Search NASA⌕ Search

SEARCH · Search NASA

Results for “problem”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Absorbing boundary conditions for exterior problems

Elliptic and hyperbolic problems in unbounded regions are considered. These problems, when one wants to solve them numerically, have the difficulty of prescribing boundary conditions at infinity. Computationally, one needs a finite region in which to solve these problems. The corresponding conditions at infinity imposed on the finite distance boundaries should dictate the boundary condition at infinity and be accurate with respect to the interior numerical scheme. Such boundary conditions are commonly referred to as absorbing boundary conditions. A treatment is given of these boundary conditions for wave-like equations.

Hariharan, S. I.↗
NASA NTRS1984

Aircraft automation - The problem of the pilot interface

In recent years, aviation has been experiencing a rapid growth. This growth is expected to continue, and aircraft operations in the IFR (instrument flight rules) environment, for example, are predicted to increase dramatically in the next 10 to 12 years. However, it has been found the IFR accidents are increasing at about the same rate as IFR operations, because an associated high workload can lead to human error. For this reason, NASA and others are exploring the use of aircraft systems technology as a means for reducing the pilot workload and enhancing the safety and utility of the aircraft operations. However, recent research has shown that automation, implemented with insufficient consideration to the human factors interface, can frequently create more problems than it solves. Some of this research is discussed, examples of the encountered problems are shown, and solutions regarding the arising problems are suggested.

Bergeron, H. P.↗
NASA NTRS1985

An efficient numerical algorithm for transverse impact problems

Transverse impact problems in which the elastic and plastic indentation effects are considered, involve a nonlinear integral equation for the contact force, which, in practice, is usually solved by an iterative scheme with small increments in time. In this paper, a numerical method is proposed wherein the iterations of the nonlinear problem are separated from the structural response computations. This makes the numerical procedures much simpler and also efficient. The proposed method is applied to some impact problems for which solutions are available, and they are found to be in good agreement. The effect of the magnitude of time increment on the results is also discussed.

Sankar, B. V.↗
NASA NTRS1985

Theoretical Problems in Materials Science

Interactions between theoretical physics and material sciences to identify problems of common interest in which some of the powerful theoretical approaches developed for other branches of physics may be applied to problems in materials science are presented. A unique structure was identified in rapidly quenched Al-14% Mn. The material has long-range directed bonds with icosahedral symmetry which does not form a regular structure but instead forms an amorphous-like quasiperiodic structure. Finite volume fractions of second phase material is advanced and is coupled with nucleation theory to describe the formation and structure of precipitating phases in alloys. Application of the theory of pattern formation to the problem of dendrite formation is studied.

Langer, J. S.↗
NASA NTRS1985

Bounding solutions of geometrically nonlinear viscoelastic problems

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Stubstad, J. M.↗
NASA NTRS1986

A methodology for airplane parameter estimation and confidence interval determination in nonlinear estimation problems

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates.

Murphy, P. C.↗
NASA NTRS1986

A combined integrating and differentiating matrix formulation for boundary value problems on rectangular domains

Integrating and differentiating matrices allow the numerical integration and differential of functions whose values are known at points of a discrete grid. Previous derivations of these matrices were restricted to one dimensional grids or to rectangular grids with uniform spacing in at least one direction. Integrating and differentiating matrices were developed for grids with nonuniform spacing in both directions. The use of these matrices as operators to reformulate boundary value problems on rectangular domains as matrix problems for a finite dimensional solution vector is considered. The method requires nonuniform grids which include near boundary points. An eigenvalue problem for the transverse vibrations of a simply supported rectangular plate is solved to illustrate the method.

Lakin, W. D.↗
NASA NTRS1986

Line Spring Model and Its Applications to Part-Through Crack Problems in Plates and Shells

The line spring model is described and extended to cover the problem of interaction of multiple internal and surface cracks in plates and shells. The shape functions for various related crack geometries obtained from the plane strain solution and the results of some multiple crack problems are presented. The problems considered include coplanar surface cracks on the same or opposite sides of a plate, nonsymmetrically located coplanar internal elliptic cracks, and in a very limited way the surface and corner cracks in a plate of finite width and a surface crack in a cylindrical shell with fixed end.

Erdogan, F.↗
NASA NTRS1986

Multiple grid problems on concurrent-processing computers

Three computer codes were studied which make use of concurrent processing computer architectures in computational fluid dynamics (CFD). The three parallel codes were tested on a two processor multiple-instruction/multiple-data (MIMD) facility at NASA Ames Research Center, and are suggested for efficient parallel computations. The first code is a well-known program which makes use of the Beam and Warming, implicit, approximate factored algorithm. This study demonstrates the parallelism found in a well-known scheme and it achieved speedups exceeding 1.9 on the two processor MIMD test facility. The second code studied made use of an embedded grid scheme which is used to solve problems having complex geometries. The particular application for this study considered an airfoil/flap geometry in an incompressible flow. The scheme eliminates some of the inherent difficulties found in adapting approximate factorization techniques onto MIMD machines and allows the use of chaotic relaxation and asynchronous iteration techniques. The third code studied is an application of overset grids to a supersonic blunt body problem. The code addresses the difficulties encountered when using embedded grids on a compressible, and therefore nonlinear, problem. The complex numerical boundary system associated with overset grids is discussed and several boundary schemes are suggested. A boundary scheme based on the method of characteristics achieved the best results.

Eberhardt, D. S.↗
NASA NTRS1985

Finite element methods on supercomputers - The scatter-problem

Certain problems arise in connection with the use of supercomputers for the implementation of finite-element methods. These problems are related to the desirability of utilizing the power of the supercomputer as fully as possible for the rapid execution of the required computations, taking into account the gain in speed possible with the aid of pipelining operations. For the finite-element method, the time-consuming operations may be divided into three categories. The first two present no problems, while the third type of operation can be a reason for the inefficient performance of finite-element programs. Two possibilities for overcoming certain difficulties are proposed, giving attention to a scatter-process.

Loehner, R.↗
NASA NTRS1986

Parabolized Navier-Stokes analysis of ducted turbulent mixing problems with finite-rate chemistry

A hybrid implicit/explicit approach for analyzing 2D ducted turbulent mixing problems with finite-rate chemistry is presented. The approach combines a fully-implicit parabolic mixing algorithm, an explicit viscous-characteristic based shock-capturing algorithm, and linearized implicit chemical kinetic algorithm. The resultant model provides spatial marching solutions of the parabolized Navier-Stokes (PNS) equations for supersonic combustion and viscous nozzle flowfields. Specialized procedures are incorporated to deal with the near wall sublayer and with small central pockets of subsonic flow. A parabolic option is available which can be utilized in the direct or inverse mode for design applications. The ability of the model to treat shock waves and wave/mixing layer interactions is assessed via comparisons of predictions with those of well established explicit shock-capturing Euler (SCIPPY) and PNS (SCIPVIS) models. Applications to a variety of supersonic combustion flowfield problems involving tangential or moderately inclined fuel injection, and, to a viscous nozzle flow problem, are presented. This paper serves to exhibit overall capabilities of the model developed and no comparisons with supersonic combustion data are presented. Such comparisons serve mainly to validate the modeling of the turbulence and turbulence/chemical interactions and will be the subject of a future paper.

Sinha, N.↗
NASA NTRS1986

An entropy maximization problem related to optical communication

In relation to a problem in optical communication, the paper considers the general problem of maximizing the entropy of a stationary radom process that is subject to an average transition cost constraint. By using a recent result of Justesen and Hoholdt, an exact solution to the problem is presented and a class of finite state encoders that give a good approximation to the exact solution is suggested.

Mceliece, R. J.↗
NASA NTRS1986

Bounding solutions of geometrically nonlinear viscoelastic problems

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Stubstad, J. M.↗
NASA NTRS1985

On a variational approach to some parameter estimation problems

Examples (1-D seismic, large flexible structures, bioturbation, nonlinear population dispersal) in which a variation setting can provide a convenient framework for convergence and stability arguments in parameter estimation problems are considered. Some of these examples are 1-D seismic, large flexible structures, bioturbation, and nonlinear population dispersal. Arguments for convergence and stability via a variational approach of least squares formulations of parameter estimation problems for partial differential equations is one aspect of the problem considered.

Banks, H. T.↗
NASA NTRS1985

Considerations on solving problems with multiple scales

An overview is given on considerations involved in the computation of solution to problems involving several scales. Examples of problems with multiple scales are studied, showing that the presence of multiple scales in a physical system may be manifested in different ways which depend on the degree of interaction between the various scales. Numerical methods commonly used to solve problems with multiple scales discussed, and it is found that the effective methods are based on subspace projection.

Chin, R. C. Y.↗
NASA NTRS1985

Understanding and avoiding potential problems in implementing automation

Technology-driven efforts to implement automation often encounter problems due to lack of acceptance or begrudging acceptance by the personnel involved. It is argued in this paper that the level of automation perceived by an individual heavily influences whether or not the automation is accepted by that individual. The factors that appear to affect perceived level of automation are discussed. Issues considered include the impact of automation on the system and the individual, correlates of acceptance, problems and risks of automation, and factors influencing alienation. Based on an understanding of these issues, a set of eight guidelines is proposed as a possible means of avoiding problems in implementing automation.

Rouse, W. B.↗
NASA NTRS1987

Solving Finite-Element Problems on a Concurrent Processor

By use of "conjugate gradients" technique, concurrent efficiency greater than 90 percent. Algorithm applies method of conjugate gradients to iterative solution of finite-element problems on concurrent processor. With algorithm, iteration rates nearly proportional to number of processors. For sufficiently large problems, fraction of proportional speedup achieved, called concurrent efficiency, exceeds 90 percent. Results indicate future application of this and related algorithms to large finite-element problems depend primarily upon applicability of iteratiave techniques, not upon issues of concurrency or efficiency.

Lyzenga, G. A.↗