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All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Issues and Methods Concerning the Evaluation of Hypersingular and Near-Hypersingular Integrals in BEM Formulations

It is known that higher order modeling of the sources and the geometry in Boundary Element Modeling (BEM) formulations is essential to highly efficient computational electromagnetics. However, in order to achieve the benefits of hIgher order basis and geometry modeling, the singular and near-singular terms arising in BEM formulations must be integrated accurately. In particular, the accurate integration of near-singular terms, which occur when observation points are near but not on source regions of the scattering object, has been considered one of the remaining limitations on the computational efficiency of integral equation methods. The method of singularity subtraction has been used extensively for the evaluation of singular and near-singular terms. Piecewise integration of the source terms in this manner, while manageable for bases of constant and linear orders, becomes unwieldy and prone to error for bases of higher order. Furthermore, we find that the singularity subtraction method is not conducive to object-oriented programming practices, particularly in the context of multiple operators. To extend the capabilities, accuracy, and maintainability of general-purpose codes, the subtraction method is being replaced in favor of the purely numerical quadrature schemes. These schemes employ singularity cancellation methods in which a change of variables is chosen such that the Jacobian of the transformation cancels the singularity. An example of the sin,oularity cancellation approach is the Duffy method, which has two major drawbacks: 1) In the resulting integrand, it produces an angular variation about the singular point that becomes nearly-singular for observation points close to an edge of the parent element, and 2) it appears not to work well when applied to nearly-singular integrals. Recently, the authors have introduced the transformation u(x(prime))= sinh (exp -1) x(prime)/Square root of ((y prime (exp 2))+ z(exp 2) for integrating functions of the form I = Integral of (lambda(r(prime))((e(exp -jkR))/(4 pi R) d D where A (r (prime)) is a vector or scalar basis function and R = Square root of( (x(prime)(exp2) + (y(prime)(exp2) + z(exp 2)) is the distance between source and observation points. This scheme has all of the advantages of the Duffy method while avoiding the disadvantages listed above. In this presentation we will survey similar approaches for handling singular and near-singular terms for kernels with 1/R(exp 2) type behavior, addressing potential pitfalls and offering techniques to efficiently handle special cases.

Fink, P. W.↗
NASA NTRS1991

Development of iterative techniques for the solution of unsteady compressible viscous flows

Efficient iterative solution methods are being developed for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. Thus, the extra work required by iterative schemes can also be designed to perform efficiently on current and future generation scalable, missively parallel machines. An obvious candidate for iteratively solving the system of coupled nonlinear algebraic equations arising in CFD applications is the Newton method. Newton's method was implemented in existing finite difference and finite volume methods. Depending on the complexity of the problem, the number of Newton iterations needed per step to solve the discretized system of equations can, however, vary dramatically from a few to several hundred. Another popular approach based on the classical conjugate gradient method, known as the GMRES (Generalized Minimum Residual) algorithm is investigated. The GMRES algorithm was used in the past by a number of researchers for solving steady viscous and inviscid flow problems with considerable success. Here, the suitability of this algorithm is investigated for solving the system of nonlinear equations that arise in unsteady Navier-Stokes solvers at each time step. Unlike the Newton method which attempts to drive the error in the solution at each and every node down to zero, the GMRES algorithm only seeks to minimize the L2 norm of the error. In the GMRES algorithm the changes in the flow properties from one time step to the next are assumed to be the sum of a set of orthogonal vectors. By choosing the number of vectors to a reasonably small value N (between 5 and 20) the work required for advancing the solution from one time step to the next may be kept to (N+1) times that of a noniterative scheme. Many of the operations required by the GMRES algorithm such as matrix-vector multiplies, matrix additions and subtractions can all be vectorized and parallelized efficiently.

Sankar, Lakshmi N.↗
NASA NTRS2004

A Study of the Non-Thermal X-ray Emission of Shell-Type Supernova Remnants

The term of the forth year of the award is the period from March 15, 2003 to March 14, 2004. During this year, Dr. Thomas Pannuti, who had been performing most of the analyses, made a transition to a new position at Caltech. As of September 2003, Dr. Michael Stage began performing most of the analyses. Dr. Stage has begun constructing a detailed catalog of the spatial and spectral properties of young supernova remnants as described in sections 1 and 4 of the proposal. Specifically, he has focused on the analysis of Chandra ACIS data. The exquisite spatial resolution of the Chandra telescope and the modest spectral resolution of the CCDs make these data ideal. Dr. Stage has developed a standard set of procedures to reduce the data, generate telescope and detector response libraries and handle instrumental and celestial background subtraction. He has also adapted some existing code to automate spectral extraction and fitting. This code enables us to analyze the spectra of tens of thousands of small subregions of supernova remnants. Dr. Stage has recently applied this process to ACIS data for the supernova remnants Cas A and Kepler. The results include maps of the fitted parameters, such as individual line intensities and centroids (i.e. Doppler shifts), the electron temperature, and the absorption column density. These maps are more accurate than simple energy-cut images because it is difficult (and sometimes impossible) to cleanly separate the line emission from the underlying continuum (especially at low energies). It is now possible to identify the locations at which emission from each element is produced. Some of the elements are seen to be layered. The electron temperature maps demonstrate that the outer edges of Cas A and Kepler are very hot with weak lines. This emission is almost certainly synchrotron dominated. Therefore, not only are the maps interesting in and of themselves, but they also provide an unbiased means of easily identifying features in the remnants that can be studied in more detail using, for example, synchrotron models. Over the next year, Dr. Stage will refine the analysis procedures, expand the analyses to include several other remnants, present the results at major scientific conferences and publish a catalog of the results. Since this work is producing impressive results, we have applied for very long Chandra observations of Kepler and Tycho to obtain enough counts to take lull advantage of the technique. A i Ms observation of Cas A is already scheduled. Over the past year, I completed a joint, spectra,l analysis of some X-ray, radio, and gamma-ray data for the supernova remnant SN 1006. The results of this analysis show that the synchrotron and, hence, electron spectrum of the remnant is curved. The amount of curvature in the electron spectrum is quantitatively consistent with predictions of the amount of curvature in the proton spectrum of the remnant. A paper describing this work is nearly complete. When Dr. Pannuti left, he was analyzing X-ray data for the young supernova remnant G266.2-1.2. Dr. Pannuti found the first evidence of thermal X-ray emission from this remnant. Furthermore, like SN 1006, the cutoff frequency varies with azimuth along the bright northeastern rim. This work will be published during the coming year.

Allen, Glenn E.↗
NASA NTRS2016

A Statistical Method for Reducing Sidelobe Clutter for the Ku-Band Precipitation Radar on Board the GPM Core Observatory

A statistical method to reduce the sidelobe clutter of the Ku-band precipitation radar (KuPR) of the Dual-Frequency Precipitation Radar (DPR) on board the Global Precipitation Measurement (GPM) Core Observatory is described and evaluated using DPR observations. The KuPR sidelobe clutter was much more severe than that of the Precipitation Radar on board the Tropical Rainfall Measuring Mission (TRMM), and it has caused the misidentification of precipitation. The statistical method to reduce sidelobe clutter was constructed by subtracting the estimated sidelobe power, based upon a multiple regression model with explanatory variables of the normalized radar cross section (NRCS) of surface, from the received power of the echo. The saturation of the NRCS at near-nadir angles, resulting from strong surface scattering, was considered in the calculation of the regression coefficients.The method was implemented in the KuPR algorithm and applied to KuPR-observed data. It was found that the received power from sidelobe clutter over the ocean was largely reduced by using the developed method, although some of the received power from the sidelobe clutter still remained. From the statistical results of the evaluations, it was shown that the number of KuPR precipitation events in the clutter region, after the method was applied, was comparable to that in the clutter-free region. This confirms the reasonable performance of the method in removing sidelobe clutter. For further improving the effectiveness of the method, it is necessary to improve the consideration of the NRCS saturation, which will be explored in future work.

Atm/Ocean Structure/ Phenomena; Precipitation; Obs↗
NASA NTRSDate not supplied

In-Lab Rapid Analytical Detection of Lunar Volatiles By Universal Gas Analyzer With Comparison to GC-MS System

Introduction: The curation of permanently shadowed regions (PSRs) [1] on the lunar surface is centered around studies based upon the observed volatiles from the LCROSS mission [2]. The rapid detection of important volatile gases and vapors present in planetary bodies and Astromaterials by a standalone analytical device is an area of intense research interest in our group and Planetary Exploration & Astromaterials Research Laboratory (PEARL) facility and this work is relevant to the future preparation of viable lunar simulants for testing curation efforts down the road. The groundbreaking results obtained from the LCROSS Mission [2] open the requirements for the direct detection of volatiles present in regolith materials collected from the lunar surface. The mass spectrometry of volatile chemicals is a general technique that utilizes a set of instruments that creates charged ions from a gaseous chemical species and measures the intensities vs. mass-to-charge ratio (m/z) [3]. In this context, we discuss in-lab experimental results and procedures for rapid qualitative analysis of main LCROSS volatiles (water, H2S, NH3, CO2, and CH3OH) by a Universal Gas Analyzer (UGA) instrument. Additionally, the instrument performance was evaluated by measuring the isotopic abundance ratio of atmospheric Ar-40 to Ar-36 present in room air since, argon is a relevant gas in planetary studies as it can provide an insight and reference point to isotope studies [4]. Additional, cross comparisons were attempted and made between the two instruments to develop a robust analytical technique by comparing mass spectral data for H2S headspace samples with a Trace-1310/ ISQ 7000 (ThermoFisher Scientific.) GC-MS system. Background: The benchtop UGA System is equipped with an SRS UGA 300 quadrupole mass spectrometer designed and built by Stanford Research Systems [5]. This system can be configured for several types of gaseous chemical analysis. The inlet line continuously samples gases at low flow rates (several milliliters per minute) through a capillary limiting the intake pressure making the instrument ideal for online analysis of select gases and/or room atmosphere. Moreover, in our current UGA system, a change in composition at the inlet can be detected in about 200 milliseconds and a complete spectrum is acquired (for a range of 1-100 amu) in under 45 sec with masses measured at rates up to 25 msec per point [5]. This system provides a quick upstream analytical data that we can then compare to results obtained by our GC-MS system. Sample Preparation: Small volume (2-4 mL) of analyte sample was taken in a 10 mL glass vial and sealed with a crimped cap and purged with pure Ar or N2 gas to displace air from the top. The headspace sample was scanned by the UGA instrument at analog, histogram, and pressure vs. time modes. The isotopic abundance ratio for 40Ar-to-36Ar was estimated by measuring partial pressure vs. time scans and setting the mass at 40 and 36 respectively. Results and Discussions: In this work, we have investigated the applicability of the UGA system by qualitative analysis of a series of LCROSS volatiles measured individually. Fig. 1 demonstrates a set of vertically offset spectra for the partial pressures measured as a function of mass-to-charge (m/z) ratios. The average acquisition time for each spectrum was less than a minute suggesting that the UGA system is ideal for quick analysis of geochemical volatiles. For the cross-comparison, we analyzed an H2S headspace sample by a Trace-1310/ISQ-7000 system and compared mass spectral data with previously measured UGA histogram scan data (Fig. 2). In both cases, major peak positions are the same, however, the intensities of fragment ions ([1H132S]+ and [32S]+) are higher for UGA suggesting that the fragment ionization process is stronger in UGA compared to that of GC-MS. To investigate how the integrated area under each chromatogram varies with the headspace sample volume, a set of five H2S headspace samples with increasing volumes was analyzed by the GC-MS system (Fig. 3, inset). A small volume (e.g., 200 to 1000 µL) of H2S/H2O vapor was withdrawn from a 20 mL stock sample vial containing ~5 mL of 0.4% H2S in water by a gas-tight syringe and added to another 20 mL vial filled with argon and analyzed by the GC-MS system. Finally, the UGA detector sensitivity was evaluated by calculating the atmospheric 40Ar-to-36Ar isotopic abundance ratio in room air by running a partial pressure vs. time scan with setting the atomic mass at 40, and 36. Fig. 4(a) shows a ~25 min duration “P vs. time” scan for 40Ar (plot for 36Ar is not shown). The partial pressure values (~100 points) were corrected by subtracting the corresponding background pressure value for 37Ar and utilized to calculate 40Ar-to-36Ar isotopic abundance ratios as shown by Fig. 4b. The average isotopic abundance ratio is ~306 with a 2*STDEV ~13. This abundance ratio is significantly close to the previously reported value of 298.56 [6] and the ratio obtained by our GC-MS system (303 for a UHP grade Ar sample). Conclusions: Our study strongly evidenced that the benchtop UGA system is a valuable analytical tool for the detection of major LCROSS volatiles. The rapid scanning capability, the inexpensiveness of the whole system, and impressive detection sensitivity prove its worthiness as an essential device for advanced geochemical applications. Moreover, cross comparisons with the GC-MS provide important bridges into advanced curatorial efforts into the future. References: [1] Bickel, V.T., et al. (2021) Nat Commun 12, 5607. [2] Colaprete, A., et al. (2010) Science, 330, 463-468. [3] Glavin, D. P. et al. (2012) 2012 IEEE Aerospace Conference, 1-11. [4] Willett, C. D., et al. (2022) Geochimica et Cosmochimica Acta 329, 119-134. [5] Operation Manual and Programming Reference. (2018) Universal gas Analyzers, Stanford Research Systems. [6] Lee, J. Y., et al. (2006) Geochimica et Cosmochimica Acta 70, 4507–4512. Notes: (4 figures are attached with text as shown by the attached file)

Curation↗