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Tesseral harmonics of coordinates using Baker- Nunn data and geopotential and dynamical procedures, noting iterative cycle for correction determination
An engineering and software specification which was written for a computer program to calculate aeroelastic structural loads including the effects of nonlinear aerodynamics is presented. The procedure used in the program for an iterative aeroelastic solution (PIAS) is to alternately execute two computer codes: one to calculate aerodynamic loads for a specific wing shape, and another to calculate the deflected shape caused by this loading. A significant advantage to the design of PIAS is that the initial aerodynamic module can be replaced with others. The leading edge vortex (LEV) program is used as the aerodynamic module in PIAS. This provides the capability to calculate aeroelastic loads, including the effects of a separation induced leading edge vortex. The finite element method available in ATLAS Integrated structural analysis and design system is used to determine the deflected wing shape for the applied aerodynamics and inertia loads. The data management capabilities in ATLAS are used by the execution control monitor (ECM) of PIAS to control the solution process.
Finite difference method for solving symmetric positive linear differential equations
Solution of heavy asymmetric gyroscope using properties of Lie operator
Existence of approximate solution for critical slab hot-spot size for entire range of practical thermal explosion problems
Size-reduction techniques for determining efficient time-domain state-space aeroservoelastic models are presented. Various rational function approximation methods of the unsteady aerodynamic force coefficients are brought to a common motion, emphasizing their differences. Among these, the classic Roger's method is the easier to apply but its resulting number of aerodynamic states is typically equal to or larger than the number of structural states. On the other hand, the minimum-state (MS) method, which typically reduces the number of aerodynamic states by 70 percent or more, requires the solution of an iterative nonlinear least-square solution. The MS computational efforts are reduced significantly when three approximation constraints are applied.
Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.
An efficiently hybrid approach to exploit hyperspectral imagery and unmix spectral pixels. This hybrid approach uses a genetic algorithm to solve the abundance vector for the first pixel of a hyperspectral image cube. This abundance vector is used as initial state in a robust filter to derive the abundance estimate for the next pixel. By using Kalman filter, the abundance estimate for a pixel can be obtained in one iteration procedure which is much fast than genetic algorithm. The output of the robust filter is fed to genetic algorithm again to derive accurate abundance estimate for the current pixel. The using of robust filter solution as starting point of the genetic algorithm speeds up the evolution of the genetic algorithm. After obtaining the accurate abundance estimate, the procedure goes to next pixel, and uses the output of genetic algorithm as the previous state estimate to derive abundance estimate for this pixel using robust filter. And again use the genetic algorithm to derive accurate abundance estimate efficiently based on the robust filter solution. This iteration continues until pixels in a hyperspectral image cube end.
A new algorithm for an iterative computation of solutions of Laplace's or Poisson's equations in two dimensions, using Green's second identity, is presented. This algorithm converges strongly and geometrically and can be applied to curved, irregular, or moving boundaries with nonlinear and/or discontinuous boundary conditions. It has been implemented in Pascal on a number of micro- and minicomputers and applied to several geometries. Cases with known analytic solutions have been tested. Convergence to within 0.1 percent to 0.01 percent of the theoretical values are obtained in a few minutes on a microcomputer.
Accounts of the symmetric Galerkin approach to boundary element analysis (BEA) have recently been published. This paper attempts to add to the understanding of this method by addressing a series of fundamental issues associated with its potential computational efficiency. A new symmetric Galerkin theoretical formulation for both the (harmonic) heat conduction and the (biharmonic) elasticity problem that employs regularized singular and hypersingular boundary integral equations (BIEs) is presented. The novel use of regularized BIEs in the Galerkin context is shown to allow straightforward incorporation of curved, isoparametric elements. A symmetric reusable intrinsic sample point (RISP) numerical integration algorithm is shown to produce a Galerkin (i.e., double) integration strategy that is competitive with its counterpart (i.e., singular) integration procedure in the collocation BEA approach when the time saved in the symmetric equation solution phase is also taken into account. This new formulation is shown to be capable of employing hypersingular BIEs while obviating the requirement of C 1 continuity, a fact that allows the employment of the popular continuous element technology. The behavior of the symmetric Galerkin BEA method with regard to both direct and iterative equation solution operations is also addressed. A series of example problems are presented to quantify the performance of this symmetric approach, relative to the more conventional unsymmetric BEA, in terms of both accuracy and efficiency. It is concluded that appropriate implementations of the symmetric Galerkin approach to BEA indeed have the potential to be competitive with, if not superior to, collocation-based BEA, for large-scale problems.
A mixed method using both the method of integral relations and the finite difference technique is developed for the solution of unsteady flow problems. The integral relations method is based upon a chosen interpolating function dependent only on the time domain. The resulting local semidiscrete finite element equations obtained are assembled into a global form. The spatial derivatives at the nodes are replaced by finite difference operators and the discretized nonlinear algebraic system is solved by an iterative scheme. Solutions are obtained for the one-dimensional gasdynamics equation, the one-dimensional wave equation and Burger's model of turbulence. Agreement with other numerical and analytical solutions is excellent for the gasdynamics problem and satisfactory for the Burger equation in cases of small viscous effects.
Algebraic matrix Riccati differential equation solution by Newton-Raphson iteration method
A hybrid numerical procedure is presented for the prediction of the aerodynamic and acoustic performance of advanced turboprops. A hybrid scheme is proposed which in principle leads to a consistent simultaneous prediction of both fields. In the inner flow a finite difference method, the Approximate-Factorization Alternating-Direction-Implicit (ADI) scheme, is used to solve the nonlinear Euler equations. In the outer flow the linearized acoustic equations are solved via a Boundary-Integral Equation (BIE) method. The two solutions are iteratively matched across a fictitious interface in the flow so as to maintain continuity. At convergence the resulting aerodynamic load prediction will automatically satisfy the appropriate free-field boundary conditions at the edge of the finite difference grid, while the acoustic predictions will reflect the back-reaction of the radiated field on the magnitude of the loading source terms, as well as refractive effects in the inner flow. The equations and logic needed to match the two solutions are developed and the computer program implementing the procedure is described. Unfortunately, no converged solutions were obtained, due to unexpectedly large running times. The reasons for this are discussed and several means to alleviate the situation are suggested.
An exact method is presented for two-dimensional subsonic flow within the limitations of the tangent gas approximation. While Woods (1961) studied these equations and proposed iterative methods for the solution of both the iterative and inverse problems, the inverse method here presented is noniterative and exact. It is shown that the direct Euler solution over the designed airfoil is very close to the input speed distribution, and that the constraints necessitated by upstream condition and closure requirements are easily incorporated.
One of the promising combinations of finite element approaches for scattering problems uses Whitney edge elements, spherical vector wave-absorbing boundary conditions, and bi-conjugate gradient solution for the frequency-domain near field. Each of these approaches may be criticized. Low-order elements require high mesh density, but also result in fast, reliable iterative convergence. Spherical wave-absorbing boundary conditions require additional space to be meshed beyond the most minimal near-space region, but result in fully sparse, symmetric matrices which keep storage and solution times low. Iterative solution is somewhat unpredictable and unfriendly to multiple right-hand sides, yet we find it to be uniformly fast on large problems to date, given the other two approaches. Implementation of these approaches on a distributed memory, message passing machine yields huge dividends, as full scalability to the largest machines appears assured and iterative solution times are well-behaved for large problems. We present times and solutions for computed RCS for a conducting cube and composite permeability/conducting sphere on the Intel ipsc860 with up to 16 processors solving over 200,000 unknowns. We estimate problems of approximately 10 million unknowns, encompassing 1000 cubic wavelengths, may be attempted on a currently available 512 processor machine, but would be exceedingly tedious to prepare. The most severe bottlenecks are due to the slow rate of mesh generation on non-parallel machines and the large transfer time from such a machine to the parallel processor. One solution, in progress, is to create and then distribute a coarse mesh among the processors, followed by systematic refinement within each processor. Elimination of redundant node definitions at the mesh-partition surfaces, snap-to-surface post processing of the resulting mesh for good modelling of curved surfaces, and load-balancing redistribution of new elements after the refinement are auxiliary steps expected to result in a robust low i/o system for very large finite element problems.
This project details the design and analysis of a structure to replace the interface of the P-3B nadir port with an optimized interface for science installations. A new nadir port plug has been designed to replace the OEM (Original Equipment Manufacturer) plug (Lockheed PN 910169) currently used in Nadir ports 1 and 2 on the NASA P-3B aircraft. The plug consists of a milled frame that can be outfitted with customizable flat plates to meet a broad range of science needs. The frame slides into place using the existing P-3B rail system using a lever and tie-rod assembly. The seal interface will contact the Fuselage skin of the aircraft and consists of a bulb E-seal that is riveted around the perimeter of the frame. The flat plate (20 inches x 31 inches) provides a large profile that can be outfitted based on science mission goals and requirements to attach multiple instruments. This is a significant increase to the aircraft capability. Previously, the OEM plug had to be modified to hold very small plates, windows, or instruments limiting the use of the ports.There were several challenges for this project that included a constrained schedule, lack of historical references, and reverse engineering. The unusually tight schedule for design, manufacture, and install limited potential approaches. In addition, design of a new interface to replace the existing plug, on an aircraft designed in the 1960's by Lockheed for the Navy with little to no documentation, required substantial reverse engineering. In order to accomplish this, a suitable method to determine interface requirements with the aircraft had to be solved. After several iterations, the solution was to implement laser scanning techniques to scan the aircraft and the OEM plug and generate a 3D model to capture the design envelope. The structure is designed to maintain a positive margin of safety when subjected to the inertial, pressure, and aerodynamic load requirements for an external installation on the P-3B, as described in the Wallops' P-3B Design Requirements 548-RQMT-0001 Rev. A . A finite element model is created in FEMAP (Finite Element Modeling And Postprocessing) and is run through NX Nastran solver to analyze the structure. After several iterations of analysis, the structure was enveloped to hold 115 pounds evenly distributed on the plate.
We recently introduced a new geometric trilateration (GT) method for GPS-style positioning. Preliminary singlepoint analysis using simplistic error assumptions indicates that the new scheme delivers almost indistinguishable localization accuracy as the traditional Newton-Raphson (NR) approach. Also, the same computation procedure can be used to perform high-accuracy relative positioning between a reference vehicle and an arbitrary number of target vehicles. This scheme has the potential to enable a) new mission concepts in collaborative science, b) in-situ navigation services for human Mars missions, and c) lower cost and faster acquisition of GPS signals for consumer-grade GPS products. The new GT scheme differs from the NR scheme as follows: 1. The new scheme is derived from Pythagoras Theorem, whereas the NR method is based on the principle of linear regression. 2. The NR method uses the absolute locations (xi, yi, zi)’s of the GPS satellites as input to each step of the localization computation. The GT method uses the Directional Cosines Ui’s from Earth’s center to the GPS satellite Si. 3. Both the NR method and the GT method iterate to converge to a localized solution. In each iteration step, multiple matrix operations are performed. The NR method constructs a different matrix in each iterative step, thus requires performing a new set of matrix operations in each step. The GT scheme uses the same matrix in each iteration, thus requiring computing the matrix operations only once for all subsequent iterations. In this paper, we perform an in-depth comparison between the GT scheme and the NR method in terms of a) GPS localization accuracy in the GPS operation environment, b) its sensitivity with respect to systematic errors and random errors, and c) computation load required to converge to a localization solution.
Iteration method for solution of differential equations and numerical treatment of cyclotron stability