields Method (VFM) is an inverse technique used for parameter estimation and calibration of constitutive models. Many assumptions and approximations—such as plane stress, incompressible plasticity, and spatial and temporal derivative calculations—are required to use VFM with full-field deformation data, for example, from Digital Image Correlation (DIC). Here, this work presents a comprehensive discussion of the effects of these assumptions and approximations on parameters identified by VFM for a viscoplastic material model for 304L stainless steel. We generated synthetic data from a Finite-Element Analysis (FEA) in order to have a reference solution with a known material model and known model parameters, and we investigated four cases in which successively more assumptions and approximations were included in the data. We found that VFM is tolerant to small deviations from the plane stress condition in a small region of the sample, and that the incompressible plasticity assumption can be used to estimate thickness changes with little error. A local polynomial fit to the displacement data was successfully employed to compute the spatial displacement gradients. The choice of temporal derivative approximation (i.e., backwards difference versus central difference) was found to have a significant influence on the computed rate of deformation and on the VFM results for the rate-dependent model used in this work. Finally, the noise introduced into the displacement data from a stereo-DIC simulator was found to have negligible influence on the VFM results. Evaluating the effects of assumptions and approximations using synthetic data is a critical first step for verifying and validating VFM for specific applications. Finally, the results of this work provide the foundation for confidently using VFM for experimental data.

304L stainless steel↗
DOE OSTI2018

Solving numerically nonlinear systems of balance laws by multivariate sigmoidal functions approximation

A numerical method for solving systems of nonlinear one-dimensional balance laws, based on multivariate sigmoidal functions approximation, is developed. Constructive approximation theorems are first established in both, uniform and L{sup p} norms. A priori as well as a posteriori error estimates are derived for the numerical solutions, when various kinds of sigmoidal functions, such as unit step, logistic and Gompertz functions, are chosen. The residual of the numerical method is also estimated. Numerical examples are given to test the performance of the algorithm, a comparison with the Godunov method is made concerning accuracy and computational cost. Finally, the numerical stability of the method is analyzed.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

Determining optical depth in different parts of the Fraunhofer line contour

The method of approximate determination of the optical depth tau in the profile of the Fraunhofer line is considered. In the method the observed profile and allocation of tau to the temperature in the photosphere must be known. If the source function B prime (tau) in the line seems not to be equal to the Planck function, the dependence B prime (tau) on tau is needed. The method for the determination of B prime (tau) using the center-to-limb observations of the central intensities of the line is suggested.

Gurtovenko, E. A.↗
NASA NTRS1974

Improvement of water resources management through the use of satellites flood plain delineation

The delineation of flood-prone areas is an important activity in several parts of the world. Conventional methods map the topography surrounding the river via ground surveys and supplementary aerophotography. The conventional method costs approximately $2,000 per river-kilometer, is laborious and time-consuming. ERTS information can supplement this method by two complementary techniques: (1) the dynamic method images the floods as they occur, exploiting the fact that visible evidence of inundation remains for a substantial period after the high waters have receded; (2) the static method utilizes the fact that several flood plains have been found recognizable on ERTS imagery from distinctive, permanent indicators left by previous floods. For areas whose full development is still in the future, the dynamic method allows the gradual buildup with time of a flood plain map, by simply correlating existing ERTS imagery. The static method allows in several areas, a first-cut indication, of proneness to floods.

Castruccio, P. A.↗
NASA NTRS2003

Energetics of Single Substitutional Impurities in NiTi

Shape-memory alloys are of considerable current interest, with applications ranging from stents to Mars rover components. In this work, we present results on the energetics of single substitutional impurities in B2 NiTi. Specifically, energies of Pd, Pt, Zr and Hf impurities at both Ni and Ti sites are computed. All energies are computed using the CASTEP ab initio code, and, for comparison, using the quantum approximate energy method of Bozzolo, Ferrante and Smith. Atomistic relaxation in the vicinity of the impurities is investigated via quantum approximate Monte Carlo simulation, and in cases where the relaxation is found to be important, the resulting relaxations are applied to the ab initio calculations. We compare our results with available experimental work.

Good, Brian S.↗
DOE OSTI2019

Scalable Extended Dynamic Mode Decomposition Using Random Kernel Approximation

The Koopman operator is a linear, infinite-dimensional operator that governs the dynamics of system observables; extended dynamic mode decomposition (EDMD) is a data-driven method for approximating the Koopman operator using functions (features) of the system state snapshots. This paper investigates an approach to EDMD in which the features used provide random approximations to a particular kernel function. The objective of this is computational economy for large data sets: EDMD is generally ill-suited for problems with large state dimension, and its dual kernel formulation (KDMD) is well-suited for such problems only if the number of data snapshots is relatively small. We discuss two specific methods for generating features: random Fourier features and the Nÿstrom method. The first method is a data-independent method for translation-invariant kernels only and involves random sampling in feature space; the second method is a data-dependent empirical method that may be used for any kernel and involves random sampling of data. We first discuss how these ideas may be applied in an EDMD context, as well as a means for adaptively adding random Fourier features. As a result, we demonstrate these methods on two example problems and conclude with an analysis of the relative benefits and drawbacks of each method.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

A minimalistic approach to static and dynamic electron correlations: Amending generalized valence bond method with extended random phase approximation correlation correction

A perfect-pairing generalized valence bond (GVB) approximation is known to be one of the simplest approximations, which allows one to capture the essence of static correlation in molecular systems. In spite of its attractive feature of being relatively computationally efficient, this approximation misses a large portion of dynamic correlation and does not offer sufficient accuracy to be generally useful for studying electronic structure of molecules. We propose to correct the GVB model and alleviate some of its deficiencies by amending it with the correlation energy correction derived from the recently formulated extended random phase approximation (ERPA). On the examples of systems of diverse electronic structures, we show that the resulting ERPA-GVB method greatly improves upon the GVB model. ERPA-GVB recovers most of the electron correlation and it yields energy barrier heights of excellent accuracy. Thanks to a balanced treatment of static and dynamic correlation, ERPA-GVB stays reliable when one moves from systems dominated by dynamic electron correlation to those for which the static correlation comes into play.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Accurate and efficient calculation of excitation energies with the active-space particle-particle random phase approximation

An efficient method for calculating excitation energies based on the particle-particle random phase approximation (ppRPA) is presented. Neglecting the contributions from the high-lying virtual states and the low-lying core states leads to the significantly smaller active-space ppRPA matrix while keeping the error to within 0.05 eV from the corresponding full ppRPA excitation energies. The resulting computational cost is significantly reduced and becomes less than the construction of the non-local Fock exchange potential matrix in the self-consistent-field (SCF) procedure. With only a modest number of active orbitals, the original ppRPA singlet-triplet (ST) gaps as well as the low-lying single and double excitation energies can be accurately reproduced at much reduced computational costs, up to 100 times faster than the iterative Davidson diagonalization of the original full ppRPA matrix. For high-lying Rydberg excitations where the Davidson algorithm fails, the computational savings of active-space ppRPA with respect to the direct diagonalization is even more dramatic. The virtues of the underlying full ppRPA combined with the significantly lower computational cost of the active-space approach will significantly expand the applicability of the ppRPA method to calculate excitation energies at a cost of O(K^{4}), with a prefactor much smaller than a single SCF Hartree-Fock (HF)/hybrid functional calculation, thus opening up new possibilities for the quantum mechanical study of excited state electronic structure of large systems.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1989

Recent activities within the Aeroservoelasticity Branch at the NASA Langley Research Center

The objective of research in aeroservoelasticity at the NASA Langley Research Center is to enhance the modeling, analysis, and multidisciplinary design methodologies for obtaining multifunction digital control systems for application to flexible flight vehicles. Recent accomplishments are discussed, and a status report on current activities within the Aeroservoelasticity Branch is presented. In the area of modeling, improvements to the Minimum-State Method of approximating unsteady aerodynamics are shown to provide precise, low-order aeroservoelastic models for design and simulation activities. Analytical methods based on Matched Filter Theory and Random Process Theory to provide efficient and direct predictions of the critical gust profile and the time-correlated gust loads for linear structural design considerations are also discussed. Two research projects leading towards improved design methodology are summarized. The first program is developing an integrated structure/control design capability based on hierarchical problem decomposition, multilevel optimization and analytical sensitivities. The second program provides procedures for obtaining low-order, robust digital control laws for aeroelastic applications. In terms of methodology validation and application the current activities associated with the Active Flexible Wing project are reviewed.

Noll, Thomas E.↗