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Results for “two-level 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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45 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

A compact solution to computational acoustics

This paper demonstrates that the linearized, dimensional Euler equations for acoustic computation can be accurately solved as a set of decoupled first-order wave equations, and that if ordered properly, this system of simple waves has unambiguous, easily implemented boundary conditions, allowing waves of same group speeds to pass through numerical boundaries or comply with wall conditions. Thus, the task of designing a complex multi-dimensional scheme with approximate far-field boundary conditions reduces to the design of higher order schemes for the one-dimensional simple wave equation. A compact finite-difference scheme and a characteristically exact but numerically n(th) order accurate boundary condition are introduced for solving the first order wave equation. Spanning a three-point two-level stencil, this low-dispersion implicit scheme has a third order spatial accuracy when used on nonuniform meshes, fourth order accurate on uniform meshes, and a temporal accuracy of second order due to the choice of trapezoidal integration for algorithmic simplicity. The robustness and accuracy of the scheme are demonstrated through a series of numerical experiments and comparisons with published results. When tested on the one-dimensional wave equation on a uniform grid, this scheme allows a Gaussian wave packet to pass through any finite domain with low numerical dispersion characteristic of a spatially fourth-order scheme and reflections at numerical boundaries maintained below truncation error. On highly stretched and irregular grids, only mild dispersions are found in the solution while solutions by other methods fail or are severely distorted. Yet, this scheme is no more sophisticated to solve or implement than the Crank-Nicolson scheme. This scheme has been tested on four categories of the ICASE/LaRC benchmark problems, which include propagation of acoustic and convective waves in Cartesian and cylindrical domains, reflection of acoustic wave at stationary/moving boundaries, and sound generation by gust-blade interaction.

Fung, K.-Y.↗
NASA NTRS1987

Theoretical studies of Resonance Enhanced Stimulated Raman Scattering (RESRS) of frequency doubled Alexandrite laser wavelength in cesium vapor

The third phase of research will focus on the propagation and energy extraction of the pump and SERS beams in a variety of configurations including oscillator structures. In order to address these questions a numerical code capable of allowing for saturation and full transverse beam evolution is required. The method proposed is based on a discretized propagation energy extraction model which uses a Kirchoff integral propagator coupled to the three level Raman model already developed. The model will have the resolution required by diffraction limits and will use the previous density matrix results in the adiabatic following limit. Owing to its large computational requirements, such a code must be implemented on a vector array processor. One code on the Cyber is being tested by using previously understood two-level laser models as guidelines for interpreting the results. Two tests were implemented: the evolution of modes in a passive resonator and the evolution of a stable state of the adiabatically eliminated laser equations. These results show mode shapes and diffraction losses for the first case and relaxation oscillations for the second one. Finally, in order to clarify the computing methodology used to exploit the speed of the Cyber's computational speed, the time it takes to perform both of the computations previously mentioned to run on the Cyber and VAX 730 must be measured. Also included is a short description of the current laser model (CAVITY.FOR) and a flow chart of the test computations.

Lawandy, Nabil M.↗
NASA NTRS1990

Automated control of hierarchical systems using value-driven methods

An introduction is given to the Value-driven methodology, which has been successfully applied to solve a variety of difficult decision, control, and optimization problems. Many real-world decision processes (e.g., those encountered in scheduling, allocation, and command and control) involve a hierarchy of complex planning considerations. For such problems it is virtually impossible to define a fixed set of rules that will operate satisfactorily over the full range of probable contingencies. Decision Science Applications' value-driven methodology offers a systematic way of automating the intuitive, common-sense approach used by human planners. The inherent responsiveness of value-driven systems to user-controlled priorities makes them particularly suitable for semi-automated applications in which the user must remain in command of the systems operation. Three examples of the practical application of the approach in the automation of hierarchical decision processes are discussed: the TAC Brawler air-to-air combat simulation is a four-level computerized hierarchy; the autonomous underwater vehicle mission planning system is a three-level control system; and the Space Station Freedom electrical power control and scheduling system is designed as a two-level hierarchy. The methodology is compared with rule-based systems and with other more widely-known optimization techniques.

Pugh, George E.↗
NASA NTRS1990

Reliable and Efficient Parallel Processing Algorithms and Architectures for Modern Signal Processing

Least-squares (LS) estimations and spectral decomposition algorithms constitute the heart of modern signal processing and communication problems. Implementations of recursive LS and spectral decomposition algorithms onto parallel processing architectures such as systolic arrays with efficient fault-tolerant schemes are the major concerns of this dissertation. There are four major results in this dissertation. First, we propose the systolic block Householder transformation with application to the recursive least-squares minimization. It is successfully implemented on a systolic array with a two-level pipelined implementation at the vector level as well as at the word level. Second, a real-time algorithm-based concurrent error detection scheme based on the residual method is proposed for the QRD RLS systolic array. The fault diagnosis, order degraded reconfiguration, and performance analysis are also considered. Third, the dynamic range, stability, error detection capability under finite-precision implementation, order degraded performance, and residual estimation under faulty situations for the QRD RLS systolic array are studied in details. Finally, we propose the use of multi-phase systolic algorithms for spectral decomposition based on the QR algorithm. Two systolic architectures, one based on triangular array and another based on rectangular array, are presented for the multiphase operations with fault-tolerant considerations. Eigenvectors and singular vectors can be easily obtained by using the multi-pase operations. Performance issues are also considered.

Liu, Kuojuey Ray↗
NASA NTRS1993

Multigrid schemes for viscous hypersonic flows

Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm employs upwind spatial discretization with explicit multistage time stepping. Two-level versions of the various multigrid algorithms are applied to the two-dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving two different hypersonic flow problems. Some new multigrid schemes, based on semicoarsening strategies, are shown to be quite effective in relieving the stiffness caused by the high-aspect-ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 x 10(exp 6).

Swanson, R. C.↗
NASA NTRS1995

Local multiplicative Schwarz algorithms for convection-diffusion equations

We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numerical examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms.

Cai, Xiao-Chuan↗
NASA NTRS2000

Preliminary Design Optimization For A Supersonic Turbine For Rocket Propulsion

In this study, we present a method for optimizing, at the preliminary design level, a supersonic turbine for rocket propulsion system application. Single-, two- and three-stage turbines are considered with the number of design variables increasing from 6 to 11 then to 15, in accordance with the number of stages. Due to its global nature and flexibility in handling different types of information, the response surface methodology (RSM) is applied in the present study. A major goal of the present Optimization effort is to balance the desire of maximizing aerodynamic performance and minimizing weight. To ascertain required predictive capability of the RSM, a two-level domain refinement approach has been adopted. The accuracy of the predicted optimal design points based on this strategy is shown to he satisfactory. Our investigation indicates that the efficiency rises quickly from single stage to 2 stages but that the increase is much less pronounced with 3 stages. A 1-stage turbine performs poorly under the engine balance boundary condition. A portion of fluid kinetic energy is lost at the turbine discharge of the 1-stage design due to high stage pressure ratio and high-energy content, mostly hydrogen, of the working fluid. Regarding the optimization technique, issues related to the design of experiments (DOE) has also been investigated. It is demonstrated that the criteria for selecting the data base exhibit significant impact on the efficiency and effectiveness of the construction of the response surface.

Papila, Nilay↗
NASA NTRS2024

Suppressing Polarization Mode Dispersion with the Quantum Zeno Effect

Polarization mode dispersion can introduce quantum decoherence in polarization encoded information, limiting the range of quantum communications protocols. Therefore, strategies to completely nullify the affect would reduce quantum decoherence and potentially increase the operational range of such technology. We construct a quantum model of polarization mode dispersion alongside a two-level absorbing material. The two-level material serves to destructively measure one of two orthogonal polarization modes, thus projecting the polarization onto the other state. The theoretical results are supported by a numerical simulation in Mathematica Documentation where we and compare the evolution of the polarization state with and without the absorbing material. We find that this strategy is effective in suppressing the effects of polarization mode dispersion, and that this method produces a global phase shift related the waveguide’s birefringent properties.

waveguides↗