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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Acoustooptic linear algebra processors - Architectures, algorithms, and applications

Architectures, algorithms, and applications for systolic processors are described with attention to the realization of parallel algorithms on various optical systolic array processors. Systolic processors for matrices with special structure and matrices of general structure, and the realization of matrix-vector, matrix-matrix, and triple-matrix products and such architectures are described. Parallel algorithms for direct and indirect solutions to systems of linear algebraic equations and their implementation on optical systolic processors are detailed with attention to the pipelining and flow of data and operations. Parallel algorithms and their optical realization for LU and QR matrix decomposition are specifically detailed. These represent the fundamental operations necessary in the implementation of least squares, eigenvalue, and SVD solutions. Specific applications (e.g., the solution of partial differential equations, adaptive noise cancellation, and optimal control) are described to typify the use of matrix processors in modern advanced signal processing.

Casasent, D.↗
NASA NTRS1986

Resonance ionization mass spectrometry for isotopic abundance measurements

Resonance ionization mass spectrometry (RIMS) is a relatively new laser-based technique for the determination of isotopic abundances. The resonance ionization process depends upon the stepwise absorption of photons from the laser, promoting atoms of the element of interest through progressively higher electronic states until an ion is formed. Sensitivity arises from the efficiency of the resonant absorption process when coupled with the power available from commercial laser sources. Selectivity derives naturally from the distinct electronic structure of different elements. This isobaric discrimination has provided the major impetus for development of the technique. Resonance ionization mass spectrometry was used for analysis of the isotopic abundances of the rare earth lutetium. Isobaric interferences from ytterbium severely effect the ability to measure small amounts of the neutron-deficient Lu isotopes by conventional mass spectrometric techniques. Resonance ionization for lutetium is performed using a continuous-wave laser operating at 452 nm, through a sequential two-photon process, with one photon exciting the intermediate resonance and the second photon causing ionization. Ion yields for microgram-sized quantities of lutetium lie between 10(6) and 10(7) ions per second, at overall ionization efficiencies approaching 10(-4). Discrimination factors against ytterbium greater than 10(6) have been measured. Resonance ionization for technetium is also being explored, again in response to an isobaric interference, molybdenum. Because of the relatively high ionization potential for Tc, three-photon, two-color RIMS processes are being developed.

Miller, C. M.↗
NASA NTRS1985

Topics in spectral methods

After detailing the construction of spectral approximations to time-dependent mixed initial boundary value problems, a study is conducted of differential equations of the form 'partial derivative of u/partial derivative of t = Lu + f', where for each t, u(t) belongs to a Hilbert space such that u satisfies homogeneous boundary conditions. For the sake of simplicity, it is assumed that L is an unbounded, time-independent linear operator. Attention is given to Fourier methods of both Galerkin and pseudospectral method types, the Galerkin method, the pseudospectral Chebyshev and Legendre methods, the error equation, hyperbolic partial differentiation equations, and time discretization and iterative methods.

Gottlieb, D.↗
NASA NTRS1986

Growth-induced anisotropy in bismuth - Rare-earth iron garnets

The bismuth-doped rare-earth iron garnets, (R3-x-yBixPby)Fe5O12 (Bi:RIG, R = Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and Y), were prepared under constant growth conditions to investigate the influence of ionic species on the bismuth-based growth-induced uniaxial anisotropy K(u) exp g. The effect of ionic species on growth-induced anisotropy in Bi:RIG was not consistent with the ionic size model of site ordering. In particular, Bi:SmIG, Bi:EuIG, and Bi:TbIG displayed high growth-induced anisotropies, up to 331,000 erg/cu cm at room temperature for x of about 0.5. The temperature dependence of these K(u) exp gs was somewhat higher than that of the well studied Bi:YIG. The site ordering of Bi can be modeled by assuming that small, low-oxygen-coordination BiOw exp +3-2 w melt complexes have a strong site selectivity for small, high-oxygen coordination sites at the growth interface.

Fratello, V. J.↗
NASA NTRS1987

An L-U implicit multigrid algorithm for the three-dimensional Euler equations

An LU implicit multigrid scheme is developed for the calculation of three-dimensional transonic flow through rotating cascades. This numerical method solves the unsteady Euler equations of gas dynamics in a finite-volume form. The implicit scheme makes it possible to take a much larger time step than is normally permitted in most explicit schemes, while the multigrid method is incorporated to accelerate the convergence rate for steady state calculations. Using this method, computational storage requirements are comparable to those of explicit schemes, while operation counts are considerably less than those found in the more widely-used ADI schemes.

Yokota, Jeffrey W.↗
NASA NTRS1987

Relaxation schemes for spectral multigrid methods

The effectiveness of relaxation schemes for solving the systems of algebraic equations which arise from spectral discretizations of elliptic equations is examined. Iterative methods are an attractive alternative to direct methods because Fourier transform techniques enable the discrete matrix-vector products to be computed almost as efficiently as for corresponding but sparse finite difference discretizations. Preconditioning is found to be essential for acceptable rates of convergence. Preconditioners based on second-order finite difference methods are used. A comparison is made of the performance of different relaxation methods on model problems with a variety of conditions specified around the boundary. The investigations show that iterations based on incomplete LU decompositions provide the most efficient methods for solving these algebraic systems.

Phillips, Timothy N.↗
NASA NTRS1987

Numerical simulation of vortical flows over a strake-delta wing

The vortical flow fields over a double-delta wing with sweep angles 80 and 60 deg are investigated by means of numerical simulations based on the LU-ADI code of Fujii and Obayashi (1986) for the three-dimensional thin-layer Navier-Stokes equations. The results obtained using an 850,000-point grid at angle of attack alpha = 6-40 deg are presented graphically, compared with experimental data, and characterized in detail. Qualitatively accurate simulations are obtained for transition phenomena such as strake/wing-vortex interaction at alpha = 12 deg, bubble-type vortex breakdown near the trailing edge at alpha = 30 deg, and spiral-type breakdown at alpha = 35 deg. It is suggested that quantitative simulations can be achieved at higher grid resolution.

Fujii, Kozo↗
NASA NTRS1987

Numerical simulations of aerodynamic contribution of flows about a space-plane-type configuration

The slightly supersonic viscous flow about the space-plane under development at the National Aerospace Laboratory (NAL) in Japan was simulated numerically using the LU-ADI algorithm. The wind-tunnel testing for the same plane also was conducted with the computations in parallel. The main purpose of the simulation is to capture the phenomena which have a great deal of influence to the aerodynamic force and efficiency but is difficult to capture by experiments. It includes more accurate representation of vortical flows with high angles of attack of an aircraft. The space-plane shape geometry simulated is the simplified model of the real space-plane, which is a combination of a flat and slender body and a double-delta type wing. The comparison between experimental results and numerical ones will be done in the near future. It could be said that numerical results show the qualitatively reliable phenomena.

Matsushima, Kisa↗
NASA NTRS1987

Numerical simulation of viscous flows over transonic aircraft configurations

Numerical simulation of compressible viscous flow fields is performed for a transonic transport configuration. A single structured grid system is constructed using analytical transformations such as conformal mapping, shearing/twisting/rotating/clustering/stretching transformations. The Reynolds-averaged, thin-layer Navier-Stokes equations are solved on a supercomputer, FACOM VP-400, using the LU-ADI factorization method.

Takanashi, Susumu↗
NASA NTRS1988

Improved 3-D turbomachinery CFD algorithm

The building blocks of a computer algorithm developed for the time-accurate flow analysis of rotating machines are described. The flow model is a finite volume method utilizing a high resolution approximate Riemann solver for interface flux definitions. This block LU implicit numerical scheme possesses apparent unconditional stability. Multi-block composite gridding is used to orderly partition the field into a specified arrangement. Block interfaces, including dynamic interfaces, are treated such as to mimic interior block communication. Special attention is given to the reduction of in-core memory requirements by placing the burden on secondary storage media. Broad applicability is implied, although the results presented are restricted to that of an even blade count configuration. Several other configurations are presently under investigation, the results of which will appear in subsequent publications.

Janus, J. Mark↗
NASA NTRS1988

Direct finite element solution on an optical laboratory matrix-vector processor

The first optical laboratory system results employing a direct LU decomposition solution of a system of linear algebraic equations are presented for a finite element problem solution. This also represents the first laboratory demonstration of the use of sign-magnitude negative number representation as well as new bit partitioning techniques to increase the accuracy of an optical encoded processor beyond the number of bit channels available.

Casasent, David↗
NASA NTRS1988

Artificial dissipation models for hypersonic external flow

Four artificial dissipation models which augment central difference schemes were examined for hypersonic external flows. The models were a first and third order dissipation model, a directionally scaled first and third order dissipation model, a flux limited dissipation model, and a flux difference split dissipation model. Each model was implemented in the lower-upper symmetric-Gauss-Seidel (LU-SGS) algorithm to solve the full Navier-Stokes equations. The latter two models can be regarded as total variation diminishing (TVD) schemes. Test results for model problems showed that the flux limited dissipation model was robust enough to predict a high speed blunt body flow with strong shock and expansion waves. The flux difference split dissipation model was capable of shock capturing with higher resolution, but was less robust. First and third order dissipation models turned out to be neither accurate nor robust enough for high Mach number flow computations.

Yoon, Seokkwan↗
NASA NTRS1987

Solving finite element equations on concurrent computers

This paper discusses the development of a concurrent algorithm for the solution of systems of equations arising in finite element applications. The approach is based on a hybrid of direct elimination method and preconditioned conjugate iteration. Two different preconditioners are used; diagonal scaling and a concurrent implementation of incomplete LU factorization. First, an automatic procedure is used to partition the finite element mesh into sub-structures. The particular mesh partition is chosen to minimize an estimate of the cost for evaluating the solution using this algorithm on a concurrent computer. These procedures are implemented in a finite element program on the JPL/CalTech MARK III hypercube computer. An overview of the structure of this program is presented. The performance of the solution method is demonstrated with the aid of a number of numerical test runs, and its advantages for concurrent implementations are discussed. Efficiency and speed-up factors over sequential machines for the numerical examples are highlighted.

Nour-Omid, B.↗
NASA NTRS1988

The ijk forms of factorization methods. I - Vector computers

This paper gives a detailed exposition of the 'ijk forms' of LU and Choleski factorization. Several aspects of these different organizations are discussed and their properties on vector computers are compared. Extensions of the ijk formalism to other algorithms is also given.

Ortega, J. M.↗
NASA NTRS1988

The ijk forms of factorization methods. II - Parallel systems

The paper considers the 'ijk forms' of LU and Cholesky factorization on certain parallel computers. This extends an earlier analysis for vector computers. Attention is restricted to local memory systems with processors that may or may not have vector capability. Special attention is given to bus architectures but qualitative analyses are given for other interconnection systems.

Ortega, J. M.↗
NASA NTRS1988

Interactive grid generation for turbomachinery flow field simulations

The control point form of algebraic grid generation presented provides the means that are needed to generate well structured grids for turbomachinery flow simulations. It uses a sparse collection of control points distributed over the flow domain. The shape and position of coordinate curves can be adjusted from these control points while the grid conforms precisely to all boundaries. An interactive program called TURBO, which uses the control point form, is being developed. Basic features of the code are discussed and sample grids are presented. A finite volume LU implicit scheme is used to simulate flow in a turbine cascade on the grid generated by the program.

Choo, Yung K.↗
NASA NTRS1989

A numerical study of chemically reacting flow in nozzles

The space station uses small rocket motors, called thrusters, for orientation control. Because of the lack of viable design tools for small rockets, the initial thruster design was basically a very small version of a large rocket motor. Thrust measurements of the initial design were lower than predicted. To improve predictions it was decided to develop a verison of the RPLUS2D reacting flow code for thruster calculations. RPLUS2D employs an implicit finite volume, lower-upper symmetric successive overrelaxation (LU-SSOR) scheme for solving the complete two-dimensional Navier-Stokes equations and species transport equations in a coupled and very efficient manner. The combustion processes are modeled by a 9-species, 18 step finite-rate chemistry model, and the turbulence is simulated by a Baldwin-Lomax algebraic model. The code is extended to handle multiple subsonic inlet conditions where the total mass flow is governed by conditions calculated at the thruster-throat. Results are shown for a thruster design where the overall mixture ratio is hydrogen rich. A calculation of a large area ratio divergent nozzle is also presented.

Vanoverbeke, Thomas J.↗
NASA NTRS1989

Bunch-Kaufman factorization for real symmetric indefinite banded matrices

The Bunch-Kaufman algorithm for factoring symmetric indefinite matrices was rejected for banded matrices because it destroys the banded structure of the matrix. Herein, it is shown that for a subclass of real symmetric matrices which arise in solving the generalized eigenvalue problem using Lanczos's method, the Bunch-Kaufman algorithm does not result in major destruction of the bandwidth. Space time complexities of the algorithm are given and used to show that the Bunch-Kaufman algorithm is a significant improvement over LU factorization.

Jones, Mark T.↗