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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Three-dimensional atmospheric entry problem using method of matched asymptotic expansions

The analysis of a three-dimensional atmospheric entry problem using the method of matched asymptotic expansions is considered. A composite solution is formed in terms of an outer solution, an inner solution and a common solution. The outer solution is obtained from the gravitationally dominant region, whereas the aerodynamically dominant region contributes to the inner solution. The common solution accounts for the overlap between the outer and inner regions. In comparison to previous work, this simplified methodology yields explicit analytical expressions for various components of the composite solution without resorting to any type of transcendental equations to be solved only by numerical methods.

Naidu, D. S.↗
DOE OSTI2026

A variational mimetic finite difference method for elliptic interface problems on non-matching polytopal meshes with geometric interface inconsistencies

A new variational mimetic finite difference method for elliptic interface problems with perfect and imperfect thermal contacts on non-matching polytopal meshes with geometric interface inconsistencies is developed and analyzed theoretically and numerically. The method is defined on multiple non-matching submeshes with gaps and overlaps along their interfaces. The discrete equations are derived from a minimization problem for the augmented Dirichlet functional. For a perfect thermal contact, the functional uses a modified mimetic gradient with extended stencil which couples unknowns from both sides of an interface, as well as penalty terms to enforce weak continuity of temperature across the interface. The method leads to a symmetric positive definite matrix for any scaling of the penalty terms. For an imperfect thermal contact, the Dirichlet functional is supplemented with a quadratic jump term along the interface related to the interface thermal resistance. We prove that the method conserves the total heat flux across each interface. In conclusion, the obtained results are verified with numerical experiments showing convergence in the discrete L 2 and L ∞ norms.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1997

Simulating and Synthesizing Substructures Using Neural Network and Genetic Algorithms

The feasibility of simulating and synthesizing substructures by computational neural network models is illustrated by investigating a statically indeterminate beam, using both a 1-D and a 2-D plane stress modelling. The beam can be decomposed into two cantilevers with free-end loads. By training neural networks to simulate the cantilever responses to different loads, the original beam problem can be solved as a match-up between two subsystems under compatible interface conditions. The genetic algorithms are successfully used to solve the match-up problem. Simulated results are found in good agreement with the analytical or FEM solutions.

Liu, Youhua↗
NASA NTRS1991

Neural-Network Simulator

F77NNS (FORTRAN 77 Neural Network Simulator) computer program simulates popular back-error-propagation neural network. Designed to take advantage of vectorization when used on computers having this capability, also used on any computer equipped with ANSI-77 FORTRAN Compiler. Problems involving matching of patterns or mathematical modeling of systems fit class of problems F77NNS designed to solve. Program has restart capability so neural network solved in stages suitable to user's resources and desires. Enables user to customize patterns of connections between layers of network. Size of neural network F77NNS applied to limited only by amount of random-access memory available to user.

Mitchell, Paul H.↗
NASA NTRS1999

Co-evolution for Problem Simplification

This paper explores a co-evolutionary approach applicable to difficult problems with limited failure/success performance feedback. Like familiar "predator-prey" frameworks this algorithm evolves two populations of individuals - the solutions (predators) and the problems (prey). The approach extends previous work by rewarding only the problems that match their difficulty to the level of solut,ion competence. In complex problem domains with limited feedback, this "tractability constraint" helps provide an adaptive fitness gradient that, effectively differentiates the candidate solutions. The algorithm generates selective pressure toward the evolution of increasingly competent solutions by rewarding solution generality and uniqueness and problem tractability and difficulty. Relative (inverse-fitness) and absolute (static objective function) approaches to evaluating problem difficulty are explored and discussed. On a simple control task, this co-evolutionary algorithm was found to have significant advantages over a genetic algorithm with either a static fitness function or a fitness function that changes on a hand-tuned schedule.

Haith, Gary L.↗
NASA NTRS1974

A multiprocessor computer simulation model employing a feedback scheduler/allocator for memory space and bandwidth matching and TMR processing

A computer simulation model for a multiprocessor computer is developed that is useful for studying the problem of matching multiprocessor's memory space, memory bandwidth and numbers and speeds of processors with aggregate job set characteristics. The model assumes an input work load of a set of recurrent jobs. The model includes a feedback scheduler/allocator which attempts to improve system performance through higher memory bandwidth utilization by matching individual job requirements for space and bandwidth with space availability and estimates of bandwidth availability at the times of memory allocation. The simulation model includes provisions for specifying precedence relations among the jobs in a job set, and provisions for specifying precedence execution of TMR (Triple Modular Redundant and SIMPLEX (non redundant) jobs.

Bradley, D. B.↗
NASA NTRS1951

Matching Characteristics of J35-A-23 Compressor and Two-stage Turbine

Component data on the J35-A-23 compressor and two-stage turbine were used to determine the problems in matching the two units for operatio n in a turbojet engine. Possible operating regions were determined an d an equilibrium operating line was also determined for the assumed c onditions of zero flight speed and a jet nozzle area approximately 5. 5 percent greater than the wide-open nozzle area.

Dugan, James F., Jr.↗
NASA NTRS1997

Efficient algorithms for robust feature matching

One of the basic building blocks in any point-based registration scheme involves matching feature points that are extracted from the sensed image to their counterparts in the reference image. This leads to the fundamental problem of point matching: given two sets of points, find the affine transformation that transforms one point set so that its distance from the other point set is minimized. Because of measurement errors and the presence of outlying data points, it is important that the distance measure between two point sets be robust to these effects. We measure distances using the generalized Hausdorff distance. Point matching can be a computationally intensive task, and there have been a number of algorithms and approaches proposed for solving this problem both theoretical and applied. We present two approaches to the point matching problem, in an attempt to reduce the computational complexity of the problem, while still providing guarantees on the quality of the final match. Our first method is an approximation algorithm, which is loosely based on a branch-and-bound approach due to Huttenlocher and Rucklidge. We show that by varying the approximation error bounds, it is possible to achieve a tradeoff between the quality of the match and the running time of the algorithm. Our second method involves a Monte Carlo method for accelerating the search process used in the first algorithm. With high probability this method succeeds in finding an approximately optimal match. We establish the efficiency of our approaches empirically.

Mount, David M.↗
DOE OSTI2025

Constrained or unconstrained? Neural-network-based equation discovery from data

Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or the accurate resolution of their solutions may be intractable. Instead, recently developed methods, including those based on parameter estimation, operator subset selection, and neural networks, allow for the data-driven discovery of both ordinary and partial differential equations (PDEs), on a spectrum of interpretability. The success of these strategies is often contingent upon the correct identification of representative equations from noisy observations of state variables and, as importantly and intertwined with that, the mathematical strategies utilized to enforce those equations. Specifically, the latter has been commonly addressed via unconstrained optimization strategies. Representing the PDE as a neural network, we propose to discover the PDE (or the associated operator) by solving a constrained optimization problem and using an intermediate state representation similar to a physics-informed neural network (PINN). The objective function of this constrained optimization problem promotes matching the data, while the constraints require that the discovered PDE is satisfied at a number of spatial collocation points. We present a penalty method and a widely used trust-region barrier method to solve this constrained optimization problem, and we compare these methods on numerical examples. Our results on several example problems demonstrate that the latter constrained method outperforms the penalty method, particularly for higher noise levels or fewer collocation points. This work motivates further exploration into using sophisticated constrained optimization methods in scientific machine learning, as opposed to their commonly used, penalty-method or unconstrained counterparts. For both of these methods, we solve these discovered neural network PDEs with classical methods, such as finite difference methods, as opposed to PINNs-type methods relying on automatic differentiation. Here, we briefly highlight how simultaneously fitting the data while discovering the PDE improves the robustness to noise and other small, yet crucial, implementation details.

Data-driven discovery↗
NASA NTRS1995

Pseudo-time method for optimal shape design using the Euler equations

We exploit a novel idea for the optimization of flows governed by the Euler equations. The algorithm consists of marching on the design hypersurface while improving the distance to the state and costate hypersurfaces. We consider the problem of matching the pressure distribution to a desired one, subject to the euler equations, both for subsonic and supersonic flows. The rate of convergence to the minimum for the cases considered is 3 to 4 times slower than that of the analysis problem. Results are given for Ringleb flow and a shockless recompression case.

Iollo, Angelo↗
NASA NTRS1979

Lifting-line theory of oblique wings in transonic flows

Three-dimensional corrections to the nonlinear mixed flow admitted by a high-aspect-ratio swept wing of practical interest are analyzed by solving a perturbation problem and matching its solution to that of an outer flow. The latter is identified with a linear solution involving a lifting line, but the centerline of the planform is not required to be straight and unyawed. The existence of a similarity in the three-dimensional flow structure for a certain oblique-wing geometry is demonstrated, along with a solution to the reduced problem in a high-subcritical case.

Cheng, H. K.↗
NASA NTRS1990

Experiments and other methods for developing expertise with design of experiments in a classroom setting

The only way to gain genuine expertise in Statistical Process Control (SPC) and the design of experiments (DOX) is with repeated practice, but not on canned problems with dead data sets. Rather, one must negotiate a wide variety of problems each with its own peculiarities and its own constantly changing data. The problems should not be of the type for which there is a single, well-defined answer that can be looked up in a fraternity file or in some text. The problems should match as closely as possible the open-ended types for which there is always an abundance of uncertainty. These are the only kinds that arise in real research, whether that be basic research in academe or engineering research in industry. To gain this kind of experience, either as a professional consultant or as an industrial employee, takes years. Vast amounts of money, not to mention careers, must be put at risk. The purpose here is to outline some realistic simulation-type lab exercises that are so simple and inexpensive to run that the students can repeat them as often as desired at virtually no cost. Simulations also allow the instructor to design problems whose outcomes are as noisy as desired but still predictable within limits. Also the instructor and the students can learn a great deal more from the postmortum conducted after the exercise is completed. One never knows for sure what the true data should have been when dealing only with real life experiments. To add a bit more realism to the exercises, it is sometimes desirable to make the students pay for each experimental result from a make-believe budget allocation for the problem.

Patterson, John W.↗
NASA NTRS1982

Solidification of a binary mixture

The time dependent concentration and temperature profiles of a finite layer of a binary mixture are investigated during solidification. The coupled time dependent Stefan problem is solved numerically using an implicit finite differencing algorithm with the method of lines. Specifically, the temporal operator is approximated via an implicit finite difference operator resulting in a coupled set of ordinary differential equations for the spatial distribution of the temperature and concentration for each time. Since the resulting differential equations set form a boundary value problem with matching conditions at an unknown spatial point, the method of invariant imbedding is used for its solution.

Antar, B. N.↗
NASA NTRS1987

On the acceleration of charged particles at relativistic shock fronts

The diffusive acceleration of highly relativistic particles at a shock is reconsidered. Using the same physical assumptions as Blandford and Ostriker (1978), but dropping the restriction to nonrelativistic shock velocities, the authors find approximate solutions of the particle kinetic equation by generalizing the diffusion approximation to higher order terms in the anisotropy of the particle distribution. The general solution of the transport equation on either side of the shock is constructed, which involves the solution of an eigenvalue problem. By matching the two solutions at the shock, the spectral index of the resulting power law is found by taking into account a sufficiently large number of eigenfunctions. Low-order truncation corresponds to the standard diffusion approximation and to a somewhat more general method described by Peacock (1981). In addition to the energy spectrum, the method yields the angular distribution of the particles and its spatial dependence.

Kirk, J. G.↗