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NASA NTRS1989

Eigenvector derivatives of repeated eigenvalues using singular value decomposition

An explicit formula is obtained for the first-order eigenvector derivative that corresponds to the eigenvector of a repeated eigenvalue, in the case of the nonself-adjoint eigenvalue problem. This method applies to the class of nondefective problems whose first eigenvalue derivatives of the repeated eigenvalues are distinct. A singular-value decomposition approach is used to compute four requisite bases for eigenspaces, as well as to keep track of the dimensions of state variables and the conditioning of the state equations.

Lim, Kyong B.↗

NASA NTRS1988

Applications of domain decomposition methods to turbomachinery flows

Domain decomposition techniques can be used to great advantage by computational fluid dynamicists in computing flows about complex geometries and adapting the grid to the solution. These techniques are particularly useful in computing flows about several bodies that are in relative motion such as rotor/stator configurations in turbomachinery or helicopter rotor/fuselage configurations. This paper discusses some of the basic ideas involved in transferring information between subdomains in a multidomain calculation and presents results for a simple rotor/stator configuration.

Rai, M. M.↗

NASA NTRS1989

Characteristic-eddy decomposition of turbulence in a channel

Lumley's proper orthogonal decomposition technique is applied to the turbulent flow in a channel. Coherent structures are extracted by decomposing the velocity field into characteristic eddies with random coefficients. A generalization of the shot-noise expansion is used to determine the characteristic eddies in homogeneous spatial directions. Three different techniques are used to determine the phases of the Fourier coefficients in the expansion: (1) one based on the bispectrum, (2) a spatial compactness requirement, and (3) a functional continuity argument. Similar results are found from each of these techniques.

Moin, Parviz↗

NASA NTRS1990

Multilevel decomposition approach to the preliminary sizing of a transport aircraft wing

A multilevel/multidisciplinary optimization scheme for sizing an aircraft wing structure is described. A methodology using nonlinear programming in application to a very large engineering problem is presented. This capability is due to the decomposition approach. Over 1300 design variables are considered for this nonlinear optimization task. In addition, a mathematical link is established coupling the detail of structural sizing to the overall system performance objective, such as fuel consumption. The scheme is implemented as a three level system analyzing aircraft mission performance at the top level, the total aircraft structure as the middle level, and individual stiffened wing skin cover panels at the bottom level. Numerical show effectiveness of the method and its good convergence characteristics.

Wrenn, Gregory A.↗

NASA NTRS1990

Decomposition of perfluoroalkylpolyethers (PFPE) in ultra-high vacuum under sliding conditions

Reactions of perfluoroalkylpolyethers (PFPE: Fomblin, Demnum and Krytox) were studied during the sliding contact of stainless steel specimens under ultrahigh vacuum conditions. All three fluids reacted with the steel specimens during sliding. Fomblin, which has acetal linkages, decomposed under the sliding conditions generating gaseous products, (COF2 and fluorinated carbons) which were detected by a quadrupole mass spectrometer. Gaseous products were not detected for the Demnum and Krytox fluids. The amount of gaseous products from Fomblin increased with increasing sliding speed. At the end of the sliding experiments, the wear scar and deposits on the specimens were examined by small spot size XPS. The oxide layer on the specimen surface was removed during sliding, and metal fluorides were formed on the worn surface. The surface of the wear scar and deposits were covered with adsorbed PFPE. Based on these results, it was concluded that the decomposition reaction on Fomblin was initiated by contacting the fluid with a fresh metal surface which was formed during sliding.

Mori, Shigeyuki↗

NASA NTRS1991

Fluidized-Bed Silane-Decomposition Reactor

Fluidized-bed pyrolysis reactor produces high-purity polycrystalline silicon from silane or halosilane via efficient heterogeneous deposition of silicon on silicon seed particles. Formation of silicon dust via homogeneous decomposition of silane minimized, and deposition of silicon on wall of reactor effectively eliminated. Silicon used to construct solar cells and other semiconductor products.

Iya, Sridhar K.↗

NASA NTRS1990

Controlled decomposition and oxidation: A treatment method for gaseous process effluents

The safe disposal of effluent gases produced by the electronics industry deserves special attention. Due to the hazardous nature of many of the materials used, it is essential to control and treat the reactants and reactant by-products as they are exhausted from the process tool and prior to their release into the manufacturing facility's exhaust system and the atmosphere. Controlled decomposition and oxidation (CDO) is one method of treating effluent gases from thin film deposition processes. CDO equipment applications, field experience, and results of the use of CDO equipment and technological advances gained from the field experiences are discussed.

Mckinley, Roger J. B., Sr.↗

NASA NTRS1991

Domain decomposition methods in computational fluid dynamics

The divide-and-conquer paradigm of iterative domain decomposition, or substructuring, has become a practical tool in computational fluid dynamic applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. These features are illustrated on the classic model problem of flow over a backstep using Newton's method as the nonlinear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately, and they can be combined synergistically. Sample performance results are included from an Intel iPSC/860 hypercube implementation.

Gropp, William D.↗

NASA NTRS1989

Inversion of imaging spectrometry data using singular value decomposition

The use of imaging spectrometers, which acquire data that are both spectrally contiguous images and spatially contiguous spectra, for quantitative remote sensing of the earth is addressed. Such data sets cannot be analyzed fully using either existing spectroscopic or image techniques. Singular value decomposition (SVD) is used here for spectral unmixing and determination of the spatial scales of mixing. It is shown that when it is used to invert the mixing endmember library, SVD allows more insight into library characteristics and more control of the inversion process than other commonly used matrix inversion techniques.

Boardman, Joe W.↗

NASA NTRS1991

An examination of coherent structures in a lobed mixer using multifractal measures in conjunction with the proper orthogonal decomposition

A 'lobed mixer' device that enhances mixing through secondary flows and streamwise vorticity is presently studied within the framework of multifractal-measures theory, in order to deepen understanding of velocity time trace data gathered on its operation. Proper orthogonal decomposition-based knowledge of coherent structures has been applied to obtain the generalized fractal dimensions and multifractal spectrum of several proper eigenmodes for data samples of the velocity time traces; this constitutes a marked departure from previous multifractal theory applications to self-similar cascades. In certain cases, a single dimension may suffice to capture the entire spectrum of scaling exponents for the velocity time trace.

Ukeiley, L.↗

NASA NTRS1990

An analysis of scatter decomposition

A formal analysis of a mapping method known as scatter decomposition (SD) is presented. SD divides an irregular domain into many equal-size pieces and distributes them modularly among processors. It is shown that, if a correlation in workload is a convex function of distance, then scattering a more finely decomposed domain yields a lower average processor workload variance; if the workload process is stationary Gaussian and the correlation function decreases linearly in distance to zero and then remains zero, scattering a more finely decomposed domain yields a lower expected maximum processor workload. Finally, if the correlation function decreases linearly across the entire domain, then (among all mappings that assign an equal number of domain pieces to each processor) SD minimizes the average processor workload variance. The dependence of these results on the assumption of decreasing correlation is illustrated with cases where a coarser granularity actually achieves better load balance.

Nicol, David M.↗

NASA NTRS1991

An algorithm for domain decomposition in finite element analysis

A simple and efficient algorithm is described for automatic decomposition of an arbitrary finite element domain into a specified number of subdomains for finite element and substructuring analysis in a multiprocessor computer environment. The algorithm is designed to balance the work loads, to minimize the communication among processors and to minimize the bandwidths of the resulting system of equations. Small- to large-scale finite element models, which have two-node elements (truss, beam element), three-node elements (triangular element) and four-node elements (quadrilateral element), are solved on the Convex computer to illustrate the effectiveness of the proposed algorithm. A FORTRAN computer program is also included.

Al-Nasra, M.↗

NASA NTRS1991

Heuristic decomposition for non-hierarchic systems

Design and optimization is substantially more complex in multidisciplinary and large-scale engineering applications due to the existing inherently coupled interactions. The paper introduces a quasi-procedural methodology for multidisciplinary optimization that is applicable for nonhierarchic systems. The necessary decision-making support for the design process is provided by means of an embedded expert systems capability. The method employs a decomposition approach whose modularity allows for implementation of specialized methods for analysis and optimization within disciplines.

Bloebaum, Christina L.↗

NASA NTRS1990

Domain decomposition methods in aerodynamics

Compressible Euler equations are solved for two-dimensional problems by a preconditioned conjugate gradient-like technique. An approximate Riemann solver is used to compute the numerical fluxes to second order accuracy in space. Two ways to achieve parallelism are tested, one which makes use of parallelism inherent in triangular solves and the other which employs domain decomposition techniques. The vectorization/parallelism in triangular solves is realized by the use of a recording technique called wavefront ordering. This process involves the interpretation of the triangular matrix as a directed graph and the analysis of the data dependencies. It is noted that the factorization can also be done in parallel with the wave front ordering. The performances of two ways of partitioning the domain, strips and slabs, are compared. Results on Cray YMP are reported for an inviscid transonic test case. The performances of linear algebra kernels are also reported.

Venkatakrishnan, V.↗

NASA NTRS1991

Aerospace plane guidance using time-scale decomposition - A geometric approach

A method is proposed for developing the necessary guidance logic to steer single-stage vehicles into orbit. The minimum-fuel ascent problem is first considered to analyze the effects of dynamic pressure, acceleration, and heating constraints on guidance systems to thereby develop the guidance logic. The optimal solution consists of behavior with two time scales, and the control law is used to develop near-optimal guidance. The solution uses the slow manifold to delineate the control for minimum-fuel reduced-order trajectory and a separate control for tracking the optimal reduced-order trajectory. A family of fast manifolds is then employed to resolve the tracking problem via the feedback linearization methodology from nonlinear geometric control theory. The two-time-scale decomposition is found to produce a near-optimal ascent by tracking the applicable state-constraint boundary, as well as to simplify the control-design task.

Van Buren, Mark A.↗

NASA NTRS1989

A restricted signature normal form for Hermitian matrices, quasi-spectral decompositions, and applications

In recent years, a number of results on the relationships between the inertias of Hermitian matrices and the inertias of their principal submatrices appeared in the literature. We study restricted congruence transformation of Hermitian matrices M which, at the same time, induce a congruence transformation of a given principal submatrix A of M. Such transformations lead to concept of the restricted signature normal form of M. In particular, by means of this normal form, we obtain short proofs of most of the known inertia theorems and also derive some new results of this type. For some applications, a special class of almost unitary restricted congruence transformations turns out to be useful. We show that, with such transformations, M can be reduced to a quasi-diagonal form which, in particular, displays the eigenvalues of A. Finally, applications of this quasi-spectral decomposition to generalize inverses and Hermitian matrix pencils are discussed.

Freund, Roland W.↗

NASA NTRS1991

Layer tracking, asymptotics, and domain decomposition

A preliminary report is presented on the work on the tracking of internal layers in a singularly-perturbed convection-diffusion equation. It is shown why such tracking may be desirable, and it is also shown how to do it using domain decomposition based on asymptotic analysis.

Brown, D. L.↗

NASA NTRS1991

Proper orthogonal decomposition based turbulence modeling

The proper orthogonal decomposition is utilized to provide one mode estimates of various turbulence quantities in the near-wall region of the turbulent boundary layer. The experimental data of Herzog (1986) and the direct numerical simulation (DNS) results of Zang (1991) proved the two-point correlation tensor. The correlation tensor is then used as the kernel in the integral eigenvalue problem from which the proper orthogonal modes are obtained. The one mode estimates of the turbulent kinetic energy, dissipation, and triple moments all exhibit the proper asymtotic behavior near the wall. As a validation test, a model for the triple moments is developed and its near-wall behavior is studied. This information can then be used to obtain an estimate of the damping function near the wall, which is then compared to known existing behavior. Since this is an initial investigation, the streamwise and spanwise dependence is surpressed and only the wall normal direction (y+) behavior of various turbulence statistics near the wall is studied. Before examining one mode estimates of the triple moments and the dissipation (on which the model is based), various second order moments are examined. If these do not exhibit the proper behavior near the wall (as discussed by Speziale et al 1990) it does not seem reasonable to expect the one mode estimate of the triple moment and dissipation to have the right behavior. Only the results obtained using the experimental data of Herzog are discussed since the results from the simulations of Zang exhibit similar behavior as discussed above.

Glauser, Mark N.↗