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NASA NTRS1986

Retrieval of aerosol size distribution moments from multiwavelength particulate extinction data

An iterative method for deriving the particle size distribution from multiwavelength satellite remote sensing data is presented and its use illustrated with an application to SAGE II data. The compression size distribution method (CSD) features interpolation and look-up features for relating the coefficients of a least-squares fit as a function of wavelength to parameters of the compression function that have been obtained by Mie calculations. Results are reported of comparisons between particulate radii predicted for the El Chichon volcano aerosol based on SAGE II data and 14 radii measured with NASA flights through the aerosol with aircraft carrying wire impactors.

Livingston, J. M.↗

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 NTRS1987

A hypermatrix formulation for subspace iteration

The computational efficiency of subspace iteration is addressed relative to the data structures adopted for the very large and generally sparse coefficient matrices. The frequent triangulations and matrix multiplications demand that access to the terms in the coefficient matrices be unbiased. Reliance on virtual memory (paging) operating systems with no special considerations for localized data access is not adequate. Specific data structures must be designed that accommodate the needs of the numerical algorithm yet eliminate unnecessary paging. An implementation of the subspace iteration method using hypermatrix data structures is presented. Use of hypermatrices is shown to provide unbiased and localized data access. The various modifications to the conventional formulation are described and an example problem illustrates the potential benefits of the hypermatrix formulation. Possibilities for adapting hypermatrix data structures to new supercomputer architectures are discussed.

Schmidt, Richard J.↗

NASA NTRS1987

Deconvolution of a pre-outburst picture of SN 1987A

The block iterative method (Young 1971) of algebraic image restoration is applied to a photographic plate of the field around SN 1987A obtained 4 yr before outburst by Chu at the CTIO 4-m telescope. By setting appropriate constraints for the solution on a pixel-by-pixel basis, the image of a starfield centered on Sk -69 202, the precursor to the supernova, is restored. It is found that this star has two companions, which others (e.g., Walborn et al., 1987 and West et al., 1987) have also noted and designated as Star 2 and Star 3. Also found is marginal evidence for Star 4, a weak source at theta = 222 deg, r = 1.9 arcsec. Correction for the contributions of these companions yields an estimate of the magnitude for Sk -69 202 alone of V = 12.37.

Heap, Sara R.↗

NASA NTRS1988

Collisional-radiative switching - A powerful technique for converging non-LTE calculations

A very simple technique has been developed to converge statistical equilibrium and model atmospheric calculations in extreme non-LTE conditions when the usual iterative methods fail to converge from an LTE starting model. The proposed technique is based on a smooth transition from a collision-dominated LTE situation to the desired non-LTE conditions in which radiation dominates, at least in the most important transitions. The proposed approach was used to successfully compute stellar models with He abundances of 0.20, 0.30, and 0.50; Teff = 30,000 K, and log g = 2.9.

Hummer, D. G.↗

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

A three dimensional calculation of elastic equilibrium for composite materials

A compact scheme is applied to three-dimensional elasticity problems for composite materials, involving simple geometries. The mathematical aspects of this approach are discussed, in particular the iteration method. A vector processor code implementing the compact scheme is presented, and several numerical experiments are summarized.

Lustman, Liviu R.↗

NASA NTRS1988

High-resolution spectroscopy of central stars of planetary nebulae - LSS 1362

High resolution spectra of the hot sdO star LSS 1362, a central star of a planetary nebula, are analyzed by means of model atmosphere techniques. Improved NLTE model atmospheres based on the newly developed 'accelerated lambda iteration' method are used. The very high effective temperature (100000 K) derived previously from the UV energy distribution is confirmed. The surface gravity (log g = 5.3) and a normal helium abundance are derived. A mass of 0.65 solar mass and a luminosity of 10 exp 3.9 solar luminosities result from a comparison with evolutionary tracks. The distance is 1.1 kpc and the nebula has a diameter of about 0.25 pc to 0.5 pc. Weak photospheric emission lines of He II, CIV, Nv, and O v are detected. These lines are slightly blue-shifted with respect to the absorption line spectrum which is regarded as evidence for an atmospheric velocity field. It is conjectured that the observed broadening of the metal lines (25 km/s) may be caused by the velocity field rather than by rotation.

Heber, U.↗

NASA NTRS1988

Numerical simulation of hypersonic flow over an aeroassist flight experiment vehicle

Solutions of wind-tunnel and entry-flight flow around the vehicle are obtained from the Navier-Stokes equations coupled with the chemical species continuity equations if needed. The time-iterative method employs several techniques: shock fitting, chemistry-split ADI and an algebraic grid in conformal spherical-polar space. Sensitivities of the results to numerical parameters and to frozen, equilibrium and finite rate reactions are investigated in the forebody computation. Quantitative results are obtained for the shock layer and the near wake for the entire vehicle corresponding to both ground test and flight conditions. Complex flow characteristics are analyzed on the basis of the complete flowfield over the aerobrake and simplified afterbodies. The method is stable and cost effective, and has yielded shock locations and wall pressure distributions which are in good agreement with wind-tunnel data.

Li, C. P.↗

NASA NTRS1989

Paradigm For Statistical Analysis Of Threshold Detection

Relative values assigned to double mistakes and changed iteratively. Method for statistical analysis of threshold detection saves experimental time by enabling use of same set of measurements with respect to two thresholds. Accounts for double mistakes, unresolvable by threshold-detection technique.

Diner, Daniel B.↗

NASA NTRS1989

Variable-Metric Algorithm For Constrained Optimization

Variable Metric Algorithm for Constrained Optimization (VMACO) is nonlinear computer program developed to calculate least value of function of n variables subject to general constraints, both equality and inequality. First set of constraints equality and remaining constraints inequalities. Program utilizes iterative method in seeking optimal solution. Written in ANSI Standard FORTRAN 77.

Frick, James D.↗

NASA NTRS1988

On the constrained Chebyshev approximation problem on ellipses

Constrained Chebyshev approximation problems of the type with minimum (p is an element of Pi(sub n):p(c)=1) and maximum (z is an element of E) with /p(z)/ are considered. Here Pi(sub n) denotes the set of all complex polynomials of degree at most n, E is any ellipse in the complex plane, and c is an element of C/E. Such approximation problems arise in the context of optimizing semi-iterative methods for the solution of large, sparse systems of linear equations Ax=b with complex non-Hermitian coefficient matrices A. The problem of obtaining optimal polynomial preconditioners for conjugate gradient type methods for Ax=b also leads to problems of this type. A new family of polynomials -- q(sub n)(z;c), n is an element of N, and c is an element of C/E -- are introduced as the polynomials which are optimal for a modified version of the Chebyshev approximation problem with Pi(sub n) replaced by a certain subfamily. Some simple properties of q(sub n) are also listed. A necessary and sufficient condition for q(sub n) to be the extremal polynomial for the approximation problem is then derived. Finally, it is shown that q(sub n) is indeed optimal for the problem for all fixed n whenever the distance between c and E is sufficiently large. Results of some numerical tests are presented.

Freund, Roland↗

NASA NTRS1988

Finite elements: Theory and application

Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.

Dwoyer, D. L.↗

NASA NTRS1990

A computational efficient modelling of laminar separation bubbles

In predicting the aerodynamic characteristics of airfoils operating at low Reynolds numbers, it is often important to account for the effects of laminar (transitional) separation bubbles. Previous approaches to the modelling of this viscous phenomenon range from fast but sometimes unreliable empirical correlations for the length of the bubble and the associated increase in momentum thickness, to more accurate but significantly slower displacement-thickness iteration methods employing inverse boundary-layer formulations in the separated regions. Since the penalty in computational time associated with the more general methods is unacceptable for airfoil design applications, use of an accurate yet computationally efficient model is highly desirable. To this end, a semi-empirical bubble model was developed and incorporated into the Eppler and Somers airfoil design and analysis program. The generality and the efficiency was achieved by successfully approximating the local viscous/inviscid interaction, the transition location, and the turbulent reattachment process within the framework of an integral boundary-layer method. Comparisons of the predicted aerodynamic characteristics with experimental measurements for several airfoils show excellent and consistent agreement for Reynolds numbers from 2,000,000 down to 100,000.

Dini, Paolo↗

NASA NTRS1990

Parallelization of implicit finite difference schemes in computational fluid dynamics

Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed.

Decker, Naomi H.↗

NASA NTRS1990

Investigation of ultra wideband multi-channel dichroic beamsplitters from 0.3 to 52 microns

The development of a set of multi-channel dichroics which includes a 6 channel dichroic operating over the wavelength region from 0.3 to 52 microns is described. In order to achieve the optimum performance, the optical constraints of PbTe, Ge, and CdTe coatings in the strongly absorptive region have been determined by use of a new iterative method using normal incidence reflectance measurement of the multilayer together with initial values of energy gap and infinite refractive index for the semiconductor model. The design and manufacture of the dichroics is discussed and the final results are presented.

Zhang, K. Q.↗

NASA NTRS1991

On the joint inversion of geophysical data for models of the coupled core-mantle system

Joint inversion of magnetic, earth rotation, geoid, and seismic data for a unified model of the coupled core-mantle system is proposed and shown to be possible. A sample objective function is offered and simplified by targeting results from independent inversions and summary travel time residuals instead of original observations. These data are parameterized in terms of a very simple, closed model of the topographically coupled core-mantle system. Minimization of the simplified objective function leads to a nonlinear inverse problem; an iterative method for solution is presented. Parameterization and method are emphasized; numerical results are not presented.

Voorhies, Coerte V.↗

NASA NTRS1990

Combined AIE/EBE/GMRES approach to incompressible flows

Adaptive implicit-explicit (AIE), grouped element-by-element (GEBE), and generalized minimum residuals (GMRES) solution techniques for incompressible flows are combined. In this approach, the GEBE and GMRES iteration methods are employed to solve the equation systems resulting from the implicitly treated elements, and therefore no direct solution effort is involved. The benchmarking results demonstrate that this approach can substantially reduce the CPU time and memory requirements in large-scale flow problems. Although the description of the concepts and the numerical demonstration are based on the incompressible flows, the approach presented here is applicable to larger class of problems in computational mechanics.

Liou, J.↗