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NASA NTRS1999

Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms

This paper presents a final report on Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms. The focus of this research is to derive and implement: 1) Wavelet based methodologies for the compression, transmission, decoding, and visualization of three dimensional finite element geometry and simulation data in a network environment; 2) methodologies for interactive algorithm monitoring and tracking in computational mechanics; and 3) Methodologies for interactive algorithm steering for the acceleration of large scale finite element simulations. Also included in this report are appendices describing the derivation of wavelet based Particle Image Velocity algorithms and reduced order input-output models for nonlinear systems by utilizing wavelet approximations.

Kurdila, Andrew J.↗

DOE OSTI2019

Ab Initio Computation of Rotationally-Averaged Pump–Probe X-ray and Electron Diffraction Signals

We develop a new algorithm for the computation of the rotationally averaged elastic molecular diffraction signal for the cases of perpendicular or parallel pump–probe geometries. The algorithm first collocates the charge density from an arbitrary ab initio wave function onto a Becke quadrature grid [A. Becke, J. Chem. Phys. 1988, 88, 2457], providing a high-fidelity multiresolution representation of the charge density. A double sum is then performed over the Becke grid points, and the interaction between points computed using the scattering kernels of Williamson and Zewail [J. C. Williamson and A. H. Zewail, J. Phys. Chem. 1994, 98, 2766]. These kernels analytically average over the molecular orientations with the cos 2 γ selection factor appropriate for one-photon dipole absorption in a perpendicular pump–probe geometry. We demonstrate that the method is converged with small grids containing <500 points/atom. We implement the algorithm on a GPU for increased efficiency and emonstrate the algorithm for molecules with up to a few dozen atoms. We explore the accuracy of the independent atom model (IAM) by comparison with our new and more accurate method. We also investigate the possibility of detecting signatures of electronic transitions in polyatomic pump–probe diffraction experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1992

Cloud-property retrieval using merged HIRS and AVHRR data

A technique is developed that uses a multispectral, multiresolution method to improve the overall retrieval of mid- to high-level cloud properties by combining HIRS sounding channel data with higher spatial resolution AVHRR radiometric data collocated with the HIRS footprint. Cirrus cloud radiative and physical properties are determined using satellite data, surface-based measurements provided by rawinsondes and lidar, and aircraft-based lidar data collected during the First International Satellite Cloud Climatology Program Regional Experiment in Wisconsin during the months of October and November 1986. HIRS cloud-height retrievals are compared to ground-based lidar and aircraft lidar when possible. Retrieved cloud heights are found to have close agreement with lidar for thin cloud, but are higher than lidar for optically thick cloud. The results of the reflectance-emittance relationships derived are compared to theoretical scattering model results for both water-droplet spheres and randomly oriented hexagonal ice crystals. It is found that the assumption of 10-micron water droplets is inadequate to describe the reflectance-emittance relationship for the ice clouds seen here. Use of this assumption would lead to lower cloud heights using the ISCCP approach. The theoretical results show that use of hexagonal ice crystal phase functions could lead to much improved results for cloud retrieval algorithms using a bispectral approach.

Baum, Bryan A.↗

NASA NTRS1996

Multilevel Algorithm for Atmospheric Data Assimilation

A multiscale algorithm for the problem of optimal statistical interpolation of observed data has been developed. This problem includes the calculation of the vector of the 'analyzed' (best estimated) atmosphere flow field w(sup a) by the formula: w(sup a) = w(sup f) + P(sup f) H(sup T) y, where the quantity y is defined by the equation (H P(sup f) H(sup T) + R)y = w(sup o) - H w(sup f), using the given model forecast first guess w(sup f) and the vector of observations w(sup o); H is an interpolation operator from the regular grid to the observation network, P(sup f) is the forecast error covariance matrix, and R is the observation error covariance matrix. At this initial stage the case of univariate analysis of single level radiosonde height data is considered. The matrix R is assumed to be diagonal, and the matrix P(sup f) is assumed to be given by the formula P(sub ij)(sup f) = sigma(sub i)(sup f) mu(sub ij) sigma(sub j)(sub f), where mu(sub ij) is a smooth, decreasing function of the distance between the i-th and the j-th points. In this paper we describe a multiscale iterative process based on a multiresolution, simultaneous displacement technique and a localized variational calculation of iteration parameters.

Brandt, Achi↗

NASA NTRS1994

Multilevel cloud retrieval using multispectral HIRS and AVHRR data: Nighttime oceanic analysis

A multispectral, multiresolution (MSMR) method is developed for analyzing scenes of overlapping cloud layers. The MSMR method is applied to data from the NOAA 11 advanced very high resolution radiometer (AVHRR) and the high-resolution infrared radiometer sounder (HIRS-2). The data are from a nighttime oceanic scene in which a semitransparent cirrus veil overlays a large-scale stratus cloud. Low-cloud and clear-sky radiances are determined using a spatial coherence technique. Middle to upper level cloud pressures and radiances are estimated from HIRS-2 15 micrometer CO2 band radiometric data. The MSMR method improves the interpretation of a nighttime, oceanic scene containing thin cirrus over a large-scale stratiform cloud. If, for example, the same scene is analyzed using only the AVHRR 10.8 micrometer channel, the accompanying retrieved cloud heights are found to be between the cirrus and stratus cloud heights and are incorrectly identified as midlevel altostratus clouds. Theoretical radiative transfer model results for both water droplet spheres and randomly oriented hexagonal ice crystals are compared to observed AVHRR brightness temperature differences (BTD) between the 3.7- and 10.8 micrometer channels (BTD(sup 34)) and between the 10.8- and 12- micrometer channels (BTD(sup 45)) to distinguish among the effects of cloud optical depth, particle size, and phase for both single-layer clouds and overlapping two-layer clouds. Theoretical BTD calculations are used to estimate the range of effective particle sizes for eac h cloud layer. The data for the cirrus in the case study region near Bermuda are consistent with theoretical results for relatively small randomly oriented hexagonal ice crystals. The observed BTD(sup 34) and BTD(sup 45) values are lower for the cirrus above a lower-level cloud than for single-level cirrus with no underlying cloud. In certain cases the BTD analysis provides a way to distinguish between clouds composed of supercooled water droplets rather than ice particles. Analysis of nighttime data permits determination of stratus infrared optical depths smaller than 4.

Baum, Bryan A.↗

NASA NTRS1997

Advanced Signal Processing Methods Applied to Digital Mammography

The work reported here is on the extension of the earlier proposal of the same title, August 1994-June 1996. The report for that work is also being submitted. The work reported there forms the foundation for this work from January 1997 to September 1997. After the earlier work was completed there were a few items that needed to be completed prior to submission of a new and more comprehensive proposal for further research. Those tasks have been completed and two new proposals have been submitted, one to NASA, and one to Health & Human Services WS). The main purpose of this extension was to refine some of the techniques that lead to automatic large scale evaluation of full mammograms. Progress on each of the proposed tasks follows. Task 1: A multiresolution segmentation of background from breast has been developed and tested. The method is based on the different noise characteristics of the two different fields. The breast field has more power in the lower octaves and the off-breast field behaves similar to a wideband process, where more power is in the high frequency octaves. After the two fields are separated by lowpass filtering, a region labeling routine is used to find the largest contiguous region, the breast. Task 2: A wavelet expansion that can decompose the image without zero padding has been developed. The method preserves all properties of the power-of-two wavelet transform and does not add appreciably to computation time or storage. This work is essential for analysis of the full mammogram, as opposed to selecting sections from the full mammogram. Task 3: A clustering method has been developed based on a simple counting mechanism. No ROC analysis has been performed (and was not proposed), so we cannot finally evaluate this work without further support. Task 4: Further testing of the filter reveals that different wavelet bases do yield slightly different qualitative results. We cannot provide quantitative conclusions about this for all possible bases without further support. Task 5: Better modeling does indeed make an improvement in the detection output. After the proposal ended, we came up with some new theoretical explanations that helps in understanding when the D4 filter should be better. This work is currently in the review process. Task 6: N/A. This no longer applies in view of Tasks 4-5. Task 7: Comprehensive plans for further work have been completed. These plans are the subject of two proposals, one to NASA and one to HHS. These proposals represent plans for a complete evaluation of the methods for identifying normal mammograms, augmented with significant further theoretical work.

Stauduhar, Richard P.↗

NASA NTRS2003

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, I: Basic Theory

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls t o limit the amount of and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids. The four advantages of the present approach over existing MHD schemes reported in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion MHD flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike exist- ing schemes for the conservative MHD equations which suffer from ill-conditioned eigen- decompositions, the present scheme makes use of a well-conditioned eigen-decomposition obtained from a minor modification of the eigenvectors of the non-conservative MHD equations t o solve the conservative form of the MHD equations. Third, this approach of using the non-conservative eigensystem when solving the conservative equations also works well in the context of standard shock-capturing schemes for the MHD equations. Fourth, a new approach to minimize the numerical error of the divergence-free magnetic condition for high order schemes is introduced. Numerical experiments with typical MHD model problems revealed the applicability of the newly developed schemes for the MHD equations.

Sjoegreen, Bjoern↗

NASA NTRS1996

Computerized mappings of the cerebral cortex: a multiresolution flattening method and a surface-based coordinate system

We present a new method for generating two-dimensional maps of the cerebral cortex. Our computerized, two-stage flattening method takes as its input any well-defined representation of a surface within the three-dimensional cortex. The first stage rapidly converts this surface to a topologically correct two-dimensional map, without regard for the amount of distortion introduced. The second stage reduces distortions using a multiresolution strategy that makes gross shape changes on a coarsely sampled map and further shape refinements on progressively finer resolution maps. We demonstrate the utility of this approach by creating flat maps of the entire cerebral cortex in the macaque monkey and by displaying various types of experimental data on such maps. We also introduce a surface-based coordinate system that has advantages over conventional stereotaxic coordinates and is relevant to studies of cortical organization in humans as well as non-human primates. Together, these methods provide an improved basis for quantitative studies of individual variability in cortical organization.

Non-NASA Center↗