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At least 37 records · Page 2

Airborne flux measurements of ammonia over the southern Great Plains using chemical ionization mass spectrometry

Abstract. Ammonia (NH3) is an abundant trace gas in the atmosphere and an important player in atmospheric chemistry, aerosol formation and the atmosphere–surface exchange of nitrogen. The accurate determination of NH3 emission rates remains a challenge, partly due to the propensity of NH3 to interact with instrument surfaces, leading to high detection limits and slow response times. In this paper, we present a new method for quantifying ambient NH3, using chemical ionization mass spectrometry (CIMS) with deuterated benzene cations as reagents. The setup aimed at limiting sample–surface interactions and achieved a 1σ precision of 10–20 pptv and an immediate 1/e response rate of < 0.4 s, which compares favorably to the existing state of the art. The sensitivity exhibited an inverse humidity dependence, in particular in relatively dry conditions. Background of up to 10 % of the total signal required consideration as well, as it responded on the order of a few minutes. To showcase the method's capabilities, we quantified NH3 mixing ratios from measurements obtained during deployment on a Gulfstream I aircraft during the HI-SCALE (Holistic Interactions of Shallow Clouds, Aerosols, and Land-Ecosystems) field campaign in rural Oklahoma during May 2016. Typical mixing ratios were 1–10 parts per billion by volume (ppbv) for the boundary layer and 0.1–1 ppbv in the lower free troposphere. Sharp plumes of up to tens of ppbv of NH3 were encountered as well. We identified two of their sources as a large fertilizer plant and a cattle farm, and our mixing ratio measurements yielded upper bounds of 350 ± 50 and 0.6 kg NH3 h−1 for their respective momentary source rates. The fast response of the CIMS also allowed us to derive vertical NH3 fluxes within the turbulent boundary layer via eddy covariance, for which we chiefly used the continuous wavelet transform technique. As expected for a region dominated by agriculture, we observed predominantly upward fluxes, implying net NH3 emissions from the surface. The corresponding analysis focused on the most suitable flight, which contained two straight-and-level legs at ∼ 300 m above ground. We derived NH3 fluxes between 1 and 11 mol km−2 h−1 for these legs, at an effective spatial resolution of 1–2 km. The analysis demonstrated how flux measurements benefit from suitably arranged flight tracks with sufficiently long straight-and-level legs, and it explores the detrimental effect of measurement discontinuities. Following flux footprint estimations, comparison to the NH3 area emissions inventory provided by the U.S. Environmental Protection Agency indicated overall agreement but also the absence of some sources, for instance the identified cattle farm. Our study concludes that high-precision CIMS measurements are a powerful tool for in situ measurements of ambient NH3 mixing ratios, and even allow for the airborne mapping of the air–surface exchange of NH3.

58 GEOSCIENCES↗

Airborne flux measurements of ammonia over the Southern Great Plains using chemical ionization mass spectrometry

Ammonia (NH 3 ) is an abundant trace gas in the atmosphere and an important player in atmospheric chemistry, aerosol formation and the atmosphere-surface exchange of nitrogen. It is recognized as a major source of aerosol pollution, and it may limit the formation of cloud nuclei in remote or cold parts of the atmosphere. For soil and plants, NH 3 -mediated nitrogen can act as a harmful pollutant or as a desirable nutrient, mostly in natural and agricultural settings, respectively. Agriculture is also the main source of atmospheric NH 3 via volatilization from fertilizers and manure processing in livestock farming. The accurate determination of NH 3 emission rates remains a challenge, partly due to the propensity of NH 3 to interact with instrument surfaces leading to high detection limits and slow response times. In this paper, we present a new method for quantifying ambient NH 3 , using chemical ionization mass spectrometry (CIMS) with deuterated benzene cations as reagents. The setup aimed at limiting sample-surface interactions and achieved a 1-σ precision of 10–20 pptv and an immediate 1/e response rate < 0.4 s, which compares favorably to the existing state of the art. The sensitivity exhibited an inverse humidity dependence, in particular in relatively dry conditions. Background of up to 10 % of the total signal required consideration as well, as it responded on the order of a few minutes. To showcase the method’s capabilities, we quantified NH3 mixing ratios from measurements obtained during deployment on a Gulfstream I aircraft during the HI-SCALE (Holistic Interactions of Shallow Clouds, Aerosols and Land Ecosystems) field campaign in rural Oklahoma during May 2016. Typical mixing ratios were 1–10 parts per billion by volume (ppbv) for the boundary layer and 0.1–1 ppbv in the lower free troposphere. Sharp plumes of up to 10s of ppbv of NH3 were encountered as well. We identified two of their sources as a large fertilizer plant and a cattle farm, and our mixing ratio measurements yielded upper bounds of 350 ± 50 and 0.6 kg NH 3 h –1 for their respective momentary source rates. The fast response of the CIMS also allowed us to derive vertical NH 3 fluxes within the turbulent boundary layer via eddy covariance, for which we chiefly used the continuous wavelet transform technique. As expected for a region dominated by agriculture, we observed predominantly upward fluxes, implying net NH 3 emissions from surface. The corresponding analysis focused on the most suitable flight, which contained two straight-and-level legs at ~300 m above ground. We derived NH 3 fluxes between –4 and 18 mol km –2 h –1 for these legs, at an effective spatial resolution of 1–2 km. The analysis demonstrated how flux measurements benefit from suitably arranged flight tracks with sufficiently long straight-and-level legs, and explores the detrimental effect of measurement discontinuities. Following flux footprint estimations, comparison to the NH 3 area emissions inventory provided by the US Environmental Protection Agency indicated overall agreement, but also the absence of some sources, for instance the identified cattle farm. Our study concludes that high-precision CIMS measurements are a powerful tool for in-situ measurements of ambient NH 3 mixing ratios, and even allow for the airborne mapping of the air-surface exchange of NH 3 .

54 ENVIRONMENTAL SCIENCES↗

Continuous wavelet analysis of coherent structures

We perform an analysis of planar cuts through three dimensional turbulent fields (planar channel flow and mixing layer) using the 2D continuous wavelet transform. We propose two new diagnostics: (1) a measure of intermittency I(r, vector x), which is the ratio of local energy and average energy at a given scale r; and (2) a local Reynolds number, defined on the local velocity contribution at a given scale, computed from the wavelet transform of the three velocity components, the scale of the transform, and molecular viscosity; this gives a representation of the local non-linearity of the flow viewed in both space and scale. We find, for the analyzed flows, strong small-scale intermittency located in the ejection regions for the channel flow and in the vortex core of the mixing layer.

Farge, M.↗

Wavelets, period-doubling, and time-frequency localization with application to organization of convection over the tropical western Pacific

In this paper, preliminary results in using orthogonal and continuous wavelet transform (WT) to identify period doubling and time-frequency localization in both synthetic and real data are presented. First, the Haar WT is applied to synthetic time series derived from a simple nonlinear dynamical system- a first-order quadratic difference equation. Second, the complex Morlet WT is used to study the time-frequency localization of tropical convection based on a high-resolution Japanese Geostationary Meteorological Satellite infrared (IR) radiance dataset. The Haar WT of the synthetic time series indicates the presence and distinct separation of multiple frequencies in a period-doubling sequence. The period-doubling process generates a multiplicity of intermediate frequencies, which are manifested in the nonuniformity in time with respect to the phase of oscillations in the lower frequencies. Wavelet transform also enables the detection of extremely weak signals in high-order subharmonics resulting from the period-doubling bifurcations. These signals are either undetected or considered statistically insignificant by traditional Fourier analysis. The Morlet WT of the IR radiance dataset indicates the presence of multiple timescales, which are localized in both frequency and time. There are two regimes in the variation of IR radiance, corresponding to the wet and dry periods. Multiple timescales, ranging from semidiurnal, diurnal, synoptic, to intraseasonal with embedding structures, are active in the wet regime. In particular, synoptic variability is more prominent during the wet phase of an intensive intraseasonal cycle. These are not only consistent with, but also show more details than, previous findings by using other techniques. The phase-locking relationships among the oscillations with different time-scales suggest that both synoptic and intraseasonal variations may be mixed oscillations due to the interaction of self-excited oscillations in the tropical atmosphere and external forcings such as annual and diurnal solar radiation variations. Both examples show that WT is a powerful tool for analysis of phenomena involving multiscale interactions that exhibit localization in both frequency and time. A discussion on the caveats in the use of WT in geophysical data analysis is also presented.

Weng, Hengyi↗

Characteristic Lifelength of Coherent Structure in the Turbulent Boundary Layer

A characteristic lifelength is defined by which a Gaussian distribution is fit to data correlated over a 3 sensor array sampling streamwise sidewall pressure. The data were acquired at subsonic, transonic and supersonic speeds aboard a Tu-144. Lifelengths are estimated using the cross spectrum and are shown to compare favorably with Efimtsov's prediction of correlation space scales. Lifelength distributions are computed in the time/frequency domain using an interval correlation technique on the continuous wavelet transform of the original time data. The median values of the lifelength distributions are found to be very close to the frequency averaged result. The interval correlation technique is shown to allow the retrieval and inspection of the original time data of each event in the lifelength distribution, thus providing a means to locate and study the nature of the coherent structure in the turbulent boundary layer. The lifelength data can be converted to lifetimes using the convection velocity. The lifetime of events in the time/frequency domain are displayed in Lifetime Maps. The primary purpose of the paper is to validate these new analysis techniques so that they can be used with confidence to further characterize coherent structure in the turbulent boundary layer.

Palumbo, Daniel L.↗

Deriving Lifetime Maps in the Time/Frequency Domain of Coherent Structures in the Turbulent Boundary Layer

The lifetimes of coherent structures are derived from data correlated over a 3 sensor array sampling streamwise sidewall pressure at high Reynolds number (> 10(exp 8)). The data were acquired at subsonic, transonic and supersonic speeds aboard a Tupolev Tu-144. The lifetimes are computed from a variant of the correlation length termed the lifelength. Characteristic lifelengths are estimated by fitting a Gaussian distribution to the sensors cross spectra and are shown to compare favorably with Efimtsov s prediction of correlation space scales. Lifelength distributions are computed in the time/frequency domain using an interval correlation technique on the continuous wavelet transform of the original time data. The median values of the lifelength distributions are found to be very close to the frequency averaged result. The interval correlation technique is shown to allow the retrieval and inspection of the original time data of each event in the lifelength distributions, thus providing a means to locate and study the nature of the coherent structure in the turbulent boundary layer. The lifelength data are converted to lifetimes using the convection velocity. The lifetime of events in the time/frequency domain are displayed in Lifetime Maps. The primary purpose of the paper is to validate these new analysis techniques so that they can be used with confidence to further characterize the behavior of coherent structures in the turbulent boundary layer.

Palumbo, Dan↗

Wavenumber Imaging For Damage Detection and Measurement

This paper presents a method for analyzing ultrasonic wavefield data using the Continuous Wavelet Transform (CWT) applied in the spatial domain. Unlike data obtained by sparse arrays of transducers, full wavefield data contains information local to the structure and can be used to obtain more detailed measurements of damage type, location, size, etc. By calculating the CWT of the wavefield in the spatial domain, the wavenumber spectrum is determined for the inspected locations. Because wavenumber is affected by the local geometry and material properties of the structure through which Lamb waves propagate, the wavenumber spectrum can be analyzed to assess the location, severity, and size of damage. The technique is first applied to experimental wavefield data obtained using a laser Doppler vibrometer and automated positioning stage. The out-of-plane velocity along the length of a composite stringer was measured to detect the presence of delaminations within the composite overwrap. Next, simulated corrosion is detected and measured within an aluminum plate using the two dimensional CWT. The experimental results show the usefulness of the technique for vehicle structure inspection applications.

Rogge, Matthew D.↗

A Wavelet Analysis Approach for Categorizing Air Traffic Behavior

In this paper two frequency domain techniques are applied to air traffic analysis. The Continuous Wavelet Transform (CWT), like the Fourier Transform, is shown to identify changes in historical traffic patterns caused by Traffic Management Initiatives (TMIs) and weather with the added benefit of detecting when in time those changes take place. Next, with the expectation that it could detect anomalies in the network and indicate the extent to which they affect traffic flows, the Spectral Graph Wavelet Transform (SGWT) is applied to a center based graph model of air traffic. When applied to simulations based on historical flight plans, it identified the traffic flows between centers that have the greatest impact on either neighboring flows, or flows between centers many centers away. Like the CWT, however, it can be difficult to interpret SGWT results and relate them to simulations where major TMIs are implemented, and more research may be warranted in this area. These frequency analysis techniques can detect off-nominal air traffic behavior, but due to the nature of air traffic time series data, so far they prove difficult to apply in a way that provides significant insight or specific identification of traffic patterns.

wavelet analysis↗

WigglyRivers: A tool to characterize the multiscale nature of meandering channels

Channel sinuosity is ubiquitous along river networks, producing complex patterns that encapsulate and influence morphodynamic processes and ecosystem services. Accurately characterizing these patterns is challenging with traditional curvature-based algorithms. Here, in this study, we present WigglyRivers, a Python package that builds on existing wavelet-based methods to create an unsupervised meander identification and characterization tool. The package uses planimetric information the user provides or from the USGS’s High-Resolution National Hydrography Dataset to characterize individual reaches or entire river networks. WigglyRivers also includes a supervised river identification tool for manually selecting individual meandering features. Here, we provide examples of idealized river transects and show the capabilities of WigglyRivers. We also use the supervised identification tool to validate the unsupervised identification on river transects across the continental US. WigglyRivers is a tool to understand better the multiscale characteristics of river networks and the link between river geomorphology and river corridor connectivity.

54 ENVIRONMENTAL SCIENCES↗

AI-enabled traveling wave protection for microgrids

Grid forming inverters provide voltage and frequency regulations for microgrids; in the meantime, new challenges are introduced for microgrid protections. For instance, inverters’ control strategies can affect protection behaviors, and low short-circuit ratios and bi-directional power flows also make protection operations complex. Protection schemes based on conventional principles such as overcurrent and distance relays do not always provide reliable, sensitive, or selective operations. Here, we devise a traveling wave protection approach for microgrids using a wavelet-driven deep neural network named WaveletKernelNet (WKN). Compared with conventional methods, the presented approach provides enhanced sensitivity, higher selectivity, and better identification of various faults in microgrids. Extensive case studies validate the efficacy and excellent performance of the devised approach.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Limits of Detection for EXAFS Characterization of Heterogeneous Single-Atom Catalysts

Single-atom catalysts (SACs), consisting of individual metal atoms dispersed on a support, attract attention due to their unique reactivity, efficient use of precious metals, and precise chemical tunability. Characterization of the metal species is crucial to substantiate structure–function relationships. Authors often use—and referees often require—X-ray absorption spectroscopy (XAS) data to prove the absence of clustered metal (or metal oxide) structures after pre-treatment and under in situ or operando conditions. However, there has been no critical assessment of the limitations of XAS in substantiating such conclusive statements, which is particularly important given the potential outsized influence of minority catalyst structures in dictating catalytic activity. Here, in this article, we quantitatively assess the detection limits of XAS to identify metal (or metal oxide) clusters in samples containing predominantly single atoms by modeling the extended X-ray absorption fine structure (EXAFS) of mixtures of structures. We identified that a significant fraction of clusters can coexist with SAC active sites (e.g., ~10% metallic Pt or ~40% oxidized Pt clusters in Pt/CeO 2 SACs), while eluding detection via EXAFS with any statistical significance. To generalize these conclusions, a descriptor-based screening of bulk metal oxides using a continuous Cauchy wavelet transform was proposed that suggests certain materials for which differentiating atomically dispersed metal species and metal oxide clusters would be infeasible by EXAFS (e.g., ReO x ). Based on this analysis, we suggest best practices for the study of SACs using EXAFS and provide recommendations to ensure that conclusions do not outpace the evidence used to support them. In this rapidly expanding research area, rigorous characterization will lead to greater understanding of the behavior of SACs and ultimately improved catalytic materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Participation In The AXAF Program As Interdisciplinary Scientist

We have supported the Advanced X-ray Astrophysics Facility (AXAF) project through specific studies and research in X-ray astronomy. Our research in X-ray astronomy has been concentrated in three projects: the ROSAT Deep Survey, the ROSAT All-sky Cluster Survey, and the study of moderate to high redshift clusters discovered serendipitously in long ROSAT pointings utilizing the wavelet transform. We have continued to develop the techniques and catalogues described in the publications listed below. The PI continued to participate in the SWG and attended its meetings except where conflicts existed. The Co-I supported the PI and attended all meetings in order to provide continuity. A post-doctoral fellow (Rosati) was hired to fully develop the techniques described above and make them applicable to the AXAF program. The results are described in the publications below. We continued to provide analysis of scientific and technical issues to the project scientist as appropriate. We made detailed simulations of the AXAF deep survey program and have made this available to the project and the ASC. The principal scientific results, discussed in great detail in the publications listed below, are as follows: (1) The wavelet transform is now a fine working tool for the analysis of faint X-ray sources especially clusters. (2) The analysis of the ROSAT DEEP CLUSTER SURVEY has given important constraints on cosmology particularly on the matter content of the universe and the amplitude of the fluctuations that created the galaxies and clusters. (3) The ROSAT DEEP SURVEY in the Lockman Hole has given an important'deep survey in the X-ray band that gives vital data on the distribution and evolution of X-ray sources. It is an important and complementary data base to compare with the AXAF deep fields. (4) The Northern ROSAT All Sky Cluster Survey now has a complete catalog and is again important and complementary to AXAF/ Chandra studies of clusters which are deeper but in a narrower area. These projects have had a significant impact on the whole field and have set up some excellent experiments to be undertaken with the AXAF/Chandra telescope such as the Chandra Deep Field South.

Giacconi, Riccardo↗

Improving the Transportability of a Deep Learning Denoising Model Using Transfer Learning Techniques

The adoption of machine learning techniques in the seismology community has led to great performance improvements in several areas, including signal processing. Specifically, the development of deep learning–based seismic waveform denoising models has the potential to yield improvements in signal detection capabilities for networks operating in particularly noisy environments. Recent advancements in the design of these deep learning denoising models have included the incorporation of continuous and discrete wavelet transform functions into the network architecture to improve the learning capabilities and efficiency of said models. These wavelet transform–based seismic denoising models have shown improved denoising capabilities in regions where there is good agreement between the data features present in the training and evaluation datasets. However, questions remain about the overall transportability of these models to other monitoring regions. Here, in this study, we will determine the baseline transportability of a newly developed multilevel wavelet‐transform convolutional neural network (MWCNN) seismic denoising model. We accomplish this by taking a version of the MWCNN denoising model trained on data collected from the Utah region and evaluating its denoising performance on datasets collected from the neighboring Nevada region, which differ with regard to monitoring sensor types and event histories. We find that there is a notable variability in denoising performance related to the degree of similarity between the initial and new target datasets. The most notable difference in denoising performance is the ability of the denoising model to preserve accurate amplitude information associated with the signal energy present in the waveform data. Finally, we evaluate the ability of transfer learning techniques to improve the transportability of the MWCNN denoising model. We find that although there is still a performance gap present in the denoising results of the MWCNN model, transfer learning did yield improved results.

Quinones, Louis [Sandia National Laboratories (SNL↗

Quantized Information in Spectral Cyberspace

The constant-Q Gabor atom is developed for spectral power, information, and uncertainty quantification from time–frequency representations. Stable multiresolution spectral entropy algorithms are constructed with continuous wavelet and Stockwell transforms. The recommended processing and scaling method will depend on the signature of interest, the desired information, and the acceptable levels of uncertainty of signal and noise features. Selected Lamb wave signatures and information spectra from the 2022 Tonga eruption are presented as representative case studies. Resilient transformations from physical to information metrics are provided for sensor-agnostic signal processing, pattern recognition, and machine learning applications.

74 ATOMIC AND MOLECULAR PHYSICS↗

Wavelet Analyses of F/A-18 Aeroelastic and Aeroservoelastic Flight Test Data

Time-frequency signal representations combined with subspace identification methods were used to analyze aeroelastic flight data from the F/A-18 Systems Research Aircraft (SRA) and aeroservoelastic data from the F/A-18 High Alpha Research Vehicle (HARV). The F/A-18 SRA data were produced from a wingtip excitation system that generated linear frequency chirps and logarithmic sweeps. HARV data were acquired from digital Schroeder-phased and sinc pulse excitation signals to actuator commands. Nondilated continuous Morlet wavelets implemented as a filter bank were chosen for the time-frequency analysis to eliminate phase distortion as it occurs with sliding window discrete Fourier transform techniques. Wavelet coefficients were filtered to reduce effects of noise and nonlinear distortions identically in all inputs and outputs. Cleaned reconstructed time domain signals were used to compute improved transfer functions. Time and frequency domain subspace identification methods were applied to enhanced reconstructed time domain data and improved transfer functions, respectively. Time domain subspace performed poorly, even with the enhanced data, compared with frequency domain techniques. A frequency domain subspace method is shown to produce better results with the data processed using the Morlet time-frequency technique.

Martin J Brenner↗

Multiresolution With Super-Compact Wavelets

The solution data computed from large scale simulations are sometimes too big for main memory, for local disks, and possibly even for a remote storage disk, creating tremendous processing time as well as technical difficulties in analyzing the data. The excessive storage demands a corresponding huge penalty in I/O time, rendering time and transmission time between different computer systems. In this paper, a multiresolution scheme is proposed to compress field simulation or experimental data without much loss of important information in the representation. Originally, the wavelet based multiresolution scheme was introduced in image processing, for the purposes of data compression and feature extraction. Unlike photographic image data which has rather simple settings, computational field simulation data needs more careful treatment in applying the multiresolution technique. While the image data sits on a regular spaced grid, the simulation data usually resides on a structured curvilinear grid or unstructured grid. In addition to the irregularity in grid spacing, the other difficulty is that the solutions consist of vectors instead of scalar values. The data characteristics demand more restrictive conditions. In general, the photographic images have very little inherent smoothness with discontinuities almost everywhere. On the other hand, the numerical solutions have smoothness almost everywhere and discontinuities in local areas (shock, vortices, and shear layers). The wavelet bases should be amenable to the solution of the problem at hand and applicable to constraints such as numerical accuracy and boundary conditions. In choosing a suitable wavelet basis for simulation data among a variety of wavelet families, the supercompact wavelets designed by Beam and Warming provide one of the most effective multiresolution schemes. Supercompact multi-wavelets retain the compactness of Haar wavelets, are piecewise polynomial and orthogonal, and can have arbitrary order of approximation. The advantages of the multiresolution algorithm are that no special treatment is required at the boundaries of the interval, and that the application to functions which are only piecewise continuous (internal boundaries) can be efficiently implemented. In this presentation, Beam's supercompact wavelets are generalized to higher dimensions using multidimensional scaling and wavelet functions rather than alternating the directions as in the 1D version. As a demonstration of actual 3D data compression, supercompact wavelet transforms are applied to a 3D data set for wing tip vortex flow solutions (2.5 million grid points). It is shown that high data compression ratio can be achieved (around 50:1 ratio) in both vector and scalar data set.

Lee, Dohyung↗

Denoising Seismic Waveforms Using a Wavelet-Transform-Based Machine-Learning Method

Seismic waveform data recorded at stations can be thought of as a superposition of the signal from a source of interest and noise from other sources. Frequency‐based filtering methods for waveform denoising do not result in desired outcomes when the targeted signal and noise occupy similar frequency bands. Recently, denoising techniques based on deep‐learning convolutional neural networks (CNNs), in which a recorded waveform is decomposed into signal and noise components, have led to improved results. These CNN methods, which use short‐time Fourier transform representations of the time series, provide signal and noise masks for the input waveform. These masks are used to create denoised signal and designaled noise waveforms, respectively. However, advancements in the field of image denoising have shown the benefits of incorporating discrete wavelet transforms (DWTs) into CNN architectures to create multilevel wavelet CNN (MWCNN) models. The MWCNN model preserves the details of the input due to the good time–frequency localization of the DWT. In this report we use a data set of over 382,000 constructed seismograms recorded by the University of Utah Seismograph Stations network to compare the performance of CNN and MWCNN‐based denoising models. Evaluation of both models on constructed test data shows that the MWCNN model outperforms the CNN model in the ability to recover the ground‐truth signal component in terms of both waveform similarity and preservation of amplitude information. Model evaluation of real‐world data shows that both the CNN and MWCNN models outperform standard band‐pass filtering (BPF; average improvement in signal‐to‐noise ratio of 9.6 and 19.7 dB, respectively, with respect to BPF). Evaluation of continuous data suggests the MWCNN denoiser can improve both signal detection capabilities and phase arrival time estimates.

58 GEOSCIENCES↗

Development of 3D electromagnetic modeling tools for airborne vehicles

The main goal of this report is to advance the development of methodologies for scattering by airborne composite vehicles. Although the primary focus continues to be the development of a general purpose computer code for analyzing the entire structure as a single unit, a number of other tasks are also being pursued in parallel with this effort. One of these tasks discussed within is on new finite element formulations and mesh termination schemes. The goal here is to decrease computation time while retaining accuracy and geometric adaptability.The second task focuses on the application of wavelets to electromagnetics. Wavelet transformations are shown to be able to reduce a full matrix to a band matrix, thereby reducing the solutions memory requirements. Included within this document are two separate papers on finite element formulations and wavelets.

Volakis, John L.↗