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All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

A Time Integration Algorithm Based on the State Transition Matrix for Structures with Time Varying and Nonlinear Properties

A variable order method of integrating the structural dynamics equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. When the time variation of the system can be modeled exactly by a polynomial it produces nearly exact solutions for a wide range of time step sizes. Solutions of a model nonlinear dynamic response exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with solutions obtained by established methods.

Bartels, Robert E.↗
NASA NTRS2002

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

Jothiprasad, Giridhar↗
NASA NTRS1989

A raingage, radar and satellite simulation study of the estimation of convective rainfall by area-time integrals

Correlations between area-averaged rainrates and the areal fraction of rainrates exceeding a preset threshold, F(T), are examined using data from a network of 22 raingages located within 120 km of the NOAA/Tropical Ocean-Global Atmosphere (TOGA) C-band meteorological radar at Darwin, Australia. The results show that the area averages of convective rainfall are highly correlated with the fraction F(T). To simulate the use of the relationship between area-averaged rainrates and F(T) to obtain space-time averaged rainrates from a satellite sensor, observations from the NOAA/TOGA radar observations are used to estimate F(T) using a reflectivity threshold. The use of area-time integral methods for inferring area-averaged rainrates from satellites is examined, noting the possible use of the methodology for the Tropical Rainfall Measuring Mission.

Short, David A.↗
NASA NTRS1986

Sequential ranging integration times in the presence of CW interference in the ranging channel

The Deep Space Network (DSN), managed by the Jet Propulsion Laboratory for NASA, is used primarily for communication with interplanetary spacecraft. The high sensitivity required to achieve planetary communications makes the DSN very susceptible to radio-frequency interference (RFI). In this paper, an analytical model is presented of the performance degradation of the DSN sequential ranging subsystem in the presence of downlink CW interference in the ranging channel. A trade-off between the ranging component integration times and the ranging signal-to-noise ratio to achieve a desired level of range measurement accuracy and the probability of error in the code components is also presented. Numerical results presented illustrate the required trade-offs under various interference conditions.

Mathur, Ashok↗
NASA NTRS1997

Massively Parallel and Scalable Implicit Time Integration Algorithms for Structural Dynamics

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because of the following additional facts: (a) explicit schemes are easier to parallelize than implicit ones, and (b) explicit schemes induce short range interprocessor communications that are relatively inexpensive, while the factorization methods used in most implicit schemes induce long range interprocessor communications that often ruin the sought-after speed-up. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet be offset by the speed of the currently available parallel hardware. Therefore, it is essential to develop efficient alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient when simulating the low-frequency dynamics of aerospace structures.

Farhat, Charbel↗
NASA NTRS2001

Designing Adaptive Low-Dissipative High Order Schemes for Long-Time Integrations

A general framework for the design of adaptive low-dissipative high order schemes is presented. It encompasses a rather complete treatment of the numerical approach based on four integrated design criteria: (1) For stability considerations, condition the governing equations before the application of the appropriate numerical scheme whenever it is possible; (2) For consistency, compatible schemes that possess stability properties, including physical and numerical boundary condition treatments, similar to those of the discrete analogue of the continuum are preferred; (3) For the minimization of numerical dissipation contamination, efficient and adaptive numerical dissipation control to further improve nonlinear stability and accuracy should be used; and (4) For practical considerations, the numerical approach should be efficient and applicable to general geometries, and an efficient and reliable dynamic grid adaptation should be used if necessary. These design criteria are, in general, very useful to a wide spectrum of flow simulations. However, the demand on the overall numerical approach for nonlinear stability and accuracy is much more stringent for long-time integration of complex multiscale viscous shock/shear/turbulence/acoustics interactions and numerical combustion. Robust classical numerical methods for less complex flow physics are not suitable or practical for such applications. The present approach is designed expressly to address such flow problems, especially unsteady flows. The minimization of employing very fine grids to overcome the production of spurious numerical solutions and/or instability due to under-resolved grids is also sought. The incremental studies to illustrate the performance of the approach are summarized. Extensive testing and full implementation of the approach is forthcoming. The results shown so far are very encouraging.

Yee, Helen C.↗
NASA NTRS2005

Designing Adaptive Low-Dissipative High Order Schemes for Long-Time Integrations

A general framework for the design of adaptive low-dissipative high order schemes is presented. It encompasses a rather complete treatment of the numerical approach based on four integrated design criteria: (1) For stability considerations, condition the governing equations before the application of the appropriate numerical scheme whenever it is possible. (2) For consistency, compatible schemes that possess stability properties, including physical and numerical boundary condition treatments, similar to those of the discrete analogue of the continuum are preferred. (3) For the minimization of numerical dissipation contamination, efficient and adaptive numerical dissipation control to further improve nonlinear stability and accuracy should be used. (4) For practical considerations, the numerical approach should be efficient and applicable to general geometries, and an efficient and reliable dynamic grid adaptation should be used if necessary. These design criteria are, in general, very useful to a wide spectrum of flow simulations. However, the demand on the overall numerical approach for non-linear stability and accuracy is much more stringent for long-time integration of complex multiscale viscous shock/shear/turbulence/acoustics interactions and numerical combustion. Robust classical numerical methods for less complex flow physics are not suitable or practical for such applications. The present approach is designed expressly to address such flow problems, especially unsteady flows.

Yee, H. C.↗
NASA NTRS1983

Mixed time integration schemes for transient conduction forced-convection analysis

A partition procedure for forced-convection conduction transient problems is presented. Mixed time partitions are defined wherein coupled conduction force-matrix equations are discretized using an implicit integration method, followed by derivation of a mixed time integration technique. Explicit-implicit and explicit-explicit partitions are performed for a stability analysis for transient conditions, e.g., those found in an actively air-cooled engine and airframe structure.

Liu, W. K.↗
NASA NTRS1982

Formulation of an explicit-multiple-time-step time integration method for use in a global primitive equation grid model

With appropriate modifications, a recently proposed explicit-multiple-time-step scheme (EMTSS) is incorporated into the UCLA model. In this scheme, the linearized terms in the governing equations that generate the gravity waves are split into different vertical modes. Each mode is integrated with an optimal time step, and at periodic intervals these modes are recombined. The other terms are integrated with a time step dictated by the CFL condition for low-frequency waves. This large time step requires a special modification of the advective terms in the polar region to maintain stability. Test runs for 72 h show that EMTSS is a stable, efficient and accurate scheme.

Chao, W. C.↗
NASA NTRS1984

Overcoming time-integration errors in SINDA's FWDBCK solution routine

The FWDBCK time step, which is usually chosen intuitively to achieve adequate accuracy at reasonable computational costs, can in fact lead to large errors. NASA observed such errors in solving cryogenic problems on the COBE spacecraft, but a similar error is also demonstrated for a single node radiating to space. An algorithm has been developed for selecting the time step during the course of the simulation. The error incurred when the time derivative is replaced by the FWDBCK time difference can be estimated from the Taylor-Series expression for the temperature. The algorithm selects the time step to keep this error small. The efficacy of the method is demonstrated on the COBE and single-node problems.

Skladany, J. T.↗
NASA NTRS2002

Real-Time Integrity Monitoring of Stored Geo-Spatial Data Using Forward-Looking Remote Sensing Technology

Terrain Awareness and Warning Systems (TAWS) and Synthetic Vision Systems (SVS) provide pilots with displays of stored geo-spatial data (e.g. terrain, obstacles, and/or features). As comprehensive validation is impractical, these databases typically have no quantifiable level of integrity. This lack of a quantifiable integrity level is one of the constraints that has limited certification and operational approval of TAWS/SVS to "advisory-only" systems for civil aviation. Previous work demonstrated the feasibility of using a real-time monitor to bound database integrity by using downward-looking remote sensing technology (i.e. radar altimeters). This paper describes an extension of the integrity monitor concept to include a forward-looking sensor to cover additional classes of terrain database faults and to reduce the exposure time associated with integrity threats. An operational concept is presented that combines established feature extraction techniques with a statistical assessment of similarity measures between the sensed and stored features using principles from classical detection theory. Finally, an implementation is presented that uses existing commercial-off-the-shelf weather radar sensor technology.

Young, Steven D.↗
NASA NTRS1990

Climatologically tuned reflectivity-rain rate relations and links to area-time integrals

An effort is made to determine relationships between reflectivity (Z) and rain rate (R) which are tuned to the local climatology. The development of such relations was motivated by the need to understand the role of precipitation in controlling general circulation and in affecting such phenomena as ENSO. Attention is given to methods of deriving such relations and how they are linked to area integral rainfall measurements. In essence, the relation is tuned so that the probability distribution of reflectivity, P(Z), replicates that of R over some predetermined space-time climatic domain. Thus, the accurate measurement of the average R over any smaller domain depends on how closely the sampled P(Z) approximates the climatic P(Z). The probability matching method used is a modification of the approach of Calheiros and Zawadzki (1987) and Rosenfeld (1980). The technique is applied to data from Germany and the eastern tropical Atlantic (GATE).

Atlas, David↗
NASA NTRS1993

Direct time integration of Maxwell's equations in two-dimensional dielectric waveguides for propagation and scattering of femtosecond electromagnetic solitons

Solution of 2D vector nonlinear Maxwell's equations is described for material media with linear and nonlinear instantaneous and Lorentz dispersion effects in the electric polarization. Finite difference time domain method is used in the analysis. The method discussed here achieves robustness by enforcing vector-field boundary conditions at all interfaces of dissimilar media.

VECTOR FIELDS↗
NASA NTRS1976

Charge coupled device integration-time coding for detection of images moving with unknown velocities

Existing techniques for the detection of a moving low light level image by a CCD array have required velocity synchronism between the image and the photogenerated charges. This was necessary to prevent blurring during the long duration of charge integration. A new detection scheme is described which causes the image to be convolved with a clock modulation signal as the photocharges are collected. The charge accumulating from each image point will now be spread over many photoelements due to the absence of velocity synchronism, but the output is not blurred in the usual sense. Instead the charge is distributed through the array in a controlled way so that the image can be reconstructed.

White, J. M.↗
NASA NTRS1990

Explicit time integration of finite element models on a vectorized, concurrent computer with shared memory

The implementation of a nonlinear explicit program on a vectorized, concurrent computer with shared memory is described and studied. The conflict between vectorization and concurrency is described and some guidelines are given for optimal block sizes. Several example problems are summarized to illustrate the types of speed-ups which can be achieved by reprogramming as compared to compiler optimization.

Gilbertsen, Noreen D.↗