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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Algebraic multigrid

The state of the art in algebraic multgrid (AMG) methods is discussed. The interaction between the relaxation process and the coarse grid correction necessary for proper behavior of the solution probes is discussed in detail. Sufficient conditions on relaxation and interpolation for the convergence of the V-cycle are given. The relaxation used in AMG, what smoothing means in an algebraic setting, and how it relates to the existing theory are considered. Some properties of the coarse grid operator are discussed, and results on the convergence of two-level and multilevel convergence are given. Details of an algorithm particularly studied for problems obtained by discretizing a single elliptic, second order partial differential equation are given. Results of experiments with such problems using both finite difference and finite element discretizations are presented.

Ruge, J. W.↗
NASA NTRS1994

On the convergence of local approximations to pseudodifferential operators with applications

We consider the approximation of a class pseudodifferential operators by sequences of operators which can be expressed as compositions of differential operators and their inverses. We show that the error in such approximations can be bounded in terms of L(1) error in approximating a convolution kernel, and use this fact to develop convergence results. Our main result is a finite time convergence analysis of the Engquist-Majda Pade approximants to the square root of the d'Alembertian. We also show that no spatially local approximation to this operator can be convergent uniformly in time. We propose some temporally local but spatially nonlocal operators with better long time behavior. These are based on Laguerre and exponential series.

Hagstrom, Thomas↗
NASA NTRS1995

Extensional flow convecting a reactant undergoing a first order homogeneous reaction and diffusional mass transfer from a sphere at low to intermediate Peclet and Damkohler numbers

Forced convective diffusion-reaction is considered for viscous axisymmetric extensional convecting velocity in the neighborhood of a sphere. For Peclet numbers in the range 0.1 less than or equal to Pe less than or equal to 500 and for Damkohler numbers increasing with increasing Pe but in the overall range 0.02 less than or equal to Da less than or equal to 10, average and local Sherwood numbers have been computed. By introducing the eigenfunction expansion c(r, Theta) = Sum of c(n)(r)P(n)(cos Theta) into the forced convective diffusion equation for the concentration of a chemical species undergoing a first order homogeneous reaction and by using properties of the Legendre functions Pn(cos Theta), the variable coefficient PDE can be reduced to a system of N + 1 second order ODEs for the radial functions c(sub n)(r), n = 0, 1, 2,..., N. The adaptive grid algorithm of Pereyra and Lentini can be used to solve the corresponding 2(N + 1) first order differential equations as a two-point boundary value problem on 1 less than or equal to r less than or equal to r(sub infinity). Convergence of the expansion for a specific value of N can thus be established and provides 'spectral' behavior as well as the full concentration field c(r, Theta).

Shah, N. Y.↗
NASA NTRS1992

Response of pontomedullary reticulospinal neurons to vestibular stimuli in vertical planes. Role in vertical vestibulospinal reflexes of the decerebrate cat

1. To investigate the neural substrate of vestibulospinal reflexes in decerebrate cats, we studied the responses of pontomedullary reticulospinal neurons to natural stimulation of the labyrinth in vertical planes. Our principal aim was to determine whether reticulospinal neurons that terminate in, or are likely to give off collaterals to, the upper cervical segments had properties similar to those of the vestibulocollic reflex (VCR). 2. Antidromic stimulation was used to determine whether the neurons projected to the neck, lower cervical, thoracic, or lumbar levels. Dynamics of the responses of spontaneously firing neurons were studied with sinusoidal stimuli delivered at 0.05-1 Hz and aligned to the plane of body rotation, that produced maximal modulation of the neuron (response vector orientation). Each neuron was assigned a vestibular input classification of otolith, vertical canal, otolith + canal, or spatial-temporal convergence (STC). 3. We found, in agreement with previous studies, that the largest fraction of pontomedullary reticulospinal neurons projected to the lumbar cord, and that only a small number ended in the neck segments. Neurons projecting to all levels of the spinal cord had similar responses to labyrinth stimulation. 4. Reticulospinal neurons that received only vertical canal inputs were rare (1 of 67 units). Most reticulospinal neurons (48%) received predominant otolith inputs, 18% received otolith + canal input, and only 9% had STC behavior. These data are in sharp contrast to the results of our previous studies of vestibulospinal neurons. A considerable portion of vestibulospinal neurons receives vertical canal input (38%), fewer receive predominantly otolith input (22%), whereas the proportion that have otolith + canal input or STC behavior is similar to our present reticulospinal data. 5. The response vector orientations of our reticulospinal neurons, particularly those with canal inputs (canal, otolith + canal, STC) were predominantly in the roll quadrants. There was no evidence of convergence of inputs from like canals across the midline (e.g., right anterior + left anterior). 6. Two characteristics of the VCR, STC behavior and bilateral input from symmetric vertical canals (in some muscles), cannot be accounted for by the reticulospinal neurons that we studied. Because these characteristics are also not seen in vestibulocollic neurons, they are likely to be the result of the appropriate convergence of vestibular signals in the spinal cord. 7. Pontomedullary reticulospinal neurons seem particularly well suited to play a role in gravity-dependent postural reflexes of neck and limbs.

NASA Discipline Neuroscience↗
DOE OSTI2024

Model-Free Control of Indoor Temperatures in Residential Buildings: Convergence Analysis

Model-free control (MFC) has recently been applied in multiple fields, including indoor air temperature regulation in buildings. It is a data-enabled feedback tracking control strategy for complex systems using a simplified representation of the ultra-local approximation model through the unique information of input-output behavior. MFC is a prevailing control strategy for systems with unknown or poorly known system dynamic models. Thus, it is a relatively simple, but efficient, trajectory tracking controller. In this paper, we investigate the convergence rate of MFC when applied to controlling indoor temperatures in residential buildings subject to outdoor weather disturbances. Numerical results show that MFC is quite robust to external disturbances, and its rate of convergence is almost one, i.e., it converges Q-sublinearly (slower than linearly).

Wu, Tumin↗
NASA NTRS1972

Finite elements of nonlinear continua.

The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

Oden, J. T.↗
NASA NTRS1977

New features of global climatology revealed by satellite-derived oceanic rainfall maps

Quantitative rainfall maps over the oceanic areas of the globe were derived from the Nimbus 5 Electrically Scanning Microwave Radiometer (ESMR) data. Analysis of satellite derived oceanic rainfall maps reveal certain distinctive characteristics of global patterns for the years 1973-74. The main ones are (1) the forking of the Intertropical Convergence Zone in the Pacific, (2) a previously unrecognized rain area in the South Atlantic, (3) the bimodal behavior of rainbelts in the Indian Ocean and (4) the large interannual variability in oceanic rainfall. These features are discussed.

Rao, M. S. V.↗
NASA NTRS1981

Stability of a diffuse linear pinch with axial boundaries

A formulation of the stability behavior of a finite-length pinch is presented. A general initial perturbation is expressed as a uniformly convergent sum over a complete discrete k set. A variational calculation is then performed, based on the energy principle, in which the end-boundary conditions appear as constraints. The requisite Lagrange multipliers mutually couple the elemental periodic excitations. The resulting extended form of delta-W still admits a proper second-variation treatment so that the minimization and stability considerations of Newcomb remain applicable. Comparison theorems are discussed as is the relevance of this end-effect model to the stability of solar coronal loops.

Einaudi, G.↗
NASA NTRS1999

A Non-Dissipative Staggered Fourth-Order Accurate Explicit Finite Difference Scheme for the Time-Domain Maxwell's Equations

We consider a divergence-free non-dissipative fourth-order explicit staggered finite difference scheme for the hyperbolic Maxwell's equations. Special one-sided difference operators are derived in order to implement the scheme near metal boundaries and dielectric interfaces. Numerical results show the scheme is long-time stable, and is fourth-order convergent over complex domains that include dielectric interfaces and perfectly conducting surfaces. We also examine the scheme's behavior near metal surfaces that are not aligned with the grid axes, and compare its accuracy to that obtained by the Yee scheme.

Yefet, Amir↗
NASA NTRS1994

Dynamics of Numerics and CFD

This lecture attempts to illustrate the basic ideas of how the recent advances in nonlinear dynamical systems theory (dynamics) can provide new insights into the understanding of numerical algorithms used in solving nonlinear differential equations (DEs). Examples will be given of the use of dynamics to explain unusual phenomena that occur in numerics. The inadequacy of the use of linearized analysis for the understanding of long time behavior of nonlinear problems will be illustrated, and the role of dynamics in studying the nonlinear stability, accuracy, convergence property and efficiency of using time- dependent approaches to obtaining steady-state numerical solutions in computational fluid dynamics (CFD) will briefly be explained.

Yee, H. C.↗
DOE OSTI2021

An investigation into the effects of cyclic strain rate on the high cycle and very high cycle fatigue behaviors of wrought and additively manufactured Inconel 718

Additive Manufacturing (AM) has increasingly been used to fabricate parts in aerospace applications, which may require service lives beyond ten-million cycles due to the imposed high loading frequencies. Understanding the very high cycle fatigue (VHCF) behavior of these additive manufactured (AM) parts is an important step towards their design and qualification processes. This study focuses on the high cycle fatigue (HCF) and VHCF behaviors of both wrought and laser beam-powder bed fusion (LB-PBF) fabricated Inconel 718 in machined/polished surface condition, emphasizing on the influence of test frequency (i.e., cyclic strain rate). Uniaxial, fully-reversed force- and stress-controlled fatigue tests were conducted utilizing a servo-hydraulic and an ultrasonic test system operating at 5 Hz and 20 kHz, respectively, on wrought as well as LB-PBF vertically and diagonally built specimens. Fatigue cracks in the majority of the specimens were found to initiate from intra-granular slip bands near or at the surface, which gives rise to strong anisotropy in fatigue resistance in LB-PBF specimens due to the presence of columnar grains along the build directions. Longer fatigue lives were obtained at 20 kHz, which was ascribed to possibly lower-than-intended stresses applied in the ultrasonic tests. The corrected stress-life fatigue data at 20 kHz were found to converge to the one obtained from conventional testing at 5 Hz, implying no effect of cyclic strain rate on the fatigue behavior of Inconel 718 regardless of the fabrication process. The findings of this work confirm the use of ultrasonic fatigue testing to expedite generation of AM materials data to keep up with the current demand; however, the applied stress may need to be corrected.

36 MATERIALS SCIENCE↗
NASA NTRS1990

Consistency and convergence for numerical radiation conditions

The problem of imposing radiation conditions at artificial boundaries for the numerical simulation of wave propagation is considered. Emphasis is on the behavior and analysis of the error which results from the restriction of the domain. The theory of error estimation is briefly outlined for boundary conditions. Use is made of the asymptotic analysis of propagating wave groups to derive and analyze boundary operators. For dissipative problems this leads to local, accurate conditions, but falls short in the hyperbolic case. A numerical experiment on the solution of the wave equation with cylindrical symmetry is described. A unified presentation of a number of conditions which have been proposed in the literature is given and the time dependence of the error which results from their use is displayed. The results are in qualitative agreement with theoretical considerations. It was found, however, that for this model problem it is particularly difficult to force the error to decay rapidly in time.

Hagstrom, Thomas↗
NASA NTRS1988

Accelerated convergence for synchronous approximate agreement

The protocol for synchronous approximate agreement presented by Dolev et. al. exhibits the undesirable property that a faulty processor, by the dissemination of a value arbitrarily far removed from the values held by good processors, may delay the termination of the protocol by an arbitrary amount of time. Such behavior is clearly undesirable in a fault tolerant dynamic system subject to hard real-time constraints. A mechanism is presented by which editing data suspected of being from Byzantine-failed processors can lead to quicker, predictable, convergence to an agreement value. Under specific assumptions about the nature of values transmitted by failed processors relative to those transmitted by good processors, a Monte Carlo simulation is presented whose qualitative results illustrate the trade-off between accelerated convergence and the accuracy of the value agreed upon.

Kearns, J. P.↗
DOE OSTI2024

A $C^1$-Conforming Arbitrary-Order Two-Dimensional Virtual Element Method for the Fourth-Order Phase-Field Equation

We present a two-dimensional conforming virtual element method for the fourth-order phase-field equation. Our proposed numerical approach to the solution of this high-order phase-field (HOPF) equation relies on the design of an arbitrary-order accurate, virtual element space with $C^1$ global regularity. Such regularity is guaranteed by taking the values of the virtual element functions and their full gradient at the mesh vertices as degrees of freedom. Attaining high-order accuracy requires also edge polynomial moments of the trace of the virtual element functions and their normal derivatives. In this work, we detail the scheme construction, and prove its convergence by deriving error estimates in different norms. A set of representative test cases allows us to assess the behavior of the method.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1981

The plasma wake of mesosonic conducting bodies. II - An experimental parametric study of the mid-wake ion density peak

An experimental investigation of the disturbed flow field created by conducting bodies in a mesosonic, collisionless plasma stream is reported. The mid-wake region is investigated, where, for bodies of the order of a Debye length in size, the focused ion streams converge to form a significant current density peak on the wake axis. A parametric description is obtained of the behavior of the amplitude, width, and position of this peak. The results also indicate that portions of the axial ion peak are created by additional mechanisms and that body geometry affects the mid-wake structure only when the sheath is sufficiently thin to conform to the shape of the body.

Stone, N. H.↗
NASA NTRS1988

Nonlinear analysis using temporal finite elements

A formulation method, based on Hamilton's law of varying action, for finite elements in space and time incorporating nonlinear geometric and material behavior is presented. Case studies using elastic-plastic axial rod elements are carried out to demonstrate the accuracy, convergence and generality of the method.

Gellin, Slade↗
NASA NTRS1997

Reduced Navier Stokes Relaxation Procedures for Internal Flows

In spite of significant advancement in the field of high speed computing, flow calculations involving complex geometries and/or flow behavior still require large amounts of CPU time and memory. In order to predict such flows without sacrificing grid convergence and accuracy, adaptive gridding techniques that provide optimal resolution are highly desirable. The present work combines multigrid techniques and domain decomposition concepts to provide local, solution adaptive, grid refinement. Several viscous compressible and incompressible, two and three-dimensional, flows with strong inviscid interaction and/or axial flow reversal, are considered with a segmented multigrid domain decomposition (SMGDD) procedure for which uniform meshes result in each domain. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable non-staggered grid computation. The SMGDD technique presented herein has previously been applied for incompressible two dimensional flows. The present work offers improvement in the gridding strategy, by allowing for disjoint subdomains that provide optimal resolution of disparate flow features. It also extends the SMGDD technique to three dimensional compressible flows. Laminar and turbulent flow in a backward facing step channel is considered; although the procedure is applicable to more severe geometries. The standard K-epsilon model is applied for turbulence closure. For Re greater than 400, differences between two-dimensional theory and experiment are resolved through a three dimensional simulation, which confirms the experimentally observed three dimensionality of the recirculation patterns on the upper and lower surfaces.

Rubin, Stanley G.↗