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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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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Parallel architectures for iterative methods on adaptive, block structured grids

A parallel computer architecture well suited to the solution of partial differential equations in complicated geometries is proposed. Algorithms for partial differential equations contain a great deal of parallelism. But this parallelism can be difficult to exploit, particularly on complex problems. One approach to extraction of this parallelism is the use of special purpose architectures tuned to a given problem class. The architecture proposed here is tuned to boundary value problems on complex domains. An adaptive elliptic algorithm which maps effectively onto the proposed architecture is considered in detail. Two levels of parallelism are exploited by the proposed architecture. First, by making use of the freedom one has in grid generation, one can construct grids which are locally regular, permitting a one to one mapping of grids to systolic style processor arrays, at least over small regions. All local parallelism can be extracted by this approach. Second, though there may be a regular global structure to the grids constructed, there will be parallelism at this level. One approach to finding and exploiting this parallelism is to use an architecture having a number of processor clusters connected by a switching network. The use of such a network creates a highly flexible architecture which automatically configures to the problem being solved.

Gannon, D.↗
NASA NTRS1991

A non-iterative method for computing the infimum in H(infinity)-optimization

The authors, as an extension of their earlier work, present a simple noniterative procedure for the computation of the exact value of the infimum in the singular H(infinity)-optimization problem and is an extension of their earlier work. The problem formulation is general and does not place any restrictions on the direct feedthrough terms between the disturbance input and the measurement output variables. The method is applicable to a class of singular H(infinity)-optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the j-omega axis and also satisfy certain geometric conditions.

Chen, Ben M.↗
NASA NTRS1986

Larger Convergence Zones for Newton's Method

Iterative technique applies over wider range of initial guesses. New theorem describes convergence zone of Newton's iterative method for finding zeros of real function. Involves two points, Xp and Xp*, called primary conjugate points. If exact solution lies between these points (Xp is less than Xz is less than Xp*) and no other conjugate points in interval, then according to theorem, subsequent iterations will converge upon exact solution if initial guess lies in interval.

Campbell, C. W.↗
NASA NTRS1974

Radiative transfer of visible radiation in turbid atmosphere

Methods are presented for solving radiative transfer problems; they include the doubling method and the closely related matrix method, iterative method, Chandrasekhar's method of discrete ordinates, and Monte Carlo method. To consider radiation transport through turbid atmosphere, an atmospheric model was developed characterizing aerosols by parameters. Intensity and polarization of radiation in turbid atmospheres is discussed, as well as lower atmospheric heating due to solar radiation absorption by aerosols.

Yamamoto, G.↗
NASA NTRS1992

Least-squares finite element solution of 3D incompressible Navier-Stokes problems

Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.

Jiang, Bo-Nan↗
DOE OSTI2017

A computationally efficient P 1 radiation model for modern combustion systems utilizing pre-conditioned conjugate gradient methods

The iterative convergence of the P 1 radiation model can be slow in optically thin scenarios when employing classical iterative methods. In order to remedy this shortcoming, an in-house P 1 radiation model was interfaced with high performance, scalable, linear solver libraries. Next, the accuracies of P 1 radiation model calculations was assessed by comparing its predictions against discrete ordinates (DO) model calculations for prototypical problems representative of modern combustion systems. Corresponding benchmark results were also included for comparison. Utilizing Pre-Conditioners (PC) to the Conjugate Gradients (CG) method, the convergence time of the P 1 radiation model reduced by a factor of 30 for modest problem sizes and a factor of 70 for larger sized problems when compared against classical Gauss Seidel sweeps. Additionally, PC provided 50% computational savings compared to employing CG in a standalone mode. The P 1 model calculation times were about 25–30% of the DO model calculation time. The time to solution also scaled linearly with an increase in problem size. The weighted sum of gray gases model employed in this study in conjunction with the P 1 model provided good agreement against benchmark data with L 2 error norms (defined relative to corresponding DO calculations) improving when isotropic intensities were prevalent.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗