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All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

A posteriori error indicators for the p-version of the finite element method

The existence of local a posteriori error indicators for the p-version of the finite element method is demonstrated through numerical examples. It is shown that it is possible to construct reliable error indicators from the residuums and tractions which have the same rate of convergence as the strain energy. The error indicators contribution of an element can be estimated by considering only the element and its immediate neighbors. The optimal sequence of p-distributions can be closely followed by the indicators even when there are only a very few elements, the elements vary greatly in size, the polynomial orders vary, the mesh grading is poor, and the smoothness indices and relative errors vary between wide limits.

Dunavant, D. A.↗
NASA NTRS1988

Error indicators and accuracy improvements of finite element solutions

Practical and reliable estimators of the discretization errors in engineering problems are developed. Error indicators for identifying the regions or elements of the solution domain which are likely to have the largest discretization errors are presented, and a simple computational procedure for improving the accuracy of the finite element solutions for shell problems is given. The similarities between the proposed procedure and a preconditioned conjugate gradient (PCG) technique are identified and exploited to generate pointwise error indicators from the PCG technique. Numerical examples in the linear static analysis of shells are presented.

Noor, Ahmed K.↗
NASA NTRS1993

Implementation of a mesh adaptive scheme based on an element-level error indicator

We investigate the formulation and application of element-level error indicators based on parametrized variational principles. The qualifier 'element-level' means that no information from adjacent elements is used for error estimation. This property is ideally suited to drive adaptive mesh refinement on parallel computers where access to neighboring elements resident on different processors may incur significant computational overhead. Furthermore, such indicators are not affected by physical jumps at junctures or interfaces. An element-level indicator has been derived from the higher-order element energy and applied to r and h mesh adaptation of meshes in plates and shell structures. We report on our initial experiments with a cylindrical shell that intersects with fist plates forming a simplified 'wing-body intersection' benchmark problem.

Keating, Scott↗
NASA NTRS1992

r-adaptive methods based on element-level error indicators for parallel analysis of plates and shells

The formulation and application of element-level error indicators based on parametrized variational principles are investigated. These indicators are ideally suited to drive adaptive mesh refinment on parallel computers where access to neighboring elements resident on different processors may incur significant computational overhead. Furthermore, such estimators are not affected by physical jumps at wavefronts or interfaces. An estimator derived from the higher-order element energy is applied to r adaptation of meshes in plates and shell structures where the exact solution is known.

Militello, Carmelo↗
NASA NTRS1993

Unstructured adaptive mesh computations of rotorcraft high-speed impulsive noise

A new method is developed for modeling helicopter high-speed impulsive (HSI) noise. The aerodynamics and acoustics near the rotor blade tip are computed by solving the Euler equations on an unstructured grid. A stationary Kirchhoff surface integral is then used to propagate these acoustic signals to the far field. The near-field Euler solver uses a solution-adaptive grid scheme to improve the resolution of the acoustic signal. Grid points are locally added and/or deleted from the mesh at each adaptive step. An important part of this procedure is the choice of an appropriate error indicator. The error indicator is computed from the flow field solution and determines the regions for mesh coarsening and refinement. Computed results for HSI noise compare favorably with experimental data for three different hovering rotor cases.

Strawn, Roger↗
NASA NTRS1994

Error estimation and adaptive mesh refinement for parallel analysis of shell structures

The formulation and application of element-level, element-independent error indicators is investigated. This research culminates in the development of an error indicator formulation which is derived based on the projection of element deformation onto the intrinsic element displacement modes. The qualifier 'element-level' means that no information from adjacent elements is used for error estimation. This property is ideally suited for obtaining error values and driving adaptive mesh refinements on parallel computers where access to neighboring elements residing on different processors may incur significant overhead. In addition such estimators are insensitive to the presence of physical interfaces and junctures. An error indicator qualifies as 'element-independent' when only visible quantities such as element stiffness and nodal displacements are used to quantify error. Error evaluation at the element level and element independence for the error indicator are highly desired properties for computing error in production-level finite element codes. Four element-level error indicators have been constructed. Two of the indicators are based on variational formulation of the element stiffness and are element-dependent. Their derivations are retained for developmental purposes. The second two indicators mimic and exceed the first two in performance but require no special formulation of the element stiffness mesh refinement which we demonstrate for two dimensional plane stress problems. The parallelizing of substructures and adaptive mesh refinement is discussed and the final error indicator using two-dimensional plane-stress and three-dimensional shell problems is demonstrated.

Keating, Scott C.↗
NASA NTRS2002

Finite Element A Posteriori Error Estimation for Heat Conduction

This research investigates residual-based a posteriori error estimates for finite element approximations of heat conduction in single-layer and multi-layered materials. The finite element approximation, based upon hierarchical modelling combined with p-version finite elements, is described with specific application to a two-dimensional, steady state, heat-conduction problem. Element error indicators are determined by solving an element equation for the error with the element residual as a source, and a global error estimate in the energy norm is computed by collecting the element contributions. Numerical results of the performance of the error estimate are presented by comparisons to the actual error. Two methods are discussed and compared for approximating the element boundary flux. The equilibrated flux method provides more accurate results for estimating the error than the average flux method. The error estimation is applied to multi-layered materials with a modification to the equilibrated flux method to approximate the discontinuous flux along a boundary at the material interfaces. A directional error indicator is developed which distinguishes between the hierarchical modeling error and the finite element error. Numerical results are presented for single-layered materials which show that the directional indicators accurately determine which contribution to the total error dominates.

Lang, Christapher G.↗
NASA NTRS1978

System for and method of freezing biological tissue

Biological tissue is frozen while a polyethylene bag placed in abutting relationship against opposed walls of a pair of heaters. The bag and tissue are cooled with refrigerating gas at a time programmed rate at least equal to the maximum cooling rate needed at any time during the freezing process. The temperature of the bag, and hence of the tissue, is compared with a time programmed desired value for the tissue temperature to derive an error indication. The heater is activated in response to the error indication so that the temperature of the tissue follows the desired value for the time programmed tissue temperature. The tissue is heated to compensate for excessive cooling of the tissue as a result of the cooling by the refrigerating gas. In response to the error signal, the heater is deactivated while the latent heat of fusion is being removed from the tissue while the tissue is changing phase from liquid to solid.

Williams, T. E.↗
NASA NTRS1992

Remote sensing of surface hemispherical reflectance (albedo) using pointable multispectral imaging spectroradiometers

Remote techniques for determining albedo are examined in terms of the range of view angles required in the use of string techniques with the Moderate Resolution Imaging Spectroradiometer (MODIS) and the High Resolution Imaging Spectroradiometer (HIRIS). Ground data are used to compute full and half strings out to 15, 30, 45, and 60 degrees for various sun angles and ground cover types. A knowledge-based system is employed to evaluate both the visible and near-IR bands, and the results indicate errors of up to 7 percent for the MODIS data, HIRIS data, and the full-string +/- 60 degrees. In the cases of large extrapolations greater ranges of error are noted indicating that 60-deg systems are most effective. The error is increased in the case of sensor systems that only view in the fore or aft direction, and the MODIS full string for +/- 45 deg is also considered a good system.

Kimes, D. S.↗
NASA NTRS1992

The global structure of the annual and semiannual sea surface height variability from Geosat altimeter data

Two years of data from the Geosat Exact Repeat Mission are employed to study the annual and semiannual variability of sea-surface height on a global basis. The data are treated with atmospheric corrections and interpolations, and the orbit error of about 40 cm RMS is purged. The spatial variability of the Geosat data is constructed for particular frequencies, and the estimate of the M2 tidal error indicates that the error is aliased to 1.15 cycles/yr and has an unusual spatial pattern. Sine and cosine coefficients are derived for the annual and semiannual frequencies by means of a least squares fit yielding the amplitude and phase of the changes in sea-surface height. A 180-deg phase difference is noted between the Northern and Southern Hemispheres for the annual variability, and large-scale westward propagating waves are identified. The Geosat data also indicate the phase relationships between major current systems and the systems of variations at work in the Intertropical Convergence Zone.

Jacobs, Gregg A.↗
NASA NTRS1986

Description of data on the Nimbus 7 LIMS map archive tape: Ozone and nitric acid

The Nimbus 7 Limb Infrared Monitor of the Stratosphere (LIMS) data set has been processed into a Fourier coefficient representation with a Kalman filter algorithm applied to profile data at individual latitudes and pressure levels. The algorithm produces synoptic data at noon Greenwich Mean Time (GMT) from the asynoptic orbital profiles. This form of the data set is easy to use and is appropriate for time series analysis and further data manipulation and display. Ozone and nitric acid results are grouped together in this report because the LIMS vertical field of views (FOV's) and analysis characteristics for these species are similar. A comparison of the orbital input data with mixing ratios derived from Kalman filter coefficients indicates errors in mixing ratio of generally less than 5 percent, with 15 percent being a maximum error. The high quality of the mapped data was indicated by coherence of both the phases and the amplitudes of waves with latitude and pressure. Examples of the mapped fields are presented, and details are given concerning the importance of diurnal variations, the removal of polar stratospheric cloud signatures, and the interpretation of bias effects in the data near the tops of profiles.

Remsberg, E. E.↗
NASA NTRS1999

Backus Effect on a Perpendicular Errors in Harmonic Models of Real vs. Synthetic Data

Measurements of geomagnetic scalar intensity on a thin spherical shell alone are not enough to separate internal from external source fields; moreover, such scalar data are not enough for accurate modeling of the vector field from internal sources because of unmodeled fields and small data errors. Spherical harmonic models of the geomagnetic potential fitted to scalar data alone therefore suffer from well-understood Backus effect and perpendicular errors. Curiously, errors in some models of simulated 'data' are very much less than those in models of real data. We analyze select Magsat vector and scalar measurements separately to illustrate Backus effect and perpendicular errors in models of real scalar data. By using a model to synthesize 'data' at the observation points, and by adding various types of 'noise', we illustrate such errors in models of synthetic 'data'. Perpendicular errors prove quite sensitive to the maximum degree in the spherical harmonic expansion of the potential field model fitted to the scalar data. Small errors in models of synthetic 'data' are found to be an artifact of matched truncation levels. For example, consider scalar synthetic 'data' computed from a degree 14 model. A degree 14 model fitted to such synthetic 'data' yields negligible error, but amplifies 4 nT (rmss) added noise into a 60 nT error (rmss); however, a degree 12 model fitted to the noisy 'data' suffers a 492 nT error (rmms through degree 12). Geomagnetic measurements remain unaware of model truncation, so the small errors indicated by some simulations cannot be realized in practice. Errors in models fitted to scalar data alone approach 1000 nT (rmss) and several thousand nT (maximum).

Voorhies, C. V.↗
NASA NTRS1984

Evaluation of a native vegetation masking technique

A crop masking technique based on Ashburn's vegetative index (AVI) was used to evaluate native vegetation as an indicator of crop moisture condition. A mask of the range areas (native vegetation) was generated for each of thirteen Great Plains LANDSAT MSS sample segments. These masks were compared to the digitized ground truth and accuracies were computed. An analysis of the types of errors indicates a consistency in errors among the segments. The mask represents a simple quick-look technique for evaluating vegetative cover.

Kinsler, M. C.↗
NASA NTRS1985

Test and evaluation of the 2.4-micron photorefractor ocular screening system

An improved 2.4-m photorefractor ocular screening system was tested and evaluated. The photorefractor system works on the principal of obtaining a colored photograph of both human eyes; and, by analysis of the retinal reflex images, certain ocular defects can be detected such a refractive error, strabismus, and lens obstructions. The 2.4-m photorefractory system uses a 35-mm camera with a telephoto lens and an electronic flash attachment. Retinal reflex images obtained from the new 2.4-m system are significantly improved over earlier systems in image quality. Other features were also improved, notably portability and reduction in mass. A total of 706 school age children were photorefracted, 211 learning disabled and 495 middle school students. The total students having abnormal retinal reflexes were 156 or 22 percent, and 133 or 85 percent of the abnormal had refractive error indicated. Ophthalmological examination was performed on 60 of these students and refractive error was verified in 57 or 95 percent of those examined. The new 2.4-m system has a NASA patent pending and is authorized by the FDA. It provides a reliable means of rapidly screening the eyes of children and young adults for vision problems. It is especially useful for infants and other non-communicative children who cannot be screened by the more conventional methods such as the familiar E chart.

Richardson, J. R.↗
NASA NTRS2003

Evaluation of Trajectory Errors in an Automated Terminal-Area Environment

A piloted simulation experiment was conducted to document the trajectory errors associated with use of an airplane's Flight Management System (FMS) in conjunction with a ground-based ATC automation system, Center-TRACON Automation System (CTAS) in the terminal area. Three different arrival procedures were compared: current-day (vectors from ATC), modified (current-day with minor updates), and data link with FMS lateral navigation. Six active airline pilots flew simulated arrivals in a fixed-base simulator. The FMS-datalink procedure resulted in the smallest time and path distance errors, indicating that use of this procedure could reduce the CTAS arrival-time prediction error by about half over the current-day procedure. Significant sources of error contributing to the arrival-time error were crosstrack errors and early speed reduction in the last 2-4 miles before the final approach fix. Pilot comments were all very positive, indicating the FMS-datalink procedure was easy to understand and use, and the increased head-down time and workload did not detract from the benefit. Issues that need to be resolved before this method of operation would be ready for commercial use include development of procedures acceptable to controllers, better speed conformance monitoring, and FMS database procedures to support the approach transitions.

Oseguera-Lohr, Rosa M.↗
NASA NTRS1979

Sensitivity of Forecast Skill to Different Objective Analysis Schemes

Numerical weather forecasts are characterized by rapidly declining skill in the first 48 to 72 h. Recent estimates of the sources of forecast error indicate that the inaccurate specification of the initial conditions contributes substantially to this error. The sensitivity of the forecast skill to the initial conditions is examined by comparing a set of real-data experiments whose initial data were obtained with two different analysis schemes. Results are presented to emphasize the importance of the objective analysis techniques used in the assimilation of observational data.

Baker, W. E.↗