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NASA NTRS2003

A Step Beyond Simple Keyword Searches: Services Enabled by a Full Content Digital Journal Archive

The problems of managing and searching large archives of scientific journal articles can potentially be addressed through data mining and statistical techniques matured primarily for quantitative scientific data analysis. A journal paper could be represented by a multivariate descriptor, e.g., the occurrence counts of a number key technical terms or phrases (keywords), perhaps derived from a controlled vocabulary ( e . g . , the American Meteorological Society's Glossary of Meteorology) or bootstrapped from the journal archive itself. With this technique, conventional statistical classification tools can be leveraged to address challenges faced by both scientists and professional societies in knowledge management. For example, cluster analyses can be used to find bundles of "most-related" papers, and address the issue of journal bifurcation (when is a new journal necessary, and what topics should it encompass). Similarly, neural networks can be trained to predict the optimal journal (within a society's collection) in which a newly submitted paper should be published. Comparable techniques could enable very powerful end-user tools for journal searches, all premised on the view of a paper as a data point in a multidimensional descriptor space, e.g.: "find papers most similar to the one I am reading", "build a personalized subscription service, based on the content of the papers I am interested in, rather than preselected keywords", "find suitable reviewers, based on the content of their own published works", etc. Such services may represent the next "quantum leap" beyond the rudimentary search interfaces currently provided to end-users, as well as a compelling value-added component needed to bridge the print-to-digital-medium gap, and help stabilize professional societies' revenue stream during the print-to-digital transition.

Boccippio, Dennis J.↗

NASA NTRS1983

Numerical solution of the Navier-Stokes equations for compressible turbulent two/three dimensional flows in the terminal shock region of an inlet/diffuser

The multidimensional, ensemble-averaged, compressible, time-dependent Navier-Stokes equations in conjunction with mixing length turbulence model and shock capturing technique have been used to study the terminal shock type of flows in various flight regimes occurring in a diffuser/inlet model. The numerical scheme for solving the governing equations is based on a linearized block implicit approach and the following high Reynolds number calculations have been carried out: (1) 2-D, steady, subsonic; (2) 2-D, steady, transonic with normal shock, (3) 2-D, steady, supersonic with terminal shock, (4) 2-D, transient process of shock development and (5) 3-D, steady, transonic with normal shock. The numerical results obtained for the 2-D and 3-D transonic shocked flows have been compared with corresponding experimental data; the calculated wall static pressure distributions agree well with the measured data. The predicted transient responses of the flow to externally applied impulsive disturbance are consistent with results obtained via asymptotic analysis.

Liu, N.-S.↗

NASA NTRS1999

Ignition, Transition, Flame Spread in Multidimensional Configurations in Microgravity

In the inhabited quarters of orbiting spacecraft, fire is a greatly feared hazard. Thus, the fire safety strategy in a spacecraft is (1) to keep any fire as small as possible, (2) to detect any fire as early as possible, and (3) to extinguish any fire as quickly as possible. This suggests that a material which undergoes a momentary ignition might be tolerable but a material which permits a transition from a localized ignition to flame spread would significantly increase the fire hazard in a spacecraft. If the transition does not take place, fire growth does not occur. Therefore, it is critical to understand what process controls the transition. Many previous works have studied ignition and flame spread separately or were limited to a two-dimensional configuration. In this study, time-dependent phenomena of the transition over a thermally thin sample is studied experimentally and theoretically in two- and three-dimensional (2D,3D) configurations. Furthermore, localized ignition can be initiated at the center portion of thermally thin paper sample instead of at one end of the sample. Thus, the transition to flame spread could occur either toward upstream or downstream or both directions simultaneously with an external flow. In this presentation, the difference in the transition between the 3D and 2D configurations is explained with the numerically calculated data. For sufficiently narrow samples edge effects exist. Some results on this issue are presented. New analysis of the surface smoldering experiments conducted in the space shuttle STS-75 flight is also described.

Kashiwagi, Takashi↗

NASA NTRS1993

Applications of wavelet-based compression to multidimensional Earth science data

A data compression algorithm involving vector quantization (VQ) and the discrete wavelet transform (DWT) is applied to two different types of multidimensional digital earth-science data. The algorithms (WVQ) is optimized for each particular application through an optimization procedure that assigns VQ parameters to the wavelet transform subbands subject to constraints on compression ratio and encoding complexity. Preliminary results of compressing global ocean model data generated on a Thinking Machines CM-200 supercomputer are presented. The WVQ scheme is used in both a predictive and nonpredictive mode. Parameters generated by the optimization algorithm are reported, as are signal-to-noise (SNR) measurements of actual quantized data. The problem of extrapolating hydrodynamic variables across the continental landmasses in order to compute the DWT on a rectangular grid is discussed. Results are also presented for compressing Landsat TM 7-band data using the WVQ scheme. The formulation of the optimization problem is presented along with SNR measurements of actual quantized data. Postprocessing applications are considered in which the seven spectral bands are clustered into 256 clusters using a k-means algorithm and analyzed using the Los Alamos multispectral data analysis program, SPECTRUM, both before and after being compressed using the WVQ program.

Bradley, Jonathan N.↗

NASA NTRS2001

One-Dimensional Spontaneous Raman Measurements Made in a Gas Turbine Combustor

The NASA Glenn Research Center and the aerospace industry are designing and testing low-emission combustor concepts to build the next generation of cleaner, more fuel efficient aircraft powerplants. These combustors will operate at much higher inlet temperatures and at pressures that are up to 3 to 5 times greater than combustors in the current fleet. From a test and analysis viewpoint, there is an increasing need for measurements from these combustors that are nonintrusive, simultaneous, multipoint, and more quantitative. Glenn researchers have developed several unique test facilities (refs. 1 and 2) that allow, for the first time, optical interrogation of combustor flow fields, including subcomponent performance, at pressures ranging from 1 to 60 bar (1 to 60 atm). Experiments conducted at Glenn are the first application of a visible laser-pumped, one-dimensional, spontaneous Raman-scattering technique to analyze the flow in a high-pressure, advanced-concept fuel injector at pressures thus far reaching 12 bar (12 atm). This technique offers a complementary method to the existing two- and three-dimensional imaging methods used, such as planar laser-induced fluorescence. Raman measurements benefit from the fact that the signal from each species is a linear function of its density, and the relative densities of all major species can be acquired simultaneously with good precision. The Raman method has the added potential to calibrate multidimensional measurements by providing an independent measurement of species number-densities at known points within the planar laser-induced fluorescence images. The visible Raman method is similar to an ultraviolet-Raman technique first tried in the same test facility (ref. 3). However, the visible method did not suffer from the ultraviolet technique's fuel-born polycyclic aromatic hydrocarbon fluorescence interferences.

DeGroot, Wilhelmus A.↗

NASA NTRS2010

Correlated Topics in a Scalable Multidimensional Text Cube: Algorithms and Aviation Safety Case Study

As world-wide air traffic continues to grow even at a modest pace, the overall complexity of the system will increase significantly. This increased complexity can lead to a larger number of fatalities per year even if the extremely low fatality rate that we currently enjoy is maintained. One important source of information about the safety of the aviation system is in Aviation Safety Text Reports which are written by members of the flight crew, air traffic controllers, and other parties involved with the aviation system. These anonymized narrative reports contain fixed-field contextual information about the flight but also contain free-form narratives that describe, in the author s own words, the nature of the safety incident and, in many cases, the contributing factors that led to the safety incident. Several thousand such reports are filed each month, each of which is read and analyzed by highly trained experts. However, it is possible that there are emerging safety issues due to the fact that they may be reported very infrequently and in different contexts with different descriptions. The goal of this research paper is to develop correlated topic models which uncover correlations in the subspaces defined by the intersection of numerous fixed fields and discovered correlated topics. This task requires the discovery of latent topics in the text reports and the creation of a topic cube. Furthermore, because the number of potential cells in the topic cube is very large, we discuss novel methods of pruning the search space in the topic cells, thereby making the analysis feasible. We demonstrate the new algorithms on an analysis of pilot fatigue and its contributing factors, as well as the safety incidents that are correlated with this phenomenon.

Zhao, Bo↗

NASA NTRS1990

Critical evaluation of Jet-A spray combustion using propane chemical kinetics in gas turbine combustion simulated by KIVA-2

Jet-A spray combustion has been evaluated in gas turbine combustion with the use of propane chemical kinetics as the first approximation for the chemical reactions. Here, the numerical solutions are obtained by using the KIVA-2 computer code. The KIVA-2 code is the most developed of the available multidimensional combustion computer programs for application of the in-cylinder combustion dynamics of internal combustion engines. The released version of KIVA-2 assumes that 12 chemical species are present; the code uses an Arrhenius kinetic-controlled combustion model governed by a four-step global chemical reaction and six equilibrium reactions. Researchers efforts involve the addition of Jet-A thermophysical properties and the implementation of detailed reaction mechanisms for propane oxidation. Three different detailed reaction mechanism models are considered. The first model consists of 131 reactions and 45 species. This is considered as the full mechanism which is developed through the study of chemical kinetics of propane combustion in an enclosed chamber. The full mechanism is evaluated by comparing calculated ignition delay times with available shock tube data. However, these detailed reactions occupy too much computer memory and CPU time for the computation. Therefore, it only serves as a benchmark case by which to evaluate other simplified models. Two possible simplified models were tested in the existing computer code KIVA-2 for the same conditions as used with the full mechanism. One model is obtained through a sensitivity analysis using LSENS, the general kinetics and sensitivity analysis program code of D. A. Bittker and K. Radhakrishnan. This model consists of 45 chemical reactions and 27 species. The other model is based on the work published by C. K. Westbrook and F. L. Dryer.

Nguyen, H. L.↗

DOE OSTI2025

Incubating advances in integrated photonics with emerging sensing and computational capabilities

As photonic technologies grow in multidimensional aspects, integrated photonics holds a unique position and continuously presents enormous possibilities for research communities. Applications include data centers, environmental monitoring, medical diagnosis, and highly compact communication components, with further possibilities continuously growing. Herein, we review state-of-the-art integrated photonic on-chip sensors that operate in the visible to mid-infrared wavelength region on various material platforms. Among the different materials, architectures, and technologies leading the way for on-chip sensors, we discuss the optical sensing principles that are commonly applied to biochemical and gas sensing. Our focus is on passive optical waveguides, including dispersion-engineered metamaterial-based structures, which are essential for enhancing the interaction between light and analytes in chip-scale sensors. We harness a diverse array of cutting-edge sensing technologies, heralding a revolutionary on-chip sensing paradigm. Our arsenal includes refractive-index-based sensing, plasmonics, and spectroscopy, which forge an unparalleled foundation for innovation and precision. Furthermore, we include a brief discussion of recent trends and computational concepts, incorporating Artificial Intelligence & Machine Learning (AI/ML) and deep learning approaches over the past few years to improve the qualitative and quantitative analysis of sensor measurements.

Jain, Sourabh (ORCID:0000000279923275)↗

DOE OSTI2025

Immersive Scientific Visualization of Molten-Salt Reactor Waste Characteristics Using Virtual Reality

Immersive visualization is changing how we explore, communicate, and understand complex scientific systems. In nuclear energy, an area in which data are often multidimensional, time-dependent, and difficult to interpret, virtual reality (VR) represents a powerful and intuitive informational medium. This work introduces a VR-based platform that visualizes the post-shutdown behavior and waste management lifecycle of molten-salt reactors (MSRs), a next-generation reactor type with unique operational and safety characteristics. The platform, built in Unity, is streamed on the Meta Quest 3 headset. It transforms high-fidelity simulation data into an interactive, immersive experience. Users can explore time-dependent reactor characteristics such as nuclide decay, which is a key factor for evaluating reactor waste strategies. The datasets were generated using the MOOSE (Multiphysics Object-Oriented Simulation Environment) framework and then processed through ParaView scripting for smooth integration into Unity. From a visualization standpoint, the platform emphasizes spatial storytelling, temporal exploration, and user-centered interaction. Users can navigate 3D reactor geometries, slice through volumetric data, and manipulate time to observe how physical phenomena evolve. Real-scale rendering and embodied interaction make the experience feel tangible. The interface is designed to be accessible, even to those without nuclear or simulation expertise. This lowers the barrier for stakeholders, policymakers, and the general public, while still supporting expert analysis and collaborative decision-making. This work shows how immersive visualization can function as both a scientific tool and a communication interface. By integrating simulation, processing, and visualization into a cohesive workflow, we offer a scalable framework for immersive scientific storytelling. The modular design supports future extensions to other reactor types and lifecycle stages, from shutdown to long-term storage, making the platform adaptable for both research and outreach.

99 - GENERAL AND MISCELLANEOUS↗

DOE OSTI2024

Metadynamics investigation of lanthanide solvation free energy landscapes and insights into separations energetics

Lanthanide ion solvation chemistry in nonaqueous phases is key to understanding and developing effective separation processes for these critical materials. Due to the complexity and inherent disorder of the solution phase, a comprehensive picture of the solvated metal ion is often difficult to generate solely from conventional spectroscopic approaches and electronic structure calculations, particularly in the extractant phase. In this work, we use classical molecular dynamics (MD) simulation with an advanced sampling technique, metadynamics, supplemented by experimental spectroscopy and speciation analysis, to measure lanthanide solvation free energy landscapes. We define coordination-based collective variables to probe the entire range of solvation configurations in the organic phase of lanthanum (La), europium (Eu), and lutetium (Lu) nitrate salts bound with a commonly used extractant, N,N′-dimethyl, N,N′-dioctylhexylethoxymalonamide (DMDOHEMA). The known lanthanide extraction trend of La ≈ Eu > Lu is readily explained by the measured free energy surfaces, which show consistent DMDOHEMA coordination from La to Eu, followed by loss of DMDOHEMA coordination from Eu to Lu. These simulations suggest how ligand crowding at the metal center can control selectivity, in this case resulting in the opposite extraction trend as observed with other conventional extractants, where the enthalpic contribution from increasing lanthanide charge density across the series dominates the extraction energetics. We also find that the presence of inner-sphere water, verified by time-resolved fluorescence, diversifies the accessible solvation structures. As a result, understanding solvation requires consideration of an entire thermodynamic ensemble, rather than the single dominant lowest-energy structure, as is often considered out of necessity in interpretation of spectroscopic data or in electronic structure-based ligand design approaches. In general, we demonstrate how metadynamics uniquely enables investigation of complex, multidimensional solvation energetic landscapes, and how it can explain selectivity trends where extraction is controlled by more complex mechanisms than simple charge density-based selectivity.

Wang, Xiaoyu↗

DOE OSTI2024

Toward Accelerating Discovery via Physics-Driven and Interactive Multifidelity Bayesian Optimization

Both computational and experimental material discovery bring forth the challenge of exploring multidimensional and often nondifferentiable parameter spaces, such as phase diagrams of Hamiltonians with multiple interactions, composition spaces of combinatorial libraries, processing spaces, and molecular embedding spaces. Often these systems are expensive or time consuming to evaluate a single instance, and hence classical approaches based on exhaustive grid or random search are too data intensive. This resulted in strong interest toward active learning methods such as Bayesian optimization (BO) where the adaptive exploration occurs based on human learning (discovery) objective. However, classical BO is based on a predefined optimization target, and policies balancing exploration and exploitation are purely data driven. In practical settings, the domain expert can pose prior knowledge of the system in the form of partially known physics laws and exploration policies often vary during the experiment. Here, we propose an interactive workflow building on multifidelity BO (MFBO), starting with classical (data-driven) MFBO, then expand to a proposed structured (physics-driven) structured MFBO (sMFBO), and finally extend it to allow human-in-the-loop interactive interactive MFBO (iMFBO) workflows for adaptive and domain expert aligned exploration. These approaches are demonstrated over highly nonsmooth multifidelity simulation data generated from an Ising model, considering spin–spin interaction as parameter space, lattice sizes as fidelity spaces, and the objective as maximizing heat capacity. Detailed analysis and comparison show the impact of physics knowledge injection and real-time human decisions for improved exploration with increased alignment to ground truth. Here, the associated notebooks allow to reproduce the reported analyses and apply them to other systems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1999

Inlet-Compressor Analysis using Coupled CFD Codes

Propulsion performance and operability are key factors in the development of a successful aircraft. For high-speed supersonic aircraft, mixed-compression inlets offer high performance but are susceptible to an instability referred to as unstart. An unstart occurs when a disturbance originating in the atmosphere or the engine causes the shock system to be expelled from the inlet. This event can have adverse effects on control of the aircraft, which is unacceptable for a passenger plane such as the high speed civil transport (HSCT). The ability to predict the transient response of such inlets to flow perturbations is, therefore, important to the proper design of the inlet and the control measures used to prevent unstart. Computational fluid dynamics (CFD) is having an increasing role in the analysis of individual propulsion components. Isolated inlet studies are relatively easy to perform, but a major uncertainty is the boundary condition used at the inlet exit to represent the engine - the so-called compressor face boundary condition. A one-dimensional (1-D) Euler inlet simulation showed that the predicted inlet unstart tolerance to free-stream pressure perturbations can vary by as much as a factor of about six, depending on the boundary condition used. Obviously a thorough understanding of dynamic interactions between inlets and compressors/fans is required to provide the proper boundary condition. To aid in this understanding and to help evaluate possible boundary conditions, an inlet-engine experiment was conducted at the University of Cincinnati. The interaction of acoustic pulses, generated in the inlet, with the engine were investigated. Because of the availability of experimental data for validation, it was decided to simulate the experiment using CFD. The philosophy here is that the inlet-engine system is best simulated by coupling (existing) specialized CFD component-codes. The objectives of this work were to aid in a better understanding of inlet-compressor interaction physics and the formulation of a more realistic compressor-face boundary condition for time-accurate CFD simulations of inlets. Previous simulations have used 1-D Euler engine simulations in conjunction with 1-D Euler and axisymmetric Euler inlet simulations. This effort is a first step toward CFD simulation of an entire engine by coupling multidimensional component codes.

Cole, Gary↗

NASA NTRS1993

Ignition Transient Calculations in the Space Shuttle Solid Rocket Motor

The work presented is part of an effort to develop a multidimensional ignition transient model for large solid propellant rocket motors. On the Space Shuttle, the ignition transient in the slot is induced when the igniter, itself a small rocket motor, is fired into the head-end portion of the main rocket motor. The computational results presented in this paper consider two different igniter configurations. The first configuration is a simulated Space Shuttle RSRM igniter which has one central nozzle that is parallel to the centerline of the motor. The second igniter configuration has a nozzle which is canted at an angle of 45 deg from the centerline of the motor. This paper presents a computational fluid dynamic (CFD) analyses of certain flow field characteristics inside the solid propellant star grain slot of the Space Shuttle during the ignition transient period of operation for each igniter configuration. The majority of studies made to date regarding ignition transient performance in solid rocket motors have concluded that the key parameter to be determined is the heat transfer rate to the propellant surface and hence the heat transfer coefficient between the gas and the propellant. In this paper the heat transfer coefficients, pressure and velocity distributions are calculated in the star slot. In order to validate the computational method and to attempt to establish a correlation between the flow field characteristics and the heat transfer rates a series of cold flow experimental investigations were conducted. The results of these experiments show excellent qualitative and quantitative agreement with the pressure and velocity distributions obtained from the CFD analysis. The CFD analysis utilized a classical pipe flow type correlation for the heat transfer rates. The experimental results provide an excellent qualitative comparison with regard to spatial distribution of the heat transfer rates as a function of nozzle configuration and igniter pressure. The results indicate that from a quantitative point of view that the pipe flow correlation gives reasonably good results. Furthermore, there appears to be a direct correlation between igniter pressure and an average Reynolds number in the star grain slot. This may lead to a simple method for modifying the convection heat transfer correlation. Calculated results of pressure-vs-time for the first 200 msec of motor firing of the Space Shuttle RSRM support the trends shown for the heat transfer rate comparisons between the cold flow CFD and experimental data.

Jenkins, Rhonald M.↗

NASA NTRS2013

Recent Development in the CESE Method for the Solution of the Navier-Stokes Equations Using Unstructured Triangular or Tetrahedral Meshes With High Aspect Ratio

In the multidimensional CESE development, triangles and tetrahedra turn out to be the most natural building blocks for 2D and 3D spatial meshes. As such the CESE method is compatible with the simplest unstructured meshes and thus can be easily applied to solve problems with complex geometries. However, because the method uses space-time staggered stencils, solution decoupling may become a real nuisance in applications involving unstructured meshes. In this paper we will describe a simple and general remedy which, according to numerical experiments, has removed any possibility of solution decoupling. Moreover, in a real-world viscous flow simulation near a solid wall, one often encounters a case where a boundary with high curvature or sharp corner is surrounded by triangular/tetrahedral meshes of extremely high aspect ratio (up to 106). For such an extreme case, the spatial projection of a space-time compounded conservation element constructed using the original CESE design may become highly concave and thus its centroid (referred to as a spatial solution point) may lie far outside of the spatial projection. It could even be embedded beyond a solid wall boundary and causes serious numerical difficulties. In this paper we will also present a new procedure for constructing conservation elements and solution elements which effectively overcomes the difficulties associated with the original design. Another difficulty issue which was addressed more recently is the wellknown fact that accuracy of gradient computations involving triangular/tetrahedral grids deteriorates rapidly as the aspect ratio of grid cells increases. The root cause of this difficulty was clearly identified and several remedies to overcome it were found through a rigorous mathematical analysis. However, because of the length of the current paper and the complexity of mathematics involved, this new work will be presented in another paper.

Chang, Sin-Chung↗

NASA NTRS2026

Mathematical Model of a Regenerative Fuel Cell for System Optimization

This thesis developed a system-level optimization model of a regenerative fuel cell (RFC) system for long-duration, off-world energy storage applications. Prior RFC design studies have typically been limited to reduced parameter sets and simplified constraints due to computational limitations relative to the number of relevant degrees of freedom. As a result, important nonlinear interactions between subsystems have not been fully captured. This work began to address that gap by developing a higher-fidelity, nonlinear optimization framework that incorporates a broader set of design variables and coupled constraints, enabling a multidimensional model that captures the coupled behavior of RFC subsystems and demonstrates the feasibility of applying optimization to such systems. An expanded system-level optimization approach was established that captures interactions between electrochemical performance, structural requirements, and storage design. This enabled a more comprehensive evaluation of trade-offs than conventional formulations. The model integrates four coupled subsystems: a fuel cell, an electrolyzer, reactant gas, and high-pressure storage tanks, and was formulated to accommodate a wide range of mission parameters, including operational time and required output power. It incorporates constraints on available solar array power, reactant mass balance between production and consumption, and pressure-dependent storage requirements. To enable reliable convergence, the optimization problem was reformulated to reduce dimensionality and improve numerical stability, with subsystem models organized for efficient evaluation. Problem dimensionality was reduced by consolidating lower-level design variables into higher-level representative quantities, and subsystem behavior was evaluated within the optimization loop. A multi-start initialization strategy was employed to mitigate sensitivity to local minima and improve solution quality, while nonlinear relationships were solved using robust numerical methods. The results showed that convergence was achieved across a range of required output power values. Specific energy reached a maximum at a critical mission power level, where the electrolyzer power matched the available solar input and operated near its voltage and current density limits. Beyond this point, further increases in required power resulted in less mass-efficient operation, increasing total system mass and reducing overall performance. The developed model represents an advancement in RFC system-level optimization by enabling analysis of a broader and more tightly coupled design space than previous considerations. While convergence behavior and computational cost remain challenges, the methods introduced improve solvability and allow inclusion of additional design variables with minimal loss of physical fidelity. However, the numerical results should not be interpreted as definitive design recommendations, as the model includes simplifying assumptions and omits several higher-order effects. Future work should extend this framework by incorporating additional subsystems and loss mechanisms, such as thermal management, parasitic power consumption, and reactant losses, to improve fidelity and ensure more representative design conclusions.

Electrochemistry↗

NASA NTRSDate not supplied

Using the Dimensionality Reduction (DR) Approach to Treat Singular and Near-Singular Source and Test Integrals on Triangles for Moment Methods

Recently, the authors presented preliminary results of an initial study of a dimensional reduction scheme for treating (near-)singular integrals (D. R. Wilton et al., “Dimensionality Reduction Approach for Treating Singular and Near-Singular Multidimensional Integrals of Electromagnetics,” 2022 URSI USNC National Radio Science Meeting, Boulder, CO, Jan. 2022). The approach reported there refined and extended several ideas appearing in a recent paper (R. R. Chang, Z. Wang, and Q. Xie, "Fast Convergent Quadrature Method for Evaluating the RWG- and SWG-Related Convolutional Integrals," IEEE Trans. Antennas Propagat., 69, Dec. 2021). That paper reported a curated collection of important, previously published results all leading to very efficient and accurate line integral methods for handling the most common (near-)singular integrals associated with triangles and tetrahedrons with RWG and SWG bases, respectively. Our contributions provided a simpler exposition as well as a more unified, systematic, and robust overall framework for deriving and applying the approach. This presentation further elucidates our extensions to the approach and broadens our initial study to examine the convergence behaviors of the various potential forms over a wider range of triangular source element shape and observation point parameters for various smoothing transformations; we also examine convergence, not just at the subtriangle level, but also overcomplete triangles. In addition, we investigate the application of the recently reported “vertex function” concept to develop faster converging test integrals (Rivero et al., “Acceleration of the Surface Test Integral Using Vertex Functions,” 2021 IEEE Int’l Symp. Ant. Propagat. and USNC-URSI Rad. Sci. Meeting,” Singapore, 4-10 Dec. 2021). Combining these separate schemes has the potential for yielding a near-optimal approach for accurately evaluating singular and near-singular integrals for moment methods.

Singular Integrals↗