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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 145 records · Page 8
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NASA NTRS1987

An Exponential Finite Difference Technique for Solving Partial Differential Equations

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

Handschuh, Robert F.↗
NASA NTRS1987

The minimal residual QR-factorization algorithm for reliably solving subset regression problems

A new algorithm to solve test subset regression problems is described, called the minimal residual QR factorization algorithm (MRQR). This scheme performs a QR factorization with a new column pivoting strategy. Basically, this strategy is based on the change in the residual of the least squares problem. Furthermore, it is demonstrated that this basic scheme might be extended in a numerically efficient way to combine the advantages of existing numerical procedures, such as the singular value decomposition, with those of more classical statistical procedures, such as stepwise regression. This extension is presented as an advisory expert system that guides the user in solving the subset regression problem. The advantages of the new procedure are highlighted by a numerical example.

Verhaegen, M. H.↗
NASA NTRS1987

Removal of spurious modes encountered in solving stability problems by spectral methods

A technique based on the Galerkin approximation is developed to remove spurious roots arising when Chebyshev spectral methods are used to solve eigenvalue problems in hydrodynamic stability. The derivation of Galerkin-Chebyshev approximations is explained, and numerical results for the Orr-Sommerfeld equations of plane Poiseuille flow and a Blasius profile are presented in tables and compared with those obtained by the method of Zebib (1984). It is pointed out that the present method does not increase the size of the algebraic system to be solved.

Zebib, Abdelfattah↗
NASA NTRS1988

A multistage mesh generator for solving the average-passage equation system

One means of numerically simulating the 3-D flow field within a multistage turbomachine is through the solution of the average-passage equation system. One requirement of a current algorithm used to solve this system of equations has been the ability to generate multiple blade row meshes which satisfy specific geometrical constraints. In addition to meeting this criterion, one desires a mesh generation code which requires minimal user input, utilizes variable mesh control parameters, generates diagnostics helpful to the user, and possesses the capability to handle widely varying geometries. A mesh generation code with these features was written and has been used in solving the inviscid form of the average-passing equation system for both ducted and unducted multiple blade row geometries. This paper serves as a user reference guide, with a description of the mesh generation algorithm, a sample input file, and examples of typical meshes generated.

Mulac, Richard A.↗
NASA NTRS1988

Algorithms and software for solving finite element equations on serial and parallel architectures

The primary objective was to compare the performance of state-of-the-art techniques for solving sparse systems with those that are currently available in the Computational Structural Mechanics (MSC) testbed. One of the first tasks was to become familiar with the structure of the testbed, and to install some or all of the SPARSPAK package in the testbed. A brief overview of the CSM Testbed software and its usage is presented. An overview of the sparse matrix research for the Testbed currently employed in the CSM Testbed is given. An interface which was designed and implemented as a research tool for installing and appraising new matrix processors in the CSM Testbed is described. The results of numerical experiments performed in solving a set of testbed demonstration problems using the processor SPK and other experimental processors are contained.

Chu, Eleanor↗
NASA NTRS1988

Reliable use of determinants to solve nonlinear structural eigenvalue problems efficiently

The analytical derivation, numerical implementation, and performance of a multiple-determinant parabolic interpolation method (MDPIM) for use in solving transcendental eigenvalue (critical buckling or undamped free vibration) problems in structural mechanics are presented. The overall bounding, eigenvalue-separation, qualified parabolic interpolation, accuracy-confirmation, and convergence-recovery stages of the MDPIM are described in detail, and the numbers of iterations required to solve sample plane-frame problems using the MDPIM are compared with those for a conventional bisection method and for the Newtonian method of Simpson (1984) in extensive tables. The MDPIM is shown to use 31 percent less computation time than bisection when accuracy of 0.0001 is required, but 62 percent less when accuracy of 10 to the -8th is required; the time savings over the Newtonian method are about 10 percent.

Williams, F. W.↗
NASA NTRS1988

Functional reasoning in diagnostic problem solving

This work is one facet of an integrated approach to diagnostic problem solving for aircraft and space systems currently under development. The authors are applying a method of modeling and reasoning about deep knowledge based on a functional viewpoint. The approach recognizes a level of device understanding which is intermediate between a compiled level of typical Expert Systems, and a deep level at which large-scale device behavior is derived from known properties of device structure and component behavior. At this intermediate functional level, a device is modeled in three steps. First, a component decomposition of the device is defined. Second, the functionality of each device/subdevice is abstractly identified. Third, the state sequences which implement each function are specified. Given a functional representation and a set of initial conditions, the functional reasoner acts as a consequence finder. The output of the consequence finder can be utilized in diagnostic problem solving. The paper also discussed ways in which this functional approach may find application in the aerospace field.

Sticklen, Jon↗
NASA NTRS1987

The generic task toolset: High level languages for the construction of planning and problem solving systems

The current generation of languages for the construction of knowledge-based systems as being at too low a level of abstraction is criticized, and the need for higher level languages for building problem solving systems is advanced. A notion of generic information processing tasks in knowledge-based problem solving is introduced. A toolset which can be used to build expert systems in a way that enhances intelligibility and productivity in knowledge acquistion and system construction is described. The power of these ideas is illustrated by paying special attention to a high level language called DSPL. A description is given of how it was used in the construction of a system called MPA, which assists with planning in the domain of offensive counter air missions.

Chandrasekaran, B.↗
NASA NTRS1988

Robust operative diagnosis as problem solving in a hypothesis space

This paper describes an approach that formulates diagnosis of physical systems in operation as problem solving in a hypothesis space. Such a formulation increases robustness by: (1) incremental hypotheses construction via dynamic inputs, (2) reasoning at a higher level of abstraction to construct hypotheses, and (3) partitioning the space by grouping fault hypotheses according to the type of physical system representation and problem solving techniques used in their construction. It was implemented for a turbofan engine and hydraulic subsystem. Evaluation of the implementation on eight actual aircraft accident cases involving engine faults provided very promising results.

Abbott, Kathy H.↗
NASA NTRS1989

Blackboard system generator (BSG) - An alternative distributed problem-solving paradigm

A status review is presented for a generic blackboard-based distributed problem-solving environment in which multiple-agent cooperation can be effected. This environment is organized into a shared information panel, a chairman control panel, and a metaplanning panel. Each panel contains a number of embedded AI techniques that facilitate its operation and that provide heuristics for solving the underlying team-agent decision problem. The status of these panels and heuristics is described along with a number of robustness considerations. The techniques for each of the three panels and for four sets of paradigm-related advances are described, along with selected results from classroom teaching experiments and from three applications.

Silverman, Barry G.↗
NASA NTRS1990

Neural Network Solves "Traveling-Salesman" Problem

Experimental electronic neural network solves "traveling-salesman" problem. Plans round trip of minimum distance among N cities, visiting every city once and only once (without backtracking). This problem is paradigm of many problems of global optimization (e.g., routing or allocation of resources) occuring in industry, business, and government. Applied to large number of cities (or resources), circuits of this kind expected to solve problem faster and more cheaply.

Thakoor, Anilkumar P.↗
NASA NTRS1990

KIPSE1: A Knowledge-based Interactive Problem Solving Environment for data estimation and pattern classification

A knowledge-based interactive problem solving environment called KIPSE1 is presented. The KIPSE1 is a system built on a commercial expert system shell, the KEE system. This environment gives user capability to carry out exploratory data analysis and pattern classification tasks. A good solution often consists of a sequence of steps with a set of methods used at each step. In KIPSE1, solution is represented in the form of a decision tree and each node of the solution tree represents a partial solution to the problem. Many methodologies are provided at each node to the user such that the user can interactively select the method and data sets to test and subsequently examine the results. Otherwise, users are allowed to make decisions at various stages of problem solving to subdivide the problem into smaller subproblems such that a large problem can be handled and a better solution can be found.

Han, Chia Yung↗
NASA NTRS1990

LANZ: Software solving the large sparse symmetric generalized eigenproblem

A package, LANZ, for solving the large symmetric generalized eigenproblem is described. The package was tested on four different architectures: Convex 200, CRAY Y-MP, Sun-3, and Sun-4. The package uses a Lanczos' method and is based on recent research into solving the generalized eigenproblem.

Jones, Mark T.↗
NASA NTRS1989

Solving sparse triangular linear systems on parallel computers

This paper describes and compares three parallel algorithms for solving sparse triangular systems of equations. These methods involve some preprocessing overhead and are primarily of interest in solving many systems with the same coefficient matrix. The first approach is to use a fixed blocksize and form the inverse of the diagonal blocks. The second approach is to use a variable blocksize and reorder the unknowns so that the diagonal blocks are diagonal matrices. The latter technique is called level scheduling because of how it is represented in the adjacency graph, and both row-wise and jagged diagonal storage for the off-diagonal blocks are considered. These techniques are analyzed for general parallel computers and experiments are presented for the eight-processor Alliant FX/8.

Anderson, Edward↗
NASA NTRS1991

Use of edge-based finite elements for solving three dimensional scattering problems

Edge based finite elements are free from drawbacks associated with node based vectorial finite elements and are, therefore, ideal for solving 3-D scattering problems. The finite element discretization using edge elements is checked by solving for the resonant frequencies of a closed inhomogeneously filled metallic cavity. Great improvements in accuracy are observed when compared to the classical node based approach with no penalty in terms of computational time and with the expected absence of spurious modes. A performance comparison between the edge based tetrahedra and rectangular brick elements is carried out and tetrahedral elements are found to be more accurate than rectangular bricks for a given storage intensity. A detailed formulation for the scattering problem with various approaches for terminating the finite element mesh is also presented.

Chatterjee, A.↗
NASA NTRS1991

Solving constrained minimum-time robot problems using the sequential gradient restoration algorithm

Three constrained minimum-time control problems of a two-link manipulator are solved using the Sequential Gradient and Restoration Algorithm (SGRA). The inequality constraints considered are reduced via Valentine-type transformations to nondifferential path equality constraints. The SGRA is then used to solve these transformed problems with equality constraints. The results obtained indicate that at least one of the two controls is at its limits at any instant in time. The remaining control then adjusts itself so that none of the system constraints is violated. Hence, the minimum-time control is either a pure bang-bang control or a combined bang-bang/singular control.

Lee, Allan Y.↗
NASA NTRS1992

High order parallel numerical schemes for solving incompressible flows

The use of parallel computers for numerically solving flow fields has gained much importance in recent years. This paper introduces a new high order numerical scheme for computational fluid dynamics (CFD) specifically designed for parallel computational environments. A distributed MIMD system gives the flexibility of treating different elements of the governing equations with totally different numerical schemes in different regions of the flow field. The parallel decomposition of the governing operator to be solved is the primary parallel split. The primary parallel split was studied using a hypercube like architecture having clusters of shared memory processors at each node. The approach is demonstrated using examples of simple steady state incompressible flows. Future studies should investigate the secondary split because, depending on the numerical scheme that each of the processors applies and the nature of the flow in the specific subdomain, it may be possible for a processor to seek better, or higher order, schemes for its particular subcase.

Lin, Avi↗
NASA NTRS1990

Solving unstructured grid problems on massively parallel computers

A highly parallel graph mapping technique that enables one to efficiently solve unstructured grid problems on massively parallel computers is presented. Many implicit and explicit methods for solving discretized partial differential equations require each point in the discretization to exchange data with its neighboring points every time step or iteration. The cost of this communication can negate the high performance promised by massively parallel computing. To eliminate this bottleneck, the graph of the irregular problem is mapped into the graph representing the interconnection topology of the computer such that the sum of the distances that the messages travel is minimized. It is shown that using the heuristic mapping algorithm significantly reduces the communication time compared to a naive assignment of processes to processors.

Hammond, Steven W.↗