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At least 1,081 records · Page 60
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NASA NTRS1986

Iterative adaption of the bidimensional wall of the French T2 wind tunnel around a C5 axisymmetrical model: Infinite variation of the Mach number at zero incidence and a test at increased incidence

The top and bottom two-dimensional walls of the T2 wind tunnel are adapted through an iterative process. The adaptation calculation takes into account the flow three-dimensionally. This method makes it possible to start with any shape of walls. The tests were performed with a C5 axisymmetric model at ambient temperature. Comparisons are made with the results of a true three-dimensional adaptation.

Archambaud, J. P.↗
NASA NTRS1984

Iterative and function-continuation Fourier deconvolution methods for enhancing mass spectrometer resolution

Mass spectrometer data in the form of ion current versus mass-to-charge ratio often include overlapping mass peaks, especially in low- and medium-resolution instruments. Numerical deconvolution of such data effectively enhances the resolution by decreasing the overlap of mass peaks. In this paper two approaches to deconvolution are presented: a function-domain iterative technique and a Fourier transform method which uses transform-domain function-continuation. Both techniques include data smoothing to reduce the sensitivity of the deconvolution to noise. The efficacy of these methods is demonstrated through application to representative mass spectrometer data and the deconvolved results are discussed and compared to data obtained from a spectrometer with sufficient resolution to achieve separation of the mass peaks studied. A case for which the deconvolution is seriously affected by Gibbs oscillations is analyzed.

Ioup, J. W.↗
NASA NTRS1985

Parallel, iterative solution of sparse linear systems - Models and architectures

Solving large, sparse, linear systems of equations is a fundamental problem in large scale scientific and engineering computation. A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. A data transfer model predicting both the probability that data must be transferred between two tasks and the amount of data to be transferred is presented. This model is used to derive an execution time model for predicting parallel execution time and an optimal number of tasks given the dimension and sparsity of the coefficient matrix and the costs of computation, synchronization, and communication. The suitability of different parallel architectures for solving randomly sparse linear systems is discussed. Based on the complexity of task scheduling, one parallel architecture, based on a broadcast bus, is presented and analyzed.

Reed, D. A.↗
NASA NTRS1985

Marching iterative methods for the Parabolized and Thin Layer Navier-Stokes equations

Downstream marching iterative schemes for the solution of the Parabolized or Thin Layer (PNS or TL) Navier-Stokes equations are described. Modifications of the primitive equation global relaxation sweep procedure result in efficient second-order marching schemes. These schemes take full account of the reduced order of the approximate equations as they behave like the SLOR for a single elliptic equation. The improved smoothing properties permit the introduction of Multi-Grid acceleration. The proposed algorithm is essentially Reynolds number independent and therefore can be applied to the solution of the subsonic Euler equations. The convergence rates are similar to those obtained by the Multi-Grid solution of a single elliptic equation; the storage is also comparable as only the pressure has to be stored on all levels. Extensions to three-dimensional and compressible subsonic flows are discussed. Numerical results are presented.

Israeli, M.↗
NASA NTRS1986

Fourier analysis of the SOR iteration

The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor omega. It is shown that for the standard model problem of Poisson's equation on a rectangle, the optimal omega and corresponding convergence rate can be rigorously obtained by Fourier analysis. The trick is to tilt the space-time grid so that the SOR stencil becomes symmetrical. The tilted grid also gives insight into the relation between convergence rates of several variants.

Leveque, R. J.↗
NASA NTRS1986

Analysis of the SOR iteration for the 9-point Laplacian

The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor omega. A theory for determining omega was given by Young (1950) for consistently ordered matrices. Here the optimal omega is determined for the 9-point stencil for the model problem of Laplace's equation on a square. Several orderings of the equations are considered, including the natural rowwise and multicolor orderings, all of which lead to non-consistently ordered matrices, and two equivalence classes of orderings are found with different convergence behavior and optimal omega's. The results for the natural rowwise ordering are compared to those of Garabedian (1956) and it is explained why both results are, in a sense, correct, even though they differ. Also analyzed is a pseudo SOR method for the model problem and it is shown that it is not as effective as the SOR methods. Finally, the point SOR methods are compared to known results for line SOR methods for this problem.

Loyce M. Adams↗
NASA NTRS1986

Iterative methods for elliptic finite element equations on general meshes

Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.

Nicolaides, R. A.↗
NASA NTRS1987

Block iterative restoration of astronomical images with the massively parallel processor

A method is described for algebraic image restoration capable of treating astronomical images. For a typical 500 x 500 image, direct algebraic restoration would require the solution of a 250,000 x 250,000 linear system. The block iterative approach is used to reduce the problem to solving 4900 121 x 121 linear systems. The algorithm was implemented on the Goddard Massively Parallel Processor, which can solve a 121 x 121 system in approximately 0.06 seconds. Examples are shown of the results for various astronomical images.

Heap, Sara R.↗
NASA NTRS1987

Decoupled dynamic analysis of combined systems by iterative determination of interface accelerations

A dynamic analysis technique is presented that can be used to determine the response of a discrete model of a large linear structural system composed of multiple substructures. The technique circumvents the costly computation of the modal characteristics of the combined system. This is accomplished by relying on a predictor-corrector scheme to converge iteratively to the interface accelerations of the combined system, while the equations of motions of the individual structures are integrated separately. In this regard, the temporal slopes of the interface accelerations (jerks) are computed at each time point of integration to predict the interface accelerations at the next time point. The proposed technique is exemplified by conducting a Space Shuttle landing loads analysis; the obtained numerical data demonstrate its reliability and efficiency.

Spanos, P. D.↗
NASA NTRS1987

An efficient iteration strategy for upwind/relaxation solutions to the thin-layer Navier-Stokes equations

A previously developed upwind/relaxation algorithm for solving the unsteady, compressible, thin-layer Navier-Stokes equations is presently modified so that the downstream influence of the subsonic part of the boundary layer in an otherwise supersonic flow is suppressed by restricting the streamwise pressure gradient. A 'parabolized' solution is then efficiently obtained by marching downstream and iterating locally in each crossflow plane until achieving convergence. This parabolized solution is an excellent final one for problems without large adverse streamwise pressure gradients.

Newsome, Richard W.↗
NASA NTRS1987

Iterative solution of the multistream electron transport equation. I - Comparison with laboratory beam injection experiments

The Neumann iteration method presently used for solving the electron transport equation in which energy, attitude, and pitch angle are independent variables is fast, and can compute numerical point-response-function solutions of the electron transport equation. Because both the inelastic cross sections and angular elastic cross sections of the model are empirically based, the solutions obtained represent a test of compatibility between various sets of cross sections and energy deposition measurements. The use of a numerical quadrature based on analytic phase function forms yields accurate phase function integrals at low computational cost.

Porter, H. S.↗
NASA NTRS1986

Simultaneous iterations algorithm for general eigenvalue problems on parallel processors

The method of simultaneous iteration with shift is extended to extraction of m-eigenpairs of a general eigenvalue problem of large order n in a parallel processing environment. The algorithm combines the power method and the Jacobi technique, and reduces to performing four basic operations. Parallel implementation of the algorithm is discussed in detail. The analysis accounts for computation and communication costs, and utilizes a parallel processing architecture of the ensemble type. Expressions for the computational efficiency and speedup are defined as a function of the problem and hardware parameters. Selected representative problems exhibit efficiencies ranging from 60 to 98 percent.

Utku, S.↗
NASA NTRS1987

Iterative-deepening heuristic search for optimal and semi-optimal resource allocation

It is demonstrated that when iterative-deepening A asterisk (IDA asterisk) is applied to one type of resource allocation problem, it uses far less storage than A asterisk, but opens far more nodes and thus has unacceptable time complexity. This is shown to be due, at least in part, to the low-valued effective branching factor that is a characteristic of problems with real-valued cost functions. The semi-optimal, epsilon-admissible IDA asterisk sub epsilon search algorithm that the authors described was shown to open fewer nodes than both A asterisk and IDA asterisk with storage complexity proportional to the depth of the search tree.

Bridges, Susan M.↗
NASA NTRS1988

Breadboard RL10-2B low-thrust operating mode (second iteration) test report

Cryogenic rocket engines requiring a cooling process to thermally condition the engine to operating temperature can be made more efficient if cooling propellants can be burned. Tank head idle and pumped idle modes can be used to burn propellants employed for cooling, thereby providing useful thrust. Such idle modes required the use of a heat exchanger to vaporize oxygen prior to injection into the combustion chamber. During December 1988, Pratt and Whitney conducted a series of engine hot firing demonstrating the operation of two new, previously untested oxidizer heat exchanger designs. The program was a second iteration of previous low thrust testing conducted in 1984, during which a first-generation heat exchanger design was used. Although operation was demonstrated at tank head idle and pumped idle, the engine experienced instability when propellants could not be supplied to the heat exchanger at design conditions.

Kanic, Paul G.↗
NASA NTRS1988

I-BIEM, an iterative boundary integral equation method for computer solutions of current distribution problems with complex boundaries: A new algorithm. I - Theoretical

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.

Cahan, B. D.↗
NASA NTRS1988

Cosmic-ray-modified stellar winds. III - A numerical iterative approach

A numerical iterative method is used to determine the modification of a stellar wind flow with a termination shock by the galactic cosmic rays. A two-fluid model consisting of cosmic rays and thermal stellar wind gas is used in which the cosmic rays are coupled to the background flow via scattering with magnetohydrodynamic waves or irregularities. A polytropic model is used to describe the thermal stellar wind gas, and the cosmic-rays are modeled as a hot, low-density gas with negligible mass flux. The positive galactic cosmic-ray pressure gradient serves to brake the outflowing stellar wind gas, and the cosmic rays modify the location of the critical point of the wind, the location of the shock, the wind fluid velocity profile, and the thermal gas entropy constants on both sides of the shock. The transfer of energy to the cosmic rays results in an outward radial flux of cosmic-ray energy.

Ko, C. M.↗
NASA NTRS1988

Iterates of maps with symmetry

Fixed-point bifurcation, period doubling, and Hopf bifurcation (HB) for iterates of equivariant mappings are investigated analytically, with a focus on HB in the presence of symmetry. An algebraic formulation for the hypotheses of the theorem of Ruelle (1973) is derived, and the case of standing waves in a system of ordinary differential equations with O(2) symmetry is considered in detail. In this case, it is shown that HB can lead directly to motion on an invariant 3-torus, with an unexpected third frequency due to drift of standing waves along the torus.

Chossat, Pascal↗