Computation research
Least squares method used in linearizing roots of polynomial and to derive approximations
APPROXIMATION METHOD↗
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.
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Transient cooling of solid bodies of classical form by radiation
An approximate analytic method is presented for analysis of the unsteady process of radiative cooling of solid bodies of classical form. The nonlinear heat transfer problem is solved by the cascade linearization technique with use of the iteration method. Comparison of the results obtained even in the first approximation with the available numerical solutions indicates adequate engineering accuracy of the proposed technique.
Novikov, V. S.↗
Implicit flux-split schemes for the Euler equations
Recent progress in the development of implicit algorithms for the Euler equations using the flux-vector splitting method is described. Comparisons of the relative efficiency of relaxation and spatially-split approximately factored methods on a vector processor for two-dimensional flows are made. For transonic flows, the higher convergence rate per iteration of the Gauss-Seidel relaxation algorithms, which are only partially vectorizable, is amply compensated for by the faster computational rate per iteration of the approximately factored algorithm. For supersonic flows, the fully-upwind line-relaxation method is more efficient since the numerical domain of dependence is more closely matched to the physical domain of dependence. A hybrid three-dimensional algorithm using relaxation in one coordinate direction and approximate factorization in the cross-flow plane is developed and applied to a forebody shape at supersonic speeds and a swept, tapered wing at transonic speeds.
Thomas, J. L.↗
The Transference Number
The performance of rechargeable batteries and other electrochemical systems depends on the rate at which the working ion (often a cation) is transported from one electrode to the other. The cation transference number is an important transport parameter that affects this rate. The purpose of this perspective is to distinguish between approximate and rigorous methods used in the literature to measure the transference number. We emphasize the fact that this parameter is dependent on the reference frame used in the analysis; care must be taken when comparing values obtained from different sources to account for differences in reference frames. We present data obtained from a well‐characterized electrolyte. We compare rigorously determined transference numbers in two reference frames with values obtained by an approximate method. We conclude with a qualitative discussion of the relationship between the transference number and salt concentration gradients that are obtained when current is drawn through a battery.
Gao, Kevin W.↗
Strain induced modification in phonon dispersion curves of monolayer boron pnictides
In the frame work of density functional theory, the biaxial strain induced phonon dispersion curves of monolayer boron pnictides (BX, X = N, P, As, and Sb) have been investigated. The electron-ion interactions have been modelled using ultrasoft pseudopotentials while exchange-correlation energies have been approximated by the method of local density approximation in the parameterization of Perdew-Zunger. The longitudinal and transverse acoustic phonon modes of boron pnictide sheets show linear dependency on wave vector k{sup →} while out of plane mode varies as k{sup 2}. The in-plane longitudinal and out of plane transverse optical modes in boron nitride displaying significant dispersion similar to graphene. We have analyzed the biaxial strain dependent behaviour of out of plane acoustic phonon mode which is linked to ripple for four BX sheets using a model equation with shell elasticity theory. The strain induces the hardening of this mode with tendency to become more linear with increase in strain percentage. The strain induced hardening of out of plane acoustic phonon mode indicates the absence of rippling in these compounds. Our band structure calculations for both unstrained and strained 2D h-BX are consistent with previous calculations.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Revisiting the ODE Method for Recursive Algorithms: Fast Convergence Using Quasi Stochastic Approximation
Several decades ago, Profs. Sean Meyn and Lei Guo were postdoctoral fellows at ANU, where they shared interest in recursive algorithms. It seems fitting to celebrate Lei Guo's 60th birthday with a review of the ODE Method and its recent evolution. The method has been regarded as a technique for algorithm analysis. It is argued that this viewpoint is backwards: The original stochastic approximation method was surely motivated by an ODE, and tools for analysis came much later (based on establishing robustness of Euler approximations). The paper presents a brief survey of recent research in machine learning that shows the power of algorithm design in continuous time, following by careful approximation to obtain a practical recursive algorithm. While these methods are usually presented in a stochastic setting, this is not a prerequisite. In fact, recent theory shows that rates of convergence can be dramatically accelerated by applying techniques inspired by quasi Monte-Carlo. Subject to conditions, the optimal rate of convergence can be obtained by applying the averaging technique of Polyak and Ruppert. The conditions are not universal, but theory suggests alternatives to achieve acceleration. The theory is illustrated with applications to gradient-free optimization, and policy gradient algorithms for reinforcement learning.
learning and adaptive systems in artificial intell↗
Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations
In this paper, we study a local discontinuous Galerkin method combined with fourth order exponential time differencing Runge-Kutta time discretization and a fourth order conservative method for solving the nonlinear Schrödinger equations. Based on different choices of numerical fluxes, we propose both energy-conserving and energy-dissipative local discontinuous Galerkin methods, and have proven the error estimates for the semi-discrete methods applied to linear Schrödinger equation. The numerical methods are proven to be highly efficient and stable for long-range soliton computations. Finally, extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.
97 MATHEMATICS AND COMPUTING↗
Methods of Constructing a Blended Performance Function Suitable for Formation Flight
This paper presents two methods for constructing an approximate performance function of a desired parameter using correlated parameters. The methods are useful when real-time measurements of a desired performance function are not available to applications such as extremum-seeking control systems. The first method approximates an a priori measured or estimated desired performance function by combining real-time measurements of readily available correlated parameters. The parameters are combined using a weighting vector determined from a minimum-squares optimization to form a blended performance function. The blended performance function better matches the desired performance function mini- mum than single-measurement performance functions. The second method expands upon the first by replacing the a priori data with near-real-time measurements of the desired performance function. The resulting blended performance function weighting vector is up- dated when measurements of the desired performance function are available. Both methods are applied to data collected during formation- flight-for-drag-reduction flight experiments.
control systems↗
Automated detection of pulmonary nodules in PET/CT images: Ensemble false-positive reduction using a convolutional neural network technique
Purpose: Automated detection of solitary pulmonary nodules using positron emission tomography (PET) and computed tomography (CT) images shows good sensitivity; however, it is difficult to detect nodules in contact with normal organs, and additional efforts are needed so that the number of false positives (FPs) can be further reduced. In this paper, the authors propose an improved FP-reduction method for the detection of pulmonary nodules in PET/CT images by means of convolutional neural networks (CNNs). Methods: The overall scheme detects pulmonary nodules using both CT and PET images. In the CT images, a massive region is first detected using an active contour filter, which is a type of contrast enhancement filter that has a deformable kernel shape. Subsequently, high-uptake regions detected by the PET images are merged with the regions detected by the CT images. FP candidates are eliminated using an ensemble method; it consists of two feature extractions, one by shape/metabolic feature analysis and the other by a CNN, followed by a two-step classifier, one step being rule based and the other being based on support vector machines. Results: The authors evaluated the detection performance using 104 PET/CT images collected by a cancer-screening program. The sensitivity in detecting candidates at an initial stage was 97.2%, with 72.8 FPs/case. After performing the proposed FP-reduction method, the sensitivity of detection was 90.1%, with 4.9 FPs/case; the proposed method eliminated approximately half the FPs existing in the previous study. Conclusions: An improved FP-reduction scheme using CNN technique has been developed for the detection of pulmonary nodules in PET/CT images. The authors’ ensemble FP-reduction method eliminated 93% of the FPs; their proposed method using CNN technique eliminates approximately half the FPs existing in the previous study. These results indicate that their method may be useful in the computer-aided detection of pulmonary nodules using PET/CT images.
60 APPLIED LIFE SCIENCES↗
Electron and bremsstrahlung penetration and dose calculation
Various techniques for the calculation of electron and bremsstrahlung dose deposition are described. Energy deposition, transmission, and reflection coefficients for electrons incident on plane slabs are presented, and methods for their use in electron dose calculations were developed. A method using the straight-ahead approximation was also developed, and the various methods were compared and found to be in good agreement. Both accurate and approximate methods of calculating bremsstrahlung dose were derived and compared. Approximation is found to give a good estimate of dose where the electron spectrum falls off exponentially with energy.
Watts, J. W., Jr.↗
A method for bounding high-order finite element functions: Applications to mesh validity and bounds-preserving limiters
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be used to locally bound any combination of these basis functions. This approach can be applied to any element/basis type at any approximation order, can provide local (i.e., subcell) extremum bounds to a desired level of accuracy, and can be evaluated efficiently on-the-fly in simulations. Furthermore, we show that this approach generally yields more accurate bounds in comparison to traditional methods based on convex hull properties (e.g., Bernstein polynomials). Furthermore, the efficacy of this technique is shown in applications such as mesh validity checks and optimization for high-order curved meshes, where positivity of the element Jacobian determinant can be ensured throughout the entire element, and continuously bounds-preserving limiters for hyperbolic systems, which can enforce maximum principle bounds across the entire solution polynomial.
Bounding box↗
Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization
In this paper, we compare and contrast the use of second-order response surface models and kriging models for approximating non-random, deterministic computer analyses. After reviewing the response surface method for constructing polynomial approximations, kriging is presented as an alternative approximation method for the design and analysis of computer experiments. Both methods are applied to the multidisciplinary design of an aerospike nozzle which consists of a computational fluid dynamics model and a finite-element model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations, and four optimization problems m formulated and solved using both sets of approximation models. The second-order response surface models and kriging models-using a constant underlying global model and a Gaussian correlation function-yield comparable results.
Simpson, Timothy W.↗
Implicit calculations of transonic flows using monotone methods
Implicit approximate-factorization algorithms have been developed that use monotone methods for the calculation of steady and unsteady transonic flows governed by the small-disturbance-potential equation. These algorithms use the new Engquist-Osher switch in the type-dependent differencing in place of the standard Murman-Cole switch. The resulting algorithms are more stable; hence, calculations can be done more efficiently. For steady flows, the convergence rate is about 35% faster, and for unsteady flows the allowable time step is about 10 times larger. These improvements are achieved with no increase in computer storage and with only minor modifications in codes that use the Murman-Cole switch. Also an implicit algorithm has been developed for the steady full-potential equation in one-dimension, which uses monotone methods.
Goorjian, P. M.↗
A new efficient approach for 3D hydrodynamics simulation
LANL’s CHICOMA code solves the compressible hydrodynamic equations on moving tetrahedral grids. Hydrodynamic equations can be solved in Lagrangian, Eulerian, and Arbitrary Lagrangian-Eulerian reference frames. The equations are solved using a finite element method coupled to approximate Riemann solvers. The methods have been extensively verified against relevant analytical solutions. CHICOMA is 10 3 -10 4 times faster than current production codes for the same level of accuracy!
42 ENGINEERING↗
Use of ground radar to detect reentering debris
The velocity of the particles is required to identify the type of particles producing the ionization trails. A method of approximating the velocity of a meteor from radar data was developed. The method requires the time between the spacings of the Fresnel interference fringes, the range to the ionization trail, and the wavelength of the radar system. The orbital mechanics of the problem are evaluated, if the particles originate with the shuttle, the orbital mechanics will substantiate the relative position of the particles with the position of the shuttle. A program to determine spacecraft orbital decay due to perturbations is utilized for a preliminary evaluation of the orbital mechanics of the problem. Many assumptions concerning the size, shape, density, etc. of the particles are necessary for the preliminary evaluation. The results do not negate the possibility that the events observed by the radar are reentering particles originating from the shuttle.
Crews, J. L.↗
A method for nonlinear optimization with discrete design variables
A numerical method is presented for the solution of nonlinear discrete optimization problems. The applicability of discrete optimization to engineering design is discussed, and several standard structural optimization problems are solved using discrete design variables. The method uses approximation techniques to create subproblems suitable for linear mixed-integer programming methods. The method employs existing software for continuous optimization and integer programming.
Olsen, Gregory R.↗
A space-marching method for the computation of viscous internal flows
A space-marching method has been developed to compute 3-D viscous flows in internal geometries. The Navier-Stokes equations have been posed as an initial-value problem by neglecting the effects of streamwise diffusion and treating the streamwise pressure gradient as a known source term. The fully coupled system of equations has been solved by a noniterative algorithm at each streamwise step of the computation. A low Mach number formulation of the equations has been used to compute incompressible flow fields. A computer program has been written to implement all aspects of the space-marching algorithm. The program is modular and is easily adapted to the widely varying geometries of internal flows. The space-marching algorithm has been tested by computing simple flows with known analytical solutions. The method has been used to predict complex 3-D turbulent flows. The algorithm is stable and very economical. A single sweep of the flow field by the space-marching method is approximately equivalent to one time-step of the time-marching method.
Govindan, T. R.↗
Physically weighted approximations of unsteady aerodynamic forces using the minimum-state method
The Minimum-State Method for rational approximation of unsteady aerodynamic force coefficient matrices, modified to allow physical weighting of the tabulated aerodynamic data, is presented. The approximation formula and the associated time-domain, state-space, open-loop equations of motion are given, and the numerical procedure for calculating the approximation matrices, with weighted data and with various equality constraints are described. Two data weighting options are presented. The first weighting is for normalizing the aerodynamic data to maximum unit value of each aerodynamic coefficient. The second weighting is one in which each tabulated coefficient, at each reduced frequency value, is weighted according to the effect of an incremental error of this coefficient on aeroelastic characteristics of the system. This weighting yields a better fit of the more important terms, at the expense of less important ones. The resulting approximate yields a relatively low number of aerodynamic lag states in the subsequent state-space model. The formulation forms the basis of the MIST computer program which is written in FORTRAN for use on the MicroVAX computer and interfaces with NASA's Interaction of Structures, Aerodynamics and Controls (ISAC) computer program. The program structure, capabilities and interfaces are outlined in the appendices, and a numerical example which utilizes Rockwell's Active Flexible Wing (AFW) model is given and discussed.
Karpel, Mordechay↗