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DOE OSTI2022

Comparison of exponential integrators and traditional time integration schemes for the shallow water equations

We report the time integration scheme is probably one of the most fundamental choices in the development of an ocean model. In this paper, we investigate several time integration schemes when applied to the shallow water equations. This set of equations is accurate enough for the modeling of a shallow ocean and is also relevant to study as it is the one solved for the barotropic (i.e. vertically averaged) component of a three dimensional ocean model. We analyze different time stepping algorithms for the linearized shallow water equations. High order explicit schemes are accurate but the time step is constrained by the Courant-Friedrichs-Lewy stability condition. Implicit schemes can be unconditionally stable but, in practice lack accuracy when used with large time steps. In this paper we propose a detailed comparison of such classical schemes with exponential integrators. The accuracy and the computational costs are analyzed in different configurations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Demonstration of a time-integrated short line of sight neutron imaging system for inertial confinement fusion

The Neutron Imaging System (NIS) is an important diagnostic for understanding implosions of deuterium-tritium capsules at the National Ignition Facility. While the detectors for the existing system must be positioned 28 m from the source to produce sufficient imaging magnification and resolution, recent testing of a new short line of sight neutron imaging system has shown sufficient resolution to allow reconstruction of the source image with quality similar to that of the existing NIS on a 11.6 m line of sight. The new system used the existing pinhole aperture array and a stack of detectors composed of 2 mm thick high-density polyethylene converter material followed by an image plate. In these detectors, neutrons enter the converter material and interact with protons, which recoil and deposit energy within the thin active layer of the image plate through ionization losses. The described system produces time-integrated images for all neutron energies passing through the pinhole. We present details of the measurement scheme for this novel technique to produce energy-integrated neutron images as well as source reconstruction results from recent experiments at NIF.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2026

Optimizing time integration for accurate recovery of shockwave interface location in radiography

We present simulations and experiments of time integrated radiographic imaging of a moving 1D shock wave front and a quantitative method for determining the statistical error in locating the shock front as a function of integration time and noise in the radiograph. We discuss the trade-off between increasing motion blur, which leads to decreased shock front location certainty, and increasing signal-to-noise, which leads to improved image quality with increasing integration time. We find an optimum integration time between a short integration time, where noise limits the error, and a long integration time, where motion blurring limits the error. This methodology can be used to tune experimental configurations to obtain the highest quality radiograph for a given experimental configuration.

Bremsstrahlung↗

DOE OSTI2017

All-sky Search for Time-integrated Neutrino Emission from Astrophysical Sources with 7 yr of IceCube Data

Since the recent detection of an astrophysical flux of high-energy neutrinos, the question of its origin has not yet fully been answered. Much of what is known about this flux comes from a small event sample of high neutrino purity, good energy resolution, but large angular uncertainties. In searches for point-like sources, on the other hand, the best performance is given by using large statistics and good angular reconstructions. Track-like muon events produced in neutrino interactions satisfy these requirements. We present here the results of searches for point-like sources with neutrinos using data acquired by the IceCube detector over 7 yr from 2008 to 2015. The discovery potential of the analysis in the northern sky is now significantly below E{sub ν}{sup 2}dϕ/dE{sub ν} = 10{sup −12} TeV cm{sup −2} s{sup −1}, on average 38% lower than the sensitivity of the previously published analysis of 4 yr exposure. No significant clustering of neutrinos above background expectation was observed, and implications for prominent neutrino source candidates are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1989

Estimation of areal rainfall using the radar echo area time integral

The Area Time Integral (ATI) method of Doneaud et al. (1984) is extended to the measurement of cumulative areawide rainfall for periods up to 12 h. The extended ATI method is used to analyze data from the Florida Area Cumulus Experiment II. The relationship between radar estimated rain volume and radar-measured area covered with echoes is examined to test the possibility of obtaining values similar to conventional reflectivity-rainfall estimates of rainfall using only area measurements. The correlation between gage-estimated rain volume and radar estimated area covered with showers is also studied, focusing on the possible estimation of rain volume values using a small number of echo area observations.

Lopez, Raul E.↗

NASA NTRS2004

Simulating Nonlinear Deformations of Solar Sail Membranes Using Explicit Time Integration

In this study, the explicit time integration method is employed to predict deformation of highly flexible solar sail structural components. The nonlinear static analysis of a highly flexible ribbon structure is presented to demonstrate the need for having the explicit time integration method in the analysis toolbox for solar sail. Static analyses of the ribbon structure produce ambiquous results whereas the explicit time integration method determines the correct results. Extensive benchmarking examples are also presented to build confidence in the use of the explicit method. Previously determined nonlinear wrinkling deformations of solar sail membranes are found by the explicit method. As the explicit method is known to often require more computational time than nonlinear static methods, a study on mass scaling was also conducted. The computational times are reported for the nonlinear static and explicit time integration solutions to calibrate the advantage of using mass scaling for these problems.

Wang, John T.↗

DOE OSTI2014

Transit light curves with finite integration time: Fisher information analysis

Kepler has revolutionized the study of transiting planets with its unprecedented photometric precision on more than 150,000 target stars. Most of the transiting planet candidates detected by Kepler have been observed as long-cadence targets with 30 minute integration times, and the upcoming Transiting Exoplanet Survey Satellite will record full frame images with a similar integration time. Integrations of 30 minutes affect the transit shape, particularly for small planets and in cases of low signal to noise. Using the Fisher information matrix technique, we derive analytic approximations for the variances and covariances on the transit parameters obtained from fitting light curve photometry collected with a finite integration time. We find that binning the light curve can significantly increase the uncertainties and covariances on the inferred parameters when comparing scenarios with constant total signal to noise (constant total integration time in the absence of read noise). Uncertainties on the transit ingress/egress time increase by a factor of 34 for Earth-size planets and 3.4 for Jupiter-size planets around Sun-like stars for integration times of 30 minutes compared to instantaneously sampled light curves. Similarly, uncertainties on the mid-transit time for Earth and Jupiter-size planets increase by factors of 3.9 and 1.4. Uncertainties on the transit depth are largely unaffected by finite integration times. While correlations among the transit depth, ingress duration, and transit duration all increase in magnitude with longer integration times, the mid-transit time remains uncorrelated with the other parameters. We provide code in Python and Mathematica for predicting the variances and covariances at www.its.caltech.edu/∼eprice.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Advanced time integration algorithms for dislocation dynamics simulations of work hardening

Efficient time integration is a necessity for dislocation dynamics simulations of work hardening to achieve experimentally relevant strains. In this work, an efficient time integration scheme using a high order explicit method with time step subcycling and a newly-developed collision detection algorithm are evaluated. First, time integrator performance is examined for an annihilating Frank–Read source, showing the effects of dislocation line collision. The integrator with subcycling is found to significantly out-perform other integration schemes. The performance of the time integration and collision detection algorithms is then tested in a work hardening simulation. The new algorithms show a 100-fold speed-up relative to traditional schemes. As a result, subcycling is shown to improve efficiency significantly while maintaining an accurate solution, and the new collision algorithm allows an arbitrarily large time step size without missing collisions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A unified formulation of splitting-based implicit time integration schemes

Splitting-based time integration approaches such as fractional step, alternating direction implicit, operator splitting, and locally one dimensional methods partition the system of interest into components, and solve individual components implicitly in a cost-effective way. Here this work proposes a unified formulation of splitting time integration schemes in the framework of general-structure additive Runge–Kutta (GARK) methods. Specifically, we develop implicit-implicit (IMIM) GARK schemes, provide the order conditions for this class, and explain their application to partitioned systems of ordinary differential equations. We show that classical splitting methods belong to the IMIM GARK family, and therefore can be studied in this unified framework. New IMIM-GARK splitting methods are developed and tested using parabolic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Interface flux recovery framework for constructing partitioned heterogeneous time-integration methods

A common approach for the development of partitioned schemes employing different time integrators on different subdomains is to lag the coupling terms in time. This can lead to accuracy issues, especially in multistage methods. Here, in this article, we present a novel framework for partitioned heterogeneous time-integration methods, which allows the coupling of arbitrary multistage and multistep methods without reducing their order of accuracy. At the core of our approach are accurate estimates of the interface flux obtained from the Schur complement of an auxiliary monolithic system. We use these estimates to construct a polynomial-in-time approximation of the interface flux over the current time coupling window. This approximation provides the interface boundary conditions necessary to decouple the subdomain problems at any point within the coupling window. In so doing our framework enables a flexible choice of time-integrators for the individual subproblems without compromising the time-accuracy at the coupled problem level. This feature is the main distinction between our framework and other approaches. To demonstrate the framework, we construct a family of partitioned heterogeneous time-integration methods, combining multistage and multistep methods, for a simplified tracer transport component of the coupled air-sea system in Earth system models. We report numerical tests evaluating accuracy and flux conservation for different pairs of time-integrators from the explicit Runge-Kutta and Adams-Moulton families.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1992

A new explicit variable time-integration self-starting methodology for computational structural dynamics

A new explicit variable time-integration methodology and architecture which possesses self-starting attributes, eliminates the need to involve acceleration computations, and which has improved accuracy characteristics in comparison to the traditional central-difference-type formulations customarily advocated is described for applicability to computational structural dynamics. To sharpen the focus of the present study, an explicit variable time-integration architecture which is relatively simple, yet effective, is described. Unlike variable explicit time-integration formulations adopted in the past, the present self-starting variable time-integration architecture and implementation aspects facilitate a simplified representation and a straightforward and effective approach for combining finite element meshes requiring different time steps in a single analysis. Numerical test cases are provided which demonstrate the applicability of the proposed formulations.

Tamma, Kumar K.↗

NASA NTRS1994

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

Slack, David C.↗

NASA NTRS1993

Finite difference schemes for long-time integration

Finite difference schemes for the evaluation of first and second derivatives are presented. These second order compact schemes were designed for long-time integration of evolution equations by solving a quadratic constrained minimization problem. The quadratic cost function measures the global truncation error while taking into account the initial data. The resulting schemes are applicable for integration times fourfold, or more, longer than similar previously studied schemes. A similar approach was used to obtain improved integration schemes.

Haras, Zigo↗

NASA NTRS1992

GaAs-based photorefractive time-integrating correlator

A potential application of the photorefractive time-integrating correlator is the real-time radar jamming interference rejection system, using the adaptive filter method; a fast photorefractive crystal is needed for adapting a rapidly changing jamming signal. An effort is presently made to demonstrate and characterize a GaAs-based photorefractive time-integrating correlator, since GaAs crystals are 2-3 orders of magnitude faster than most other alternatives.

Liu, Duncan T. H.↗

DOE OSTI2021

Conservative High-Order Time Integration for Lagrangian Hydrodynamics

In tis study, we develop novel time integration methods for the compressible Euler equations in the Lagrangian frame that are of arbitrary high order and exactly preserve the mass, momentum, and total energy of the system. The equations are considered in nonconservative form, that is, common for staggered grid hydrodynamics (SGH) methods; namely, the evolved quantities are mass, momentum, and internal energy. A general family of time integration schemes is formulated, and practical pairs for orders three and four are derived. Numerical results on standard hydrodynamics benchmarks confirm the high-order convergence on smooth problems and the exact numerical preservation of all physically conserved quantities.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1981

Interferometric surface-wave acousto-optic time-integrating correlators

A structure for a coherent-interferometric acousto-optic (AO) time-integrating correlator was implemented by using a single surface acoustic wave (SAW) device with tilted transducers to reduce intermodulation terms. The SAW device was fabricated on Y-Z LiNbO3 with a center frequency of 175 MHz, a bandwidth of 60 MHz, and a time aperture of about 10 micros. The density of the photodetector array, with a potential of 120 MHz. Typical integration times are 30 to 40 ms, providing processing gains in excess of 10 to the 6th power. Such a device is useful in providing fast synchronization of communication links and in demodulating to base band and simultaneously acting as a synchronization lock monitor for moderate data rates. Where processing may be limited by Doppler shifts, a two dimensional architecture was implemented to allow full processing gain. Two one-dimensional, SAW AO time-integrating correlators and a two dimensional correlator are evaluated.

Berg, N. J.↗

NASA NTRS1979

Integration Time Required to Extract Accurate Data from Transonic Wind-Tunnel Tests

Because the forces and pressures on wind-tunnel models tested at transonic speeds are not steady, even for static aerodynamic tests, integration time is required to obtain data of acceptable accuracy. The integration time required for both static and dynamic tests is evaluated analytically and confirmed by experimental measurements. It is shown that, for static and dynamic tests, the accuracy obtained is a function of integration time, frequency of the signal, and the ratio of the dynamic amplitude to the full signal of interest. In addition, for the dynamic case, the frequency bandwidth used in analysis is important. Results of this study indicate that, for typical data accuracy desired from models in a large transonic wind tunnel (11- by 11-ft), up to the following integration times are required: static force and moment tests, 0.5 s; static pressure tests, 1 s; flutter tests, 30 to 60 s; and random-dynamic tests, 10 s.

Muhlstein, Lado, Jr.↗

NASA NTRS1975

Integration time required to extract accurate static and dynamic data from transonic wind-tunnel tests

Because the forces and pressures on wind-tunnel models tested at transonic speeds are not steady, even for 'static' aerodynamic tests, integration time is required to obtain data of acceptable accuracy. The integration time required for both static and dynamic tests is evaluated analytically and confirmed by experimental measurements. It is shown that, for static and dynamic tests, the accuracy obtained is a function of integration time, frequency content of the signal, and the ratio of the dynamic amplitude to the full signal of interest. In addition, for the dynamic case, the frequency band width used in analysis is important. Results of this study indicate that, for typical data accuracy desired from models in a large transonic wind tunnel (11- by 11-ft), up to the following integration times are required: static force and moment tests, 0.5 sec; static pressure tests, 0.1 sec; flutter tests, 30 to 60 sec; and random-dynamic tests, 10 sec.

Muhlstein, L., Jr.↗