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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

The multigrid preconditioned conjugate gradient method

A multigrid preconditioned conjugate gradient method (MGCG method), which uses the multigrid method as a preconditioner of the PCG method, is proposed. The multigrid method has inherent high parallelism and improves convergence of long wavelength components, which is important in iterative methods. By using this method as a preconditioner of the PCG method, an efficient method with high parallelism and fast convergence is obtained. First, it is considered a necessary condition of the multigrid preconditioner in order to satisfy requirements of a preconditioner of the PCG method. Next numerical experiments show a behavior of the MGCG method and that the MGCG method is superior to both the ICCG method and the multigrid method in point of fast convergence and high parallelism. This fast convergence is understood in terms of the eigenvalue analysis of the preconditioned matrix. From this observation of the multigrid preconditioner, it is realized that the MGCG method converges in very few iterations and the multigrid preconditioner is a desirable preconditioner of the conjugate gradient method.

Tatebe, Osamu↗
NASA NTRS2000

On the Local Convergence of Pattern Search

We examine the local convergence properties of pattern search methods, complementing the previously established global convergence properties for this class of algorithms. We show that the step-length control parameter which appears in the definition of pattern search algorithms provides a reliable asymptotic measure of first-order stationarity. This gives an analytical justification for a traditional stopping criterion for pattern search methods. Using this measure of first-order stationarity, we analyze the behavior of pattern search in the neighborhood of an isolated local minimizer. We show that a recognizable subsequence converges r-linearly to the minimizer.

Dolan, Elizabeth D.↗
DOE OSTI2023

Geometry of conformal manifolds and the inversion formula

Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed using Euclidean and Lorentzian inversion formulae, which combine the operator content of the conformal field theory into an analytic function. Analogously, operators of fixed dimension define bundles over the conformal manifold whose curvatures can also be computed using inversion formulae. These results relate curvatures to integrated four-point correlation functions which are sensitive only to the behavior of the theory at separated points. We apply these inversion formulae to derive convergent sum rules expressing the curvature in terms of the spectrum of local operators and their three-point function coefficients. We further show that the curvature can smoothly diverge only if a conserved current appears in the spectrum, or if the theory develops a continuum. We verify our results explicitly in 2d examples. In particular, for 2d (2,2) superconformal field theories we derive a lower bound on the scalar curvature, which is saturated by free theories when the central charge is a multiple of three.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

TANTE: Time-adaptive operator learning via neural Taylor expansion

Operator learning for time-dependent partial differential equations (PDEs) has seen rapid progress in recent years, enabling efficient approximation of complex spatiotemporal dynamics. However, most existing methods rely on fixed time step sizes during rollout, which limits their ability to adapt to varying temporal complexity and often leads to error accumulation. In this work, we propose the Time-Adaptive Transformer with Neural Taylor Expansion (TANTE), a novel operator-learning framework that produces continuous-time predictions with adaptive step sizes. TANTE predicts future states by performing a Taylor expansion at the current state, where neural networks learn both the higher-order temporal derivatives and the local radius of convergence. This allows the model to dynamically adjust its rollout based on the local behavior of the solution, thereby reducing cumulative error and improving computational efficiency. We demonstrate the effectiveness of TANTE across a wide range of PDE benchmarks, achieving superior accuracy and adaptability compared to fixed-step baselines, delivering accuracy gains of 60-80 % and speed-ups of 30-40 % at inference time.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1978

On a new algorithm for time step integration of nonlinear systems

A new implicit algorithm for time step integration of finite element structural dynamic equations is presented. Convergence, stability and numerical damping properties are discussed. Due to the way nonlinear structural behavior is taken into account, the algorithm is expected to compare favorably with existing ones. Some simple numerical results are presented. A related explicit algorithm is also derived and shortly discussed.

Anderheggen, E.↗
NASA NTRS1984

Extension of constrained incremental Newton-Raphson scheme to generalized loading fields

This paper develops numerical strategies which enable the constrained incremental Newton-Raphson scheme to handle the static response of structure to loading fields with completely generalized histories. This is made possible through the use of specially warped hyperelliptic constraint surfaces which control successive or clustered load steps in the vicinity of loading events with specific timing schedules. Such an approach enables improved convergence and stability characteristics. Due to the generality of the methodology, pre- and postbuckling behavior caused by both kinematic and material nonlinearity can be handled. To demonstrate the scheme, the results of several bench-mark problems are also presented. These include situations involving nonlinear kinematics as well as highly history-dependent elastic-plastic and thermoelastic-plastic material behavior.

Padovan, J.↗
NASA NTRS1992

The structure of intense vorticity in homogeneous isotropic turbulence

The structure of the intense vorticity regions is studied in numerically simulated homogeneous, isotropic, equilibrium turbulent flow fields at four different Reynolds numbers in the range Re(sub lambda) = 36-171. In accordance with previous investigators, this vorticity is found to be organized in coherent, cylindrical or ribbon-like, vortices ('worms'). A statistical study suggests that they are just especially intense features of the background, O(omega'), vorticity. Their radii scale with the Kolmogorov microscale and their lengths with the integral scale of the flow. An interesting observation is that the Reynolds number based on the circulation of the intense vortices, gamma/nu, increases monotonically with Re(sub lambda), raising the question of the stability of the structures in the limit of Re(sub lambda) approaching infinity. One and two-dimensional statistics of vorticity and strain are presented; they are non-gaussian, and the behavior of their tails depends strongly on the Reynolds number. There is no evidence of convergence to a limiting distribution in our range of Re(sub lambda), even though the energy spectra and the energy dissipation rate show good asymptotic properties in the higher Reynolds number cases. Evidence is presented to show that worms are natural features of the flow and that they do not depend on the particular forcing scheme.

Jimenez, J.↗
NASA NTRS1996

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Ibrahim, A. H.↗
NASA NTRS1972

Liquid inflow to a baffled cylindrical tank during weightlessness

An experimental investigation was conducted in which the behavior of liquid inflow to a cylindrical tank containing inlet baffles was observed during weightlessness. A single tank radius (2 cm), inlet radius (0.2 cm), and liquid (ethanol)were used. The inlet end of the tank was hemispherical with a 30 deg convergent inlet. All the baffle configurations tested were cylindrically symmetric and mounted coaxially with the tank within the hemispherical end. Both stable and unstable inflow behavior were observed using each baffle. It was found that, depending on which of the baffles was used, the critical inflow velocity at which a transition to unstable inflow began was from 2.5 to 12 times greater than the corresponding velocity in an unbaffled tank.

Staskus, J. V.↗
NASA NTRS1997

Multistage Schemes with Multigrid for Euler and Navier-Strokes Equations: Components and Analysis

A class of explicit multistage time-stepping schemes with centered spatial differencing and multigrids are considered for the compressible Euler and Navier-Stokes equations. These schemes are the basis for a family of computer programs (flow codes with multigrid (FLOMG) series) currently used to solve a wide range of fluid dynamics problems, including internal and external flows. In this paper, the components of these multistage time-stepping schemes are defined, discussed, and in many cases analyzed to provide additional insight into their behavior. Special emphasis is given to numerical dissipation, stability of Runge-Kutta schemes, and the convergence acceleration techniques of multigrid and implicit residual smoothing. Both the Baldwin and Lomax algebraic equilibrium model and the Johnson and King one-half equation nonequilibrium model are used to establish turbulence closure. Implementation of these models is described.

Swanson, R. C.↗
NASA NTRS2002

Verification Assessment of Flow Boundary Conditions for CFD Analysis of Supersonic Inlet Flows

Boundary conditions for subsonic inflow, bleed, and subsonic outflow as implemented into the WIND CFD code are assessed with respect to verification for steady and unsteady flows associated with supersonic inlets. Verification procedures include grid convergence studies and comparisons to analytical data. The objective is to examine errors, limitations, capabilities, and behavior of the boundary conditions. Computational studies were performed on configurations derived from a "parameterized" supersonic inlet. These include steady supersonic flows with normal and oblique shocks, steady subsonic flow in a diffuser, and unsteady flow with the propagation and reflection of an acoustic disturbance.

Slater, John W.↗
NASA NTRS2005

Fluctuations in Conjunction Miss Distance Projections as Time Approaches Time of Closest Approach

A responsibility of the Trajectory Operations Officer is to ensure that the International Space Station (ISS) avoids colliding with debris. United States Space Command (USSPACECOM) tracks and catalogs a portion of the debris in Earth orbit, but only objects with a perigee less than 600 km and a radar cross section (RCS) greater than 10 cm-objects that, in fact, represent only a small fraction of the objects in Earth orbit. To accommodate for this, the ISS uses shielding to protect against collisions with smaller objects. This study provides a better understanding of how quickly, and to what degree, USSPACECOM projections tend to converge to the final, true miss distance. The information included is formulated to better predict the behavior of miss distance data during real-time operations. It was determined that the driving components, in order of impact on miss distance fluctuations, are energy dissipation rate (EDR), RCS, and inclination. Data used in this analysis, calculations made, and conclusions drawn are stored in Microsoft Excel log sheets. A separate log sheet, created for each conjunction, contains information such as predicted miss distances, apogee and perigee of debris orbit, EDR, RCS, inclination, tracks and observations, statistical data, and other evaluation/orbital parameters.

Christian, John A., III↗
NASA NTRS1989

The proximity of hotspots to convergent and divergent plate boundaries

An analysis of four different hotspot distributions, ranging from Morgan's (1972) original list of 19 to Vogt's (1981) list of 117 reveals that the hotspots are preferentially located near divergent plate boundaries. The probability of this proximity occurring by chance alone is quite remote, less than 0.01 for all four hotspot distributions. The same analysis also reveals that the hotspots are preferentially excluded from regions near convergent plate boundaries. The probability of this exclusion occurring by chance alone is 0.1 or less for three out of the four distributions examined. We interpret this behavior as being a consequence of the effects of large scale convective circulation on ascending mantle plumes. Mantle thermal plumes, the most probable source of hotspots, arise from instabilities in a basal thermal boundary layer. Plumes are suppressed from regions beneath convergent boundaries by descending flow and are entrained into the upwelling flow beneath spreading centers. Plate-scale convective circulation driven by subduction may also advect mantle thermal plumes toward spreading centers.

Weinstein, Stuart A.↗
DOE OSTI2025

Nontrivial critical behavior at magnetic transitions: A case study of Sm 7 ⁢Pd 3

We present a comprehensive analysis of the critical behavior of Sm 7 ⁢Pd 3 in the vicinity of its second-order magnetoelastic transition at 𝑇 c =173 K. The critical exponents (CEs) 𝛽 and 𝛾, determined using both the standard convergence procedure and the average normalized slope (ANS) method, diverge at 𝑇 c –-a characteristic typically associated with first-order transitions. Notably, none of the established universality classes satisfactorily describe the critical behavior of Sm 7 ⁢Pd 3 , and we discuss the possible origins of this deviation in the context of the strong spin-lattice coupling intrinsic to the sample. We emphasize the importance of accurately selecting the critical temperature and magnetic field ranges to ensure robust critical behavior analysis, and propose a quantitative approach to assess the reliability of the extracted CEs. Additionally, we demonstrate that in the ANS method, the critical exponents 𝛽 and 𝛾 should be calculated separately using data for 𝑇 ⩽ 𝑇 c and 𝑇 ⩾ 𝑇 c , respectively. In conclusion, our findings underscore the need for a revised theoretical framework to accurately describe second-order magnetoelastic transitions.

Ferrimagnets↗
DOE OSTI2023

Improved multiphysics model of the High Temperature Engineering Test Reactor for the simulation of loss-of-forced-cooling experiments

We present a multiphysics model of the High Temperature Engineering Test Reactor for comparison with past and predict future loss-of-forced-cooling (LOFC) experiments. The approach selected combines (1) 3-D full-core superhomogenization-corrected neutronics, (2) 3-D full-core homogenized or semi-heterogeneous heat transfer (macroscale), (3) 2-D axisymmetric fuel rod heat transfer (mesoscale), and (4) 1-D thermal-hydraulics channels. Although large sensitivities remain and the available experimental data are insufficient for use in a rigorous validation exercise, the overall transient behavior is successfully reproduced. The novelty of our work includes (1) a new macroscale-mesoscale heat transfer coupling approach relying on gap conductance to drastically speed up numerical convergence by two orders of magnitude, (2) determination of a radial effective thermal conductivity that yields reasonably close results between the homogenized and semi-heterogeneous macroscale thermal models, and (3) a preliminary study of the reactor's early behavior following a LOFC event, thus enabling further assessment of numerical models against fission power measurements.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1990

On domains of convergence in optimization problems

Numerical optimization algorithms require the knowledge of an initial set of design variables. Starting from an initial design x(sup 0), improved solutions are obtained by updating the design iteratively in a way prescribed by the particular algorithm used. If the algorithm is successful, convergence is achieved to a local optimal solution. Let A denote the iterative procedure that characterizes a typical optimization algorithm, applied to the problem: Find x belonging to R(sup n) that maximizes f(x) subject to x belonging to Omega contained in R(sup n). We are interested in problems with several local maxima (x(sub j))(sup *), j=1, ..., m, in the feasible design space Omega. In general, convergence of the algorithm A to a specific solution (x(sub j))(sup *) is determined by the choice of initial design x(sup 0). The domain of convergence D(sub j) of A associated with a local maximum (x(sub j))(sup *) is a subset of initial designs x(sup 0) in Omega such that the sequence (x(sup k)), k=0,1,2,... defined by x(sup k+1) = A(x(sup k)), k=0,1,... converges to (x(sub j))(sup *). The set D(sub j) is also called the basin of attraction of (x(sub j))(sup *). Cayley first proposed the problem of finding the basin of attraction for Newton's method in 1897. It has been shown that the basin of attraction for Newton's method exhibits chaotic behavior in problems with polynomial objective. This implies that there may be regions in the feasible design space where arbitrarily close starting points will converge to different local optimal solutions. Furthermore, the boundaries of the domains of convergence may have a very complex, even fractal structure. In this paper we show that even simple structural optimization problems solved using standard gradient based (first order) algorithms exhibit similar features.

Diaz, Alejandro R.↗
DOE OSTI2021

KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation

This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the underlying partial differential equation is a Laplace-like operator. In this paper, we extend some of the prior convergence results to Helmholtz-based optimization applications. Our analysis examines situations where control variables and observations are restricted to subregions of the computational domain. We prove that solver convergence rates do not deteriorate as the mesh is refined or as the wavenumber increases. More specifically, for one of the preconditioners we prove accelerated convergence as the wavenumber increases. Additionally, in situations where the control and observation subregions are disjoint, we observe that solver convergence rates have a weak dependence on the regularization parameter. We give a partial analysis of this behavior. We illustrate the performance of the preconditioners on control problems motivated by acoustic testing.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1978

Theory of the classical electron gas

In a previous paper Cohen and Murphy (1969) used the Meeron resummation (1958) of the Mayer diagrams (1950) to calculate the pair correlation for the classical electron gas in thermal equilibrium. They found that successive terms in the expression for the pair correlation were more and more singular for small interparticle spacing, actually dominating the Debye-Hueckel result for sufficiently small distances. This led to apparent divergence in the higher order contributions to the internal energy. The present paper shows that the apparent anomalies in the Cohen-Murphy results can be removed without further resummation by a more careful treatment of the region of small interparticle spacing. It is shown that there is really no anomalous behavior at short range in any order and all integrals in the expression for the internal energy converge.

Guernsey, R. L.↗