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Numerical technique increases the efficiencies of the numerical methods involving Toeplitz matrices by reducing the number of multiplications required by an N-order Toeplitz matrix from N-cubed to N-squared multiplications. Some efficient algorithms are given.
An alternative to the Kalman filtering technique, based on logical rather than numerical techniques, is presented. It can be implemented on one or more microprocessors (with a fixed communications protocol between the individual microprocessors); requires only limited preprocessing of the input data; can have its constituent subsystem changed without major revision to the combiner as new or better navigation techniques, such as the global positioning system (GPS) or Loran-C, become available; and tolerates a wide variety of sensor, hardware, and software errors. The basic structure of the method and results of simulations of its performance in the presence of errors common to low-cost sensors (such as VOR or basic Omega) are presented, along with a discussion of possible extensions.
The thermoviscoelastic characterization of Kevlar 49/Fiberite 7714A epoxy composite lamina and the development of a numerical procedure to predict the viscoelastic response of any general laminate constructed from the same material were studied. The four orthotropic material properties, S sub 11, S sub 12, S sub 22, and S sub 66, were characterized by 20 minute static creep tests on unidirectional (0) sub 8, (10) sub 8, and (90) sub 16 lamina specimens. The Time-Temperature Superposition-Principle (TTSP) was used successfully to accelerate the characterization process. A nonlinear constitutive model was developed to describe the stress dependent viscoelastic response for each of the material properties. A numerical procedure to predict long term laminate properties from lamina properties (obtained experimentally) was developed. Numerical instabilities and time constraints associated with viscoelastic numerical techniques were discussed and solved. The numerical procedure was incorporated into a user friendly microcomputer program called Viscoelastic Composite Analysis Program (VCAP), which is available for IBM PC type computers. The program was designed for ease of use. The final phase involved testing actual laminates constructed from the characterized material, Kevlar/epoxy, at various temperatures and load level for 4 to 5 weeks. These results were compared with the VCAP program predictions to verify the testing procedure and to check the numerical procedure used in the program. The actual tests and predictions agreed for all test cases which included 1, 2, 3, and 4 fiber direction laminates.
A high-order physics-informed meshless finite difference numerical technique is introduced for solving the time-harmonic cold plasma wave equation in toroidal geometries, presenting a novel application of the generalized finite difference (GFD) method to plasma wave simulations. The algorithm employs an irregular distribution of computational points, with local point density informed by the shortest wavelength derived from the cold plasma dispersion relation. Numerical stability and robustness are addressed using regularization techniques. The algorithm, implemented for two spatial dimensions, solves for the wave electric field and is demonstrated to achieve convergence rates of $\mathcal{O}$($\mathcal{h}$ $\mathcal{P}$ ). Verification tests reproduce plane wave solutions, and example simulations of ion cyclotron resonance heating and electron cyclotron resonance heating demonstrate its capability, approaching realistic tokamak plasma scenarios. This work contributes to laying a foundation for the GFD method to be used in more sophisticated, optimized, and physically realistic full-wave simulations in time-harmonic plasma wave research.
The numerical technique is applied to the prediction of self-sustained oscillations in a two-axis model of the nonlinear system with sampled data. The sampled-data two-axis LST system model, and its stability equation are analyzed along with the exact solution of the stability equation by numerical-iterative techniques.
An application of a simple numerical technique which allows for the rapid construction of orthogonal coordinate systems about two dimensional and axisymmetric bodies is presented. The technique is based on a predictor corrector numerical method. It can be used to generate orthogonal meshes which have unequally spaced points in two directions. These orthogonal meshes in their transformed computational plane are, however, equally spaced so that the differencing for the metric coefficients and the fluid dynamic equation terms can be easily determined using equally spaced central finite differences. Solutions to the Navier-Stokes equations for flow over blunt bodies with reverse curvature are presented. The coupling of the time dependent fluid dynamic equations and the coordinate generator worked well with no undesirable effects noted.
Numerical techniques for constructing nonlinear predictive models to forecast solar flux directly from its time series are presented. This approach makes it possible to extract dynamical invariants of our system without reference to any underlying solar physics. We consider the dynamical evolution of solar activity in a reconstructed phase space that captures the attractor (strange), given a procedure for constructing a predictor of future solar activity, and discuss extraction of dynamical invariants such as Lyapunov exponents and attractor dimension.
Thermohydrodynamic effects in journal bearings operating under steady load in laminar regime are investigated. An analytical model for the finite and infinitely long journal bearings is formulated. The model includes correction factors for the cavitation effects in the unloaded region of the bearing and the mixing of the recirculating oil and supply oil at the oil inlet. A finite difference computer program is developed to numerically solve the governing equations of the continuity, Reynolds, energy, Laplace heat conduction, and a viscosity-temperature relation simultaneously. The program includes a numerical technique for obtaining an isothermal shaft temperature. The numerical results of temperature distribution and the heat effects on the bearing load carrying capacity agree closely with those of experimental findings. Several different sets of simpler boundary conditions for the energy equation are studied.
The study and development of two numerical techniques for the analysis of electromagnetic scattering from a rectangular wire mesh are described. Both techniques follow from one basic formulation and they are both solved in the spectral domain. These techniques were developed as a result of an investigation towards more efficient numerical computation for mesh scattering. These techniques are efficient for the following reasons: (a1) make use of the Fast Fourier Transform; (b2) they avoid any convolution problems by converting integrodifferential equations into algebraic equations; and (c3) they do not require inversions of any matrices. The first method, the SIT or Spectral Iteration Technique, is applied for regions where the spacing between wires is not less than two wavelengths. The second method, the SDCG or Spectral Domain Conjugate Gradient approach, can be used for any spacing between adjacent wires. A study of electromagnetic wave properties, such as reflection coefficient, induced currents and aperture fields, as functions of frequency, angle of incidence, polarization and thickness of wires is presented. Examples and comparisons or results with other methods are also included to support the validity of the new algorithms.
The Advisory Group for Aerospace Research and Development (AGARD) has requested my participation in the lecture series entitled Parallel Computing in Computational Fluid Dynamics to be held at the von Karman Institute in Brussels, Belgium on May 15-19, 1995. In addition, a request has been made from the US Coordinator for AGARD at the Pentagon for NASA Ames to hold a repetition of the lecture series on October 16-20, 1995. I have been asked to be a local coordinator for the Ames event. All AGARD lecture series events have attendance limited to NATO allied countries. A brief of the lecture series is provided in the attached enclosure. Specifically, I have been asked to give two lectures of approximately 75 minutes each on the subject of parallel solution techniques for the fluid flow equations on unstructured meshes. The title of my lectures is "Parallel CFD Algorithms for Aerodynamical Flow Solvers on Unstructured Meshes" (Parts I-II). The contents of these lectures will be largely review in nature and will draw upon previously published work in this area. Topics of my lectures will include: (1) Mesh partitioning algorithms. Recursive techniques based on coordinate bisection, Cuthill-McKee level structures, and spectral bisection. (2) Newton's method for large scale CFD problems. Size and complexity estimates for Newton's method, modifications for insuring global convergence. (3) Techniques for constructing the Jacobian matrix. Analytic and numerical techniques for Jacobian matrix-vector products, constructing the transposed matrix, extensions to optimization and homotopy theories. (4) Iterative solution algorithms. Practical experience with GIVIRES and BICG-STAB matrix solvers. (5) Parallel matrix preconditioning. Incomplete Lower-Upper (ILU) factorization, domain-decomposed ILU, approximate Schur complement strategies.
The goal of a coordinated effort between groups at GWU and NASA GSFC is the development of a low-cost, global, surface instrument network that continuously monitors three key carbon cycle gases in the atmospheric column: carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), as well as oxygen (O2) for atmospheric pressure profiles. The network will implement a low-cost, miniaturized, laser heterodyne radiometer (mini-LHR) that has recently been developed at NASA Goddard Space Flight Center. This mini-LHR is designed to operate in tandem with the passive aerosol sensor currently used in AERONET (a well established network of more than 450 ground aerosol monitoring instruments worldwide), and could be rapidly deployed into this established global network. Laser heterodyne radiometry is a well-established technique for detecting weak signals that was adapted from radio receiver technology. Here, a weak light signal, that has undergone absorption by atmospheric components, is mixed with light from a distributed feedback (DFB) telecommunications laser on a single-mode optical fiber. The RF component of the signal is detected on a fast photoreceiver. Scanning the laser through an absorption feature in the infrared, results in a scanned heterodyne signal io the RF. Deconvolution of this signal through the retrieval algorithm allows for the extraction of altitude contributions to the column signal. The retrieval algorithm is based on a spectral simulation program, SpecSyn, developed at GWU for high-resolution infrared spectroscopies. Variations io pressure, temperature, composition, and refractive index through the atmosphere; that are all functions of latitude, longitude, time of day, altitude, etc.; are modeled using algorithms developed in the MODTRAN program developed in part by the US Air Force Research Laboratory. In these calculations the atmosphere is modeled as a series of spherically symmetric shells with boundaries specified at defined altitudes. Temperature, pressure, and species mixing ratios are defined at these boundaries. Between the boundaries, temperature is assumed to vary linearly with altitude while pressure (and thus gas density) vary exponentially. The observed spectrum at the LHR instrument will be the integration of the contributions along this light path. For any absorption measurement the signal at a particular spectral frequency is a linear combination of spectral line contributions from several species. For each species that might absorb in a spectral region, we have pre-calculated its contribution as a function of temperature and pressure. The integrated path absorption spectrum can then by calculated using the initial sun angle (from location, date, and time) and assumptions about pressure and temperature profiles from an atmospheric model. The modeled spectrum is iterated to match the experimental observation using standard multilinear regression techniques. In addition to the layer concentrations, the numerical technique also provides uncertainty estimates for these quantities as well as dependencies on assumptions inherent in the atmospheric models.
The development and application of a numerical technique for rapid calculation of the far-field radiation patterns of a reflector antenna from either a measured or computed feed pattern are reported. The reflector is defined by the intersection of a cone with any surface of revolution or an offset sector of any surface of revolution. The feed is assumed to be linearly polarized and can have an arbitrary location. Both the copolarized and the cross-polarized reflector radiation patterns are computed. Calculations using the technique compare closely with measured radiation patterns of a waveguide-fed offset parabolic reflector. Unique features of this technique are freedom from restrictive feed assumptions and the numerical methods used in preparing the aperture-plane electric-field data for integration.
An algorithm has been developed to extrapolate nonlinear force-free magnetic fields from a source surface, given the proper boundary conditions. The results of this work; describing the mathematical formalism that was developed, the numerical techniques employed, and the stability criteria developed for these numerical schemes are presented. An analytical solution is used for a test case; the results show that the computational accuracy for the case of a nonlinear force-free magnetic field was on the order of a few percent ( 5%).
Several experimental studies [1,2,3] indicate that differences in the grain size of the target relative to the projectile could influence the cratering process. Impacts into coarse sand grains of size comparable to the projectile show some discrepancies with existing relationships for crater growth [e.g. 4]. Similarly, targets of ne grained, uniform in diameter glass spheres show differences in crater depth, transient crater diameter, and volume of ejecta excavated as a function of grain size [2,3]. The purpose of this work is to continue investigating how the relative grain size may influence early time coupling between a projectile and target, with implications for subsequent ejecta excavation and crater growth. In previous efforts we used numerical techniques to focus on the propagation of shock waves in coarse, granular media emphasizing the influence of relative grain size on crater growth, ejecta production, cratering efficiency, target strength, and crater shape [5,6,7]. In this study, we use experimental techniques - in part as a reality check for the numerical studies - to report on how coarse grained targets might influence ejecta excavation and crater shape. This body of work possesses important implications for ejecta excavation and cratering efficiency on asteroids that may possess rubble pile-like structures, and on planets that may possess either pre-fractured surfaces or large-scale heterogeneities in shock impedance.
An evaluation is conducted of two numerical techniques developed by Richmond (1961, 1966) for wire antennas and scattering bodies. It is concluded that a more efficient and accurate scheme can be devised by suitably combining the two techniques. This scheme, which is called the 'hybrid method', is well suited for a wire antenna mounted in a cavity. Reaction matching is employed in the case of the antenna, while point matching is used for the support structure. The described approach makes it possible to consider voltage generators without the use of any equivalent magnetic frill current sources. The number of unknown currents to be determined is essentially optimized by this combination of reaction matching and point matching. The resulting current distribution is a quantized distribution on the support structure and is continuous on the main radiator.
This paper presents numerical techniques for constructing nonlinear predictive models to forecast solar flux directly from its time series. This approach makes it possible to extract dynamical in variants of our system without reference to any underlying solar physics. We consider the dynamical evolution of solar activity in a reconstructed phase space that captures the attractor (strange), give a procedure for constructing a predictor of future solar activity, and discuss extraction of dynamical invariants such as Lyapunov exponents and attractor dimension.
A code for the simulation of nonequilibrium plasmas is being developed, with the capability to couple the plasma fluid-dynamics for a single fluid with a collisional-radiative model, where electronic states are treated as separate species. The model allows for non-Boltzmann distribution of the electronic states. Deviations from the Boltzmann distributions are expected to occur in the rapidly ionizing regime behind a strong shock or in the recombining regime during a fast expansion. This additional step in modeling complexity is expected to yield more accurate predictions of the nonequilibrium state and the radiation spectrum and intensity. An attempt at extending the code to molecular plasma flows is presented. The numerical techniques used, the thermochemical model, and the results of some numerical tests are described.
Numerical simulations of thermographic responses in composite materials have been a useful for evaluating and optimizing thermographic analysis techniques. Numerical solutions are particularly beneficial for thermographic techniques, since the fabrication of specimens with realistic flaws is difficult. Simulations are presented with different ply layups that incorporated the anisotropic thermal properties that exist in each ply. The results are compared to analytical series solutions and thermal measurements on composites with flat bottom holes and delaminations.