Engineering Papers⌕ Search

SEARCH · Engineering Papers

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 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Surface Segregation Energies of BCC Binaries from Ab Initio and Quantum Approximate Calculations

We compare dilute-limit segregation energies for selected BCC transition metal binaries computed using ab initio and quantum approximate energy method. Ab initio calculations are carried out using the CASTEP plane-wave pseudopotential computer code, while quantum approximate results are computed using the Bozzolo-Ferrante-Smith (BFS) method with the most recent parameterization. Quantum approximate segregation energies are computed with and without atomistic relaxation. The ab initio calculations are performed without relaxation for the most part, but predicted relaxations from quantum approximate calculations are used in selected cases to compute approximate relaxed ab initio segregation energies. Results are discussed within the context of segregation models driven by strain and bond-breaking effects. We compare our results with other quantum approximate and ab initio theoretical work, and available experimental results.

Good, Brian S.↗
DOE OSTI2018

Numerical multi-scaling method to solve the linear stochastic partial differential equations

In this paper, we propose a multi-scaling method to solve a class of the stochastic partial differential equations (SPDEs) of Itô-type. By this method, we approximate the solution of the SPDEs with strongly elliptic operator on a finite domain. The method is based on B-spline wavelet approximations; some of these functions are reshaped to satisfy on boundary conditions exactly. We prove the consistency and stability of the method. Illustrative examples are included to demonstrate the validity and applicability of our proposed technique.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Geometric multigrid for an implicit-time immersed boundary method

The immersed boundary (IB) method is an approach to fluid-structure interaction that uses Lagrangian variables to describe the deformations and resulting forces of the structure and Eulerian variables to describe the motion and forces of the fluid. Explicit time stepping schemes for the IB method require solvers only for Eulerian equations, for which fast Cartesian grid solution methods are available. Such methods are relatively straightforward to develop and are widely used in practice but often require very small time steps to maintain stability. Implicit-time IB methods permit the stable use of large time steps, but efficient implementations of such methods require significantly more complex solvers that effectively treat both Lagrangian and Eulerian variables simultaneously. Moreover, several different approaches to solving the coupled Lagrangian-Eulerian equations have been proposed, but a complete understanding of this problem is still emerging. This paper presents a geometric multigrid method for an implicit-time discretization of the IB equations. This multigrid scheme uses a generalization of box relaxation that is shown to handle problems in which the physical stiffness of the structure is very large. Numerical examples are provided to illustrate the effectiveness and efficiency of the algorithms described herein. Finally, these tests show that using multigrid as a preconditioner for a Krylov method yields improvements in both robustness and efficiency as compared to using multigrid as a solver. They also demonstrate that with a time step 100–1000 times larger than that permitted by an explicit IB method, the multigrid-preconditioned implicit IB method is approximately 50–200 times more efficient than the explicit method.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1976

High conductivity magnetic tearing instability

Linearized equations of magnetohydrodynamics are used to investigate the tearing mode, for arbitrary values of the conductivity, through a consideration of the additional effect of the electron-inertia contribution to Ohm's law. A description is provided of the equilibrium and subsequent instability in the magnetohydrodynamic approximation. A method for solving the perturbation equations in the linear approximation is discussed and attention is given to the results in the high conductivity limit.

Cross, M. A.↗
NASA NTRS2002

Approach for Input Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

An implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for quasi 3-D Euler CFD code is presented. Given uncertainties in statistically independent, random, normally distributed input variables, first- and second-order statistical moment procedures are performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, these moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Putko, Michele M.↗
DOE OSTI2017

Accelerated solution of discrete ordinates approximation to the Boltzmann transport equation via model reduction

Radiation heat transfer is an important phenomenon in many physical systems of practical interest. When participating media is important, the radiative transfer equation (RTE) must be solved for the radiative intensity as a function of location, time, direction, and wavelength. In many heat-transfer applications, a quasi-steady assumption is valid, thereby removing time dependence. The dependence on wavelength is often treated through a weighted sum of gray gases (WSGG) approach. The discrete ordinates method (DOM) is one of the most common methods for approximating the angular (i.e., directional) dependence. The DOM exactly solves for the radiative intensity for a finite number of discrete ordinate directions and computes approximations to integrals over the angular space using a quadrature rule; the chosen ordinate directions correspond to the nodes of this quadrature rule. This paper applies a projection-based model-reduction approach to make high-order quadrature computationally feasible for the DOM for purely absorbing applications. First, the proposed approach constructs a reduced basis from (high-fidelity) solutions of the radiative intensity computed at a relatively small number of ordinate directions. Then, the method computes inexpensive approximations of the radiative intensity at the (remaining) quadrature points of a high-order quadrature using a reduced-order model constructed from the reduced basis. Finally, this results in a much more accurate solution than might have been achieved using only the ordinate directions used to compute the reduced basis. One- and three-dimensional test problems highlight the efficiency of the proposed method.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1986

A methodology for airplane parameter estimation and confidence interval determination in nonlinear estimation problems

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates.

Murphy, P. C.↗
NASA NTRS1992

Approximate Solutions Of Equations Of Steady Diffusion

Rigorous analysis yields reliable criteria for "best-fit" functions. Improved "curve-fitting" method yields approximate solutions to differential equations of steady-state diffusion. Method applies to problems in which rates of diffusion depend linearly or nonlinearly on concentrations of diffusants, approximate solutions analytic or numerical, and boundary conditions of Dirichlet type, of Neumann type, or mixture of both types. Applied to equations for diffusion of charge carriers in semiconductors in which mobilities and lifetimes of charge carriers depend on concentrations.

Edmonds, Larry D.↗
NASA NTRS2001

Approach for Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1-D Euler CFD (computational fluid dynamics) code. Given uncertainties in statistically independent, random, normally distributed input variables, a first- and second-order statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Putko, Michele M.↗
NASA NTRS1974

Inelastic scattering in atom-diatomic molecule collisions. I - Rotational transitions in the sudden approximation

The impact parameter method and the sudden approximation are applied to determine the total probability of inelastic rotational transitions arising from a collision of an atom and a homonuclear diatomic molecule at large impact parameters. An analytical approximation to this probability is found for conditions where the electron exchange or overlap forces dominate the scattering. An approximate upper bound to the range of impact parameters for which rotational scattering can be important is determined. In addition, an estimate of the total inelastic cross section is found at conditions for which a statistical model describes the scattering well. The results of this analysis are applied to Ar-O2 collisions and may be readily applied to other combinations of atoms and molecules.

Stallcop, J. R.↗
NASA NTRS1998

Response Surface Model Building and Multidisciplinary Optimization Using D-Optimal Designs

This paper discusses response surface methods for approximation model building and multidisciplinary design optimization. The response surface methods discussed are central composite designs, Bayesian methods and D-optimal designs. An over-determined D-optimal design is applied to a configuration design and optimization study of a wing-body, launch vehicle. Results suggest that over determined D-optimal designs may provide an efficient approach for approximation model building and for multidisciplinary design optimization.

Unal, Resit↗
DOE OSTI2014

Approximate Hessian for accelerating ab initio structure relaxation by force fitting

We present a method to approximate the Hessian matrix of the Born-Oppenheimer energy landscape by using a simple force field model whose parameters are fitted to on-the-flight ab initio results. The inversed Hessian matrix is used as the preconditioner of conjugate gradient algorithms to speed up the atomic structure relaxation, resulting in a speedup factor of 2 to 5 on systems of bulk, slab, sheets, and atomic clusters. Because the force field model employed is simple and general, the parameter fitting is straightforward; the method is applicable to a variety of complicated systems for minimum structure relaxation. In the metal cluster new structure search, the new method yields better structures than the one obtained before with conventional algorithms.

36 MATERIALS SCIENCE↗
NASA NTRS2004

Heats of Segregation of BCC Binaries from ab Initio and Quantum Approximate Calculations

We compare dilute-limit heats of segregation for selected BCC transition metal binaries computed using ab initio and quantum approximate energy methods. Ab initio calculations are carried out using the CASTEP plane-wave pseudopotential computer code, while quantum approximate results are computed using the Bozzolo-Ferrante-Smith (BFS) method with the most recent LMTO-based parameters. Quantum approximate segregation energies are computed with and without atomistic relaxation, while the ab initio calculations are performed without relaxation. Results are discussed within the context of a segregation model driven by strain and bond-breaking effects. We compare our results with full-potential quantum calculations and with available experimental results.

Good, Brian S.↗
NASA NTRS2006

Approximations of distant retrograde orbits for mission design

Distant retrograde orbits (DROs) are stable periodic orbit solutions of the equations of motion in the circular restricted three body problem. Since no closed form expressions for DROs are known, we present methods for approximating a family of planar DROs for an arbitrary, fixed mass ratio. Furthermore we give methods for computing the first and second derivatives of the position and velocity with respect to the variables that parameterize the family. The approximation and derivative methods described allow a mission designer to target specific DROs or a range of DROs with no regard to phasing in contrast to the more limited case of targeting a six-state only.

Distant Retrograde Orbits (DRO)↗
DOE OSTI2021

Nucleon clustering at kinetic freezeout of heavy-ion collisions via path-integral Monte Carlo

Clustering of the four-nucleon system at kinetic freezeout conditions is studied using path-integral Monte Carlo techniques. This method seeks to improve upon previous calculations which relied on approximate semiclassical methods or few-body quantum mechanics. Estimates are given for the decay probabilities of the 4N system into various light nuclei decay channels and the strength of spatial correlations is characterized. Additionally, a simple model is presented to describe the impact of this clustering on nucleon multiplicity distributions. Additionally, the effects of a possible modification of the inter-nucleon interaction due to the close critical line (and hypothetical QCD critical point) on the clustering are also studied.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Trigonometric polynomial approximation, K-functionals and generalized moduli of smoothness

Best approximation and approximation by families of linear polynomial operators (FLPO) in the spaces L{sub p}, 0<p⩽+∞, are investigated for periodic functions of an arbitrary number of variables in terms of the generalized modulus of smoothness generated by a periodic generator which, near the origin, is assumed to be close in a certain sense to some homogeneous function of positive order. Direct and inverse theorems (Jackson- and Bernstein-type estimates) are proved; conditions on the generators are obtained under which the approximation error by an FLPO is equivalent to an appropriate modulus of smoothness. These problems are solved by going over from the modulus to an equivalent K-functional. The general results obtained are applied to classical objects in the theory of approximation and smoothness. In particular, they are applied to the methods of approximation generated by Fejér, Riesz and Bochner-Riesz kernels, and also to the moduli of smoothness and K-functionals corresponding to the conventional, Weyl and Riesz derivatives and to the Laplace operator. Bibliography: 24 titles. (paper)

97 MATHEMATICS AND COMPUTING↗