Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Function approximation”

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 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
NASA NTRS1968

Computation and analysis

Direct summation of series involving higher transcendental functions, integrals of confluent hypergeometric functions, and computer methods for approximating continuous functions

Source record↗
NASA NTRS1977

Finite state modeling of aeroelastic systems

A general theory of finite state modeling of aerodynamic loads on thin airfoils and lifting surfaces performing completely arbitrary, small, time-dependent motions in an airstream is developed and presented. The nature of the behavior of the unsteady airloads in the frequency domain is explained, using as raw materials any of the unsteady linearized theories that have been mechanized for simple harmonic oscillations. Each desired aerodynamic transfer function is approximated by means of an appropriate Pade approximant, that is, a rational function of finite degree polynomials in the Laplace transform variable. The modeling technique is applied to several two dimensional and three dimensional airfoils. Circular, elliptic, rectangular and tapered planforms are considered as examples. Identical functions are also obtained for control surfaces for two and three dimensional airfoils.

Vepa, R.↗
DOE OSTI2018

Band and Impurity States in Dimond with the (MV){sup –} (M = Si, Ge, Sn) Centers Based on ab Initio Calculations

Ab initio calculations were used to determine the structure, electronic zone dispersion, partial (atomic and orbital) densities of states, and levels of impurity–vacancy cluster (MV){sup –} (M = Si, Ge, Sn) in diamond. Wavefunctions were determined in the density functional theory approximation using hybrid exchange-correlation functional, localized basis set of Gaussians, and a supercell consisting of 192 atoms. Results are compared with data on undoped diamond and with experimental results. The dependence of the direct and indirect energy gap on the cluster type is discussed. Calculations are carried out taking into account the spin–orbit interaction to identify impurity levels in the valence band. The effect of electron–electron interaction on the position of impurity levels is discussed. The dominant contribution of the d orbitals to the density of states at the impurity level in all clusters is detected.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

A Christoffel function weighted least squares algorithm for collocation approximations

Here, we propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the (weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis to motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

Calculation of the total electron excitation cross section in the Born approximation using Slater wave functions for the Li (2s yields 2p), Li (2s yields 3p), Na (3s yields 4p), Mg (3p yields 4s), Ca (4s yields 4p) and K (4s yields 4p) excitations

Excitation of neutral atoms by inelastic scattering of incident electrons in gaseous nebulae were investigated using Slater Wave functions to describe the initial and final states of the atom. Total cross sections using the Born Approximation are calculated for: Li(2s yields 2p), Na(3s yields 4p), k(4s yields 4p). The intensity of emitted radiation from gaseous nebulae is also calculated, and Maxwell distribution is employed to average the kinetic energy of electrons.

Simsic, P. L.↗
DOE OSTI2022

Performance improvements of the windowed multipole formalism using a rational fraction approximation of the Faddeeva function

The windowed multipole (WMP) formalism was introduced as a way to calculate Doppler broadened cross sections on the fly during Monte Carlo simulations. While more arithmetic is needed compared to point-wise cross section look-ups, performance remained competitive from the large memory reductions and sequential data access. The single most expensive function call in a depleted fuel assembly problem using WMP comes from the evaluation of the Faddeeva function, which previously relied on a highly accurate, highly-branching algorithm. This paper explores the use of rational fraction approximations tailored to the domain interest of reactor physics applications and the development of lower accuracy approximations sufficient for our application. The rational approximations were implemented and tested in OpenMC on an infinite medium problem to stress the cross section calculation routine and a PWR assembly problem. In both cases, the rational approximation nearly eliminated the ∼ 20% penalty previously observed when comparing to point-wise libraries. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1979

Theory of direct scattering of neutral and charged atoms

The theory for direct elastic and inelastic collisions between composite atomic systems formulated within the framework of the Glauber approximation is presented. It is shown that the phase-shift function is the sum of a point Coulomb contribution and of an expression in terms of the known electron-hydrogen-atom and proton-hydrogen-atom phase shift function. The scattering amplitude is reexpressed, the pure Coulomb scattering in the case of elastic collisions between ions is isolated, and the exact optical profile function is approximated by a first-order expansion in Glauber theory which takes into account some multiple collisions. The approximate optical profile function terms corresponding to interactions involving one and two electrons are obtained in forms of Meijer G functions and as a one-dimensional integral, and for collisions involving one or two neutral atoms, the scattering amplitude is further reduced to a simple closed-form expression.

Franco, V.↗
DOE OSTI2018

Adaptive Sparse Grid Construction in a Context of Local Anisotropy and Multiple Hierarchical Parents

We consider general strategy for hierarchical multidimensional interpolation based on sparse grids, where the interpolation nodes and locally supported basis functions are constructed from tensors of a one dimensional hierarchical rule. We consider four different hierarchies that are tailored towards general functions, high or low order polynomial approximation, or functions that satisfy homogeneous boundary conditions. The main advantage of the locally supported basis is the ability to choose a set of functions based on the observed behavior of the target function. We present an alternative to the classical surplus refinement techniques, where we exploit local anisotropy and refine using functions with not strictly decreasing support. The more flexible refinement strategy improves stability and reduces the total number of expensive simulations, resulting in significant computational saving. We demonstrate the advantages of the different hierarchies and refinement techniques by application to series of simple functions as well as a system of ordinary differential equations given by the Kermack-McKendrick SIR model.

Stoyanov, Miroslav K.↗
DOE OSTI2017

Regression-based reduced-order models to predict transient thermal output for enhanced geothermal systems

Reduced-order modeling is a promising approach, as many phenomena can be described by a few parameters/mechanisms. An advantage and attractive aspect of a reduced-order model is that it is computational inexpensive to evaluate when compared to running a high-fidelity numerical simulation. A reduced-order model takes couple of seconds to run on a laptop while a high-fidelity simulation may take couple of hours to run on a high-performance computing cluster. The goal of this paper is to assess the utility of regression-based reduced-order models (ROMs) developed from high-fidelity numerical simulations for predicting transient thermal power output for an enhanced geothermal reservoir while explicitly accounting for uncertainties in the subsurface system and site-specific details. Numerical simulations are performed based on equally spaced values in the specified range of model parameters. Key sensitive parameters are then identified from these simulations, which are fracture zone permeability, well/skin factor, bottom hole pressure, and injection flow rate. We found the fracture zone permeability to be the most sensitive parameter. The fracture zone permeability along with time, are used to build regression-based ROMs for the thermal power output. The ROMs are trained and validated using detailed physics-based numerical simulations. Finally, predictions from the ROMs are then compared with field data. We propose three different ROMs with different levels of model parsimony, each describing key and essential features of the power production curves. The coefficients in the proposed regression-based ROMs are developed by minimizing a non-linear least-squares misfit function using the Levenberg–Marquardt algorithm. The misfit function is based on the difference between numerical simulation data and reduced-order model. ROM-1 is constructed based on polynomials up to fourth order. ROM-1 is able to accurately reproduce the power output of numerical simulations for low values of permeabilities and certain features of the field-scale data. ROM-2 is a model with more analytical functions consisting of polynomials up to order eight, exponential functions and smooth approximations of Heaviside functions, and accurately describes the field-data. At higher permeabilities, ROM-2 reproduces numerical results better than ROM-1, however, there is a considerable deviation from numerical results at low fracture zone permeabilities. ROM-3 consists of polynomials up to order ten, and is developed by taking the best aspects of ROM-1 and ROM-2. ROM-1 is relatively parsimonious than ROM-2 and ROM-3, while ROM-2 overfits the data. ROM-3 on the other hand, provides a middle ground for model parsimony. Based on R 2 -values for training, validation, and prediction data sets we found that ROM-3 is better model than ROM-2 and ROM-1. For predicting thermal drawdown in EGS applications, where high fracture zone permeabilities (typically greater than 10 –15 m 2 ) are desired, ROM-2 and ROM-3 outperform ROM-1. As per computational time, all the ROMs are 10 4 times faster when compared to running a high-fidelity numerical simulation. In conclusion, this makes the proposed regression-based ROMs attractive for real-time EGS applications because they are fast and provide reasonably good predictions for thermal power output.

58 GEOSCIENCES↗
NASA NTRS1976

Effects of multiple scattering on light pulses reflected by turbid atmospheres

Multiple scattering contributions to lidar returns from turbid atmospheres are derived by means of an analytical theory. It is assumed that scattering takes place mainly at small angles except for one event that scatters the light backward. The phase functions are approximated by the sum of Gaussian functions of the scattering angle in both the forward and backward directions. The three-dimensional radiative transfer equation is transformed to a one-dimensional problem by means of Fourier transforms. Neumann solutions to the transformed equation of radiative transfer are then found. A number of examples are presented for cloud, fog and haze models. The results are found to be in satisfactory agreement with results obtained from the Monte Carlo analysis of Kunkel (1974) and the theory of light pulses doubly scattered by turbid atmospheres which was developed by Eloranta (1972).

Weinman, J. A.↗
NASA NTRS1987

Piecewise linear approximation for hereditary control problems

Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.

Propst, Georg↗
NASA NTRS2003

Estimation of Instantaneous TOA Albedo at 670 nm over Ice Clouds from POLDER Multidirectional Measurements

An algorithm that determines the 670-nm top-of-atmosphere (TOA) albedo of ice clouds over ocean using Polarization and Directionality of the Earth's Reflectance ( POLDER) multidirectional measurements is developed. A plane-parallel layer of ice cloud with various optical thicknesses and light scattering phase functions is assumed. For simplicity, we use a double Henyey-Greenstein phase function to approximate the volume-averaged phase function of the ice clouds. A multidirectional reflectance best-fit match between theoretical and POLDER reflectances is used to infer effective cloud optical thickness, phase function and TOA albedo. Sensitivity tests show that while the method does not provide accurate independent retrievals of effective cloud optical depth and phase function, TOA albedo retrievals are accurate to within similar to 3% for both a single layer of ice clouds or a multilayer system of ice clouds and water clouds. When the method is applied to POLDER measurements and retrieved albedos are compared with albedos based on empirical angular distribution models (ADMs), zonal albedo differences are generally smaller than similar to 3%. When albedos are compared with those on the POLDER-I ERB and Cloud product, the differences can reach similar to 15% at small solar zenith angles.

Sun, W.↗
NASA NTRS1984

MMIC devices for active phased array antennas

The study of printed circuit discontinuities is necessary in order to design, for example, transitions between rectangular waveguides and printed circuits. New developments with respect to the analytical approaches to this problem are discussed. A summary of the progress in the experimental approach is presented. The accurate solution for the modes in various millimeter-wave waveguides is essential in the analysis of many integrated circuit components, such as filters and impedance transformers. Problems associated with the numerical computation of these modes in two frequently used waveguide forms, namely, the finline and microstrip, are presented. The spectral domain method of formulation, with a moment method solution, is considered. This approach can be readily extended to analyze an arbitrary configuration of dielectric and metallized regions in a shielded enclosure. Galerkin's method is used, where the testing and basic functions are the same. It is shown that the mode functions, or eigenfunctions, are more sensitive to errors than the phase constants, or eigenvalues. The approximate mode functions do not satisfy the orthogonality relationship well, resulting in difficulties when these modal solutions are used to form an approximate Green's function or are used in a mode matching analysis.

Mittra, R.↗