PROPOSED STUDIES IN THE FIELD OF MULTIVARIATE APPROXIMATIONS
Numerical analysis of functions with independent variables - guidance systems
MATHEMATICS↗
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Results for “numerical approximation and analysis”
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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Chemical control of rate and onset temperature of nadimide polymerization
The chemistry of norbornenyl capped imide compounds (nadimides) is briefly reviewed with emphasis on the contribution of Diels-Alder reversion in controlling the rate and onset of the thermal polymerization reaction. Control of onset temperature of the cure exotherm by adjusting the concentration of maleimide is demonstrated using selected model compounds. The effects of nitrophenyl compounds as free radical retarders on nadimide reactivity are discussed. A simple copolymerization model is proposed for the overall nadimide cure reaction. An approximate numerical analysis is carried out to demonstrate the ability of the model to simulate the trends observed for both maleimide and nitrophenyl additions.
Lauver, R. W.↗
Synchrotron emissivity near the electron cyclotron and upper hybrid frequencies
The spontaneous synchrotron emissivity from a high density, weakly relativistic plasma in thermal equilibrium is discussed. Thermal effects on the dielectric polarization of the plasma are included in the analysis, and the result is compared with computations of the emissivity based upon the cold plasma approximation. A numerical analysis is performed for frequencies in the vicinity of both the electron cyclotron frequency and the upper hybrid resonance. Significant modifications to the synchrotron emissivity in the cold plasma approximation are found in both of these frequency regimes.
Freund, H. P.↗
Structure-preserving neural networks for the regularized entropy-based closure of a linear, kinetic, radiative transport equation
The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural network-based approximation to the entropy-based closure method to accurately compute the solution of the multi-dimensional moment system with a low memory footprint and competitive computational time. We extend methods developed for the standard entropy-based closure to the regularized entropy-based closures. The main idea is to interpret structure-preserving neural network approximations of the regularized entropy-based closure as a two-stage approximation to the original entropy-based closure. We conduct a numerical analysis of this approximation and investigate optimal parameter choices. Our numerical experiments demonstrate that the method has a much lower memory footprint than traditional methods with competitive computation times and simulation accuracy. The code and all trained networks are provided on GitHub.
entropy closure↗
CSM research: Methods and application studies
Computational mechanics is that discipline of applied science and engineering devoted to the study of physical phenomena by means of computational methods based on mathematical modeling and simulation, utilizing digital computers. The discipline combines theoretical and applied mechanics, approximation theory, numerical analysis, and computer science. Computational mechanics has had a major impact on engineering analysis and design. When applied to structural mechanics, the discipline is referred to herein as computational structural mechanics. Complex structures being considered by NASA for the 1990's include composite primary aircraft structures and the space station. These structures will be much more difficult to analyze than today's structures and necessitate a major upgrade in computerized structural analysis technology. NASA has initiated a research activity in structural analysis called Computational Structural Mechanics (CSM). The broad objective of the CSM activity is to develop advanced structural analysis technology that will exploit modern and emerging computers, such as those with vector and/or parallel processing capabilities. Here, the current research directions for the Methods and Application Studies Team of the Langley CSM activity are described.
Knight, Norman F., Jr.↗
Computers boost structural technology
Derived from matrix methods of structural analysis and finite element methods developed over the last three decades, computational structures technology (CST) blends computer science, numerical analysis, and approximation theory into structural analysis and synthesis. Recent significant advances in CST include stochastic-based modeling, strategies for performing large-scale structural calculations on new computing systems, and the integration of CST with other disciplinary modules for multidisciplinary analysis and design. New methodologies have been developed at NASA for integrated fluid-thermal structural analysis and integrated aerodynamic-structure-control design. The need for multiple views of data for different modules also led to the development of a number of sophisticated data-base management systems. For CST to play a role in the future development of structures technology and in the multidisciplinary design of future flight vehicles, major advances and computational tools are needed in a number of key areas.
Noor, Ahmed K.↗
Computational structures technology and UVA Center for CST
Rapid advances in computer hardware have had a profound effect on various engineering and mechanics disciplines, including the materials, structures, and dynamics disciplines. A new technology, computational structures technology (CST), has recently emerged as an insightful blend between material modeling, structural and dynamic analysis and synthesis on the one hand, and other disciplines such as computer science, numerical analysis, and approximation theory, on the other hand. CST is an outgrowth of finite element methods developed over the last three decades. The focus of this presentation is on some aspects of CST which can impact future airframes and propulsion systems, as well as on the newly established University of Virginia (UVA) Center for CST. The background and goals for CST are described along with the motivations for developing CST, and a brief discussion is made on computational material modeling. We look at the future in terms of technical needs, computing environment, and research directions. The newly established UVA Center for CST is described. One of the research projects of the Center is described, and a brief summary of the presentation is given.
Noor, Ahmed K.↗
Computational structures technology
Computational structures technology (CST), which has emerged from FEM developments, is a fusion of materials modeling, structural and dynamic analysis and synthesis methods, on the one hand, and numerical analysis and approximation theory, on the other. In addition to computational materials modeling, CST encompasses computational methods for predicting the response, performance, failure, and service life of structures and their components, as well as automated methods for structural synthesis and optimization.
Noor, Ahmed K.↗
A scaling law for energy transfer by inelastic electron-molecule collisions in mixtures
The equation governing the electron energy distribution in the presence of a spatially uniform electric field in a weakly ionized gas was reformulated into an integral equation for the logarithmic slope of the distribution function. For gas mixtures in which the dominant electron energy loss mechanism is by vibrational excitation of the molecules, this equation is suitable for approximate analysis and exact numerical solution by iteration. Superelastic collisions are easily included in this formulation, and do not seriously effect the convergence of the numerical scheme. The approximate analytical results are only qualitatively correct, but suggest appropriate parameters which correlate the exact numerical results very well. The distribution function as well as certain gross properties such as net energy transfer into vibration, mean energy, and drift velocity depend primarily on a single nondimensional parameter involving only E/N and the cross sections.
Bienkowski, G. K.↗
Stability analysis of numerical boundary conditions and implicit difference approximations for hyperbolic equations
Implicit, noniterative, finite difference schemes were recently developed by several authors for multidimensional systems of nonlinear hyperbolic partial differential equations. When applied to linear model equations with periodic boundary conditions those schemes are unconditionally stable (A-stable). As applied in practice the algorithms often face a severe time step restriction. A major source of the difficulty is the treatment of the numerical boundary conditions. One conjecture was that unconditional stability requires implicit numerical boundary conditions. An apparent counter example was the space time extrapolation considered by Gustafsson, Kreiss, and Sunstrom. Spatial (implicit) and space time (explicit) extrapolation using normal mode analysis for a finite and infinite number of spatial mesh intervals are examined. The results indicate that for unconditional stability with a finite number of spatial mesh intervals, the numerical boundary conditions must be implicit.
Beam, R. M.↗
Stability analysis of numerical boundary conditions and implicit difference approximations for hyperbolic equations
Previously announced in STAR as N81-33870
Beam, R. M.↗
Comparison of approximate and numerical analyses of nonlinear combustion instability
At the present time, there are three general analytical techniques available to study problems of unsteady motions in rocket motors: linear stability analysis; approximate nonlinear analysis, founded on examining the behavior of coupled normal modes; and numerical calculations based on the conservation equations for one-dimensional flows. The last two yield the linear results as a limit. It is the main purpose of this paper to check the accuracy of the approximate analysis against the numerical analysis for some special cases. The results provide some justification for using the approximate analysis to study three-dimensional problems.
Culick, F. E. C.↗
Derivation and evaluation of an approximate analysis for three-dimensional viscous subsonic flow with large secondary velocities
An approximate analysis is presented for calculating three-dimensional, low Mach number, laminar viscous flows in curved passages with large secondary flows and corner boundary layers. The analysis is based on the decomposition of the overall velocity field into inviscid and viscous components with the overall velocity being determined from superposition. An incompressible vorticity transport equation is used to estimate inviscid secondary flow velocities to be used as corrections to the potential flow velocity field. A parabolized streamwise momentum equation coupled to an adiabatic energy equation and global continuity equation is used to obtain an approximate viscous correction to the pressure and longitudinal velocity fields. A collateral flow assumption is invoked to estimate the viscous correction to the transverse velocity fields. The approximate analysis is solved numerically using an implicit ADI solution for the viscous pressure and velocity fields. An iterative ADI procedure is used to solve for the inviscid secondary vorticity and velocity fields. This method was applied to computing the flow within a turbine vane passage with inlet flow conditions of M = 0.1 and M = 0.25, Re = 1000 and adiabatic walls, and for a constant radius curved rectangular duct with R/D = 12 and 14 and with inlet flow conditions of M = 0.1, Re = 1000, and adiabatic walls.
Anderson, O. L.↗
Turbulent flow field predictions in sharply curved turn around ducts
In this investigation, two-dimensional turbulent flow of incompressible Newtonian fluids in sharply curved 180 deg turn around ducts is studied. Results of an approximate numerical flow field analysis utilizing an orthogonal, body-fitted, curvilinear coordinate system are compared to results based on a traditional cylindrical reference frame. Qualitative indication of general streamfield characteristics as well as quantitative benchmarks for the planning of future experimentation are provided. In addition, preliminary results of an augmented kappa-epsilon turbulence model analysis, which explicitly accounts for the effects of streamline curvature and pressure strain in internal turbulent flows, are presented. Specific model difficulties are discussed and comparisons with standard kappa-esilon model predictions are included.
Santi, L. M.↗
Turbulent flow field predictions in sharply curved turn-around ducts
Two-dimensional turbulent flow of incompressible Newtonian fluids in sharply curved 180 deg turn around ducts is studied. Results of an approximate numerical flow field analysis utilizing an orthogonal, body-fitted, curvilinear coordinate system are compared to results based on a traditional cylindrical reference frame. Qualitative induction of general streamfield characteristics as well as quantitative benchmarks for the planning of future experimentation are provided. In addition, preliminary results of an augmented kappa - epsilon turbulence model analysis, which explicitly accounts for the effects of streamline curvature and pressure strain in internal turbulent flows, are presented. Specific model difficulties are discussed and comparisons with standard kappa - epsilon model predictions are included.
Santi, L. M.↗
Difference-Equation/Flow-Graph Circuit Analysis
Numerical technique enables rapid, approximate analyses of electronic circuits containing linear and nonlinear elements. Practiced in variety of computer languages on large and small computers; for circuits simple enough, programmable hand calculators used. Although some combinations of circuit elements make numerical solutions diverge, enables quick identification of divergence and correction of circuit models to make solutions converge.
Mcvey, I. M.↗
Automatic Generation of Algorithms for the Statistical Analysis of Planetary Nebulae Images
Analyzing data sets collected in experiments or by observations is a Core scientific activity. Typically, experimentd and observational data are &aught with uncertainty, and the analysis is based on a statistical model of the conjectured underlying processes, The large data volumes collected by modern instruments make computer support indispensible for this. Consequently, scientists spend significant amounts of their time with the development and refinement of the data analysis programs. AutoBayes [GF+02, FS03] is a fully automatic synthesis system for generating statistical data analysis programs. Externally, it looks like a compiler: it takes an abstract problem specification and translates it into executable code. Its input is a concise description of a data analysis problem in the form of a statistical model as shown in Figure 1; its output is optimized and fully documented C/C++ code which can be linked dynamically into the Matlab and Octave environments. Internally, however, it is quite different: AutoBayes derives a customized algorithm implementing the given model using a schema-based process, and then further refines and optimizes the algorithm into code. A schema is a parameterized code template with associated semantic constraints which define and restrict the template s applicability. The schema parameters are instantiated in a problem-specific way during synthesis as AutoBayes checks the constraints against the original model or, recursively, against emerging sub-problems. AutoBayes schema library contains problem decomposition operators (which are justified by theorems in a formal logic in the domain of Bayesian networks) as well as machine learning algorithms (e.g., EM, k-Means) and nu- meric optimization methods (e.g., Nelder-Mead simplex, conjugate gradient). AutoBayes augments this schema-based approach by symbolic computation to derive closed-form solutions whenever possible. This is a major advantage over other statistical data analysis systems which use numerical approximations even in cases where closed-form solutions exist. AutoBayes is implemented in Prolog and comprises approximately 75.000 lines of code. In this paper, we take one typical scientific data analysis problem-analyzing planetary nebulae images taken by the Hubble Space Telescope-and show how AutoBayes can be used to automate the implementation of the necessary anal- ysis programs. We initially follow the analysis described by Knuth and Hajian [KHO2] and use AutoBayes to derive code for the published models. We show the details of the code derivation process, including the symbolic computations and automatic integration of library procedures, and compare the results of the automatically generated and manually implemented code. We then go beyond the original analysis and use AutoBayes to derive code for a simple image segmentation procedure based on a mixture model which can be used to automate a manual preproceesing step. Finally, we combine the original approach with the simple segmentation which yields a more detailed analysis. This also demonstrates that AutoBayes makes it easy to combine different aspects of data analysis.
Fischer, Bernd↗
Analytical and experimental study of flow phenomena in noncavitating rocket pump inducers
The flow processes in rocket pump inducers are summarized. The experimental investigations were carried out with air as the test medium. The major characteristics features of the rocket pump inducers are low flow coefficient (0.05 to 0.2) large stagger angle (70 deg to 85 deg) and high solidity blades of little or no camber. The investigations are concerned with the effect of viscosity not the effects of cavitation. Flow visualization, conventional and hot wire probe measurement inside and at the exit of the blade passage, were the analytical methods used. The experiment was carried out using four three and two bladed inducers with cambered blades. Both the passage and the exit flow were measured. The basic research and boundary layer investigation was carried out using a helical flat plate (of some dimensions as the inducer blades tested), and flat plate helical inducer (four bladed). Detailed mean and turbulence flow field inside the passage as well as the exit of the rotor were derived from these measurement. The boundary layer, endwall, and other passage data reveal extremely complex nature of the flow, with major effects of viscosity present across the entire passage. Several analyses were carried out to predict the flow field in inducers. These included an approximate analysis, the shear pumping analysis, and a numerical solution of exact viscous equations with approximate modeling for the viscous terms.
Lakshminarayana, B.↗