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A Least-Squares Finite Element Method for Electromagnetic Scattering Problems

The least-squares finite element method (LSFEM) is applied to electromagnetic scattering and radar cross section (RCS) calculations. In contrast to most existing numerical approaches, in which divergence-free constraints are omitted, the LSFF-M directly incorporates two divergence equations in the discretization process. The importance of including the divergence equations is demonstrated by showing that otherwise spurious solutions with large divergence occur near the scatterers. The LSFEM is based on unstructured grids and possesses full flexibility in handling complex geometry and local refinement Moreover, the LSFEM does not require any special handling, such as upwinding, staggered grids, artificial dissipation, flux-differencing, etc. Implicit time discretization is used and the scheme is unconditionally stable. By using a matrix-free iterative method, the computational cost and memory requirement for the present scheme is competitive with other approaches. The accuracy of the LSFEM is verified by several benchmark test problems.

Wu, Jie↗

New digital measurement methods for left ventricular volume using real-time three-dimensional echocardiography: comparison with electromagnetic flow method and magnetic resonance imaging

AIM: The aim of this study was to investigate the feasibility and accuracy of using symmetrically rotated apical long axis planes for the determination of left ventricular (LV) volumes with real-time three-dimensional echocardiography (3DE). METHODS AND RESULTS: Real-time 3DE was performed in six sheep during 24 haemodynamic conditions with electromagnetic flow measurements (EM), and in 29 patients with magnetic resonance imaging measurements (MRI). LV volumes were calculated by Simpson's rule with five 3DE methods (i.e. apical biplane, four-plane, six-plane, nine-plane (in which the angle between each long axis plane was 90 degrees, 45 degrees, 30 degrees or 20 degrees, respectively) and standard short axis views (SAX)). Real-time 3DE correlated well with EM for LV stroke volumes in animals (r=0.68-0.95) and with MRI for absolute volumes in patients (r-values=0.93-0.98). However, agreement between MRI and apical nine-plane, six-plane, and SAX methods in patients was better than those with apical four-plane and bi-plane methods (mean difference = -15, -18, -13, vs. -31 and -48 ml for end-diastolic volume, respectively, P<0.05). CONCLUSION: Apically rotated measurement methods of real-time 3DE correlated well with reference standards for calculating LV volumes. Balancing accuracy and required time for these LV volume measurements, the apical six-plane method is recommended for clinical use.

Evaluation Studies↗

Heuristic Sonification Methods for Electromagnetic Signals Report

Sonification algorithms convert information to audible representations. The 2025 Seed Money project “Exploring Electromagnetic Signals through Sonification” seeks to create machine-learning based methods to convert electromagnetic signals to sound for human interpretation. However, as a precursor to ML-based methods, some heuristic methods have been investigated in preparation for the seed project. This report covers some example methods, applied to the “Flaming Moes” dataset of unintended radiative emissions (URE), with some simple metrics to study the device discrimination properties of the sonification as well as the “pleasantness” of the methods.

42 ENGINEERING↗

Finite-element boundary-integral simulation of thin wires and inhomogeneous penetrable bodies in subsurface multilayered anisotropic media

With the prevailing presence of drilling wells near the subsurface in mature oil and gas fields, the application of electromagnetic methods can be particularly challenging where the electromagnetic field is affected by the steel casing. In the past decades, borehole-to-surface and crosswell electromagnetic methods have been utilized for monitoring of reservoir and underground CO 2 storage. This paper presents a unified finite-element boundary-integral (FEBI) method capable of simultaneously modeling the complex electromagnetic interactions between thin metallic wires (representing steel casings) with 3D trajectory and arbitrary 3D inhomogeneous penetrable bodies (such as CO 2 plumes or hydrocarbon reservoirs) within anisotropic multilayered subsurface environments. Unlike existing approaches that treat these components separately or require dense discretization, or are limited to vertical wells, our unified formulation preserves flexible electromagnetic coupling while delivering improved computational efficiency. Assuming the background formation is multilayered anisotropic media, the surface integral equation method is applied to model the thin wires and boundaries of the inhomogeneous bodies. Meanwhile, the finite element method is applied to model the volume of inhomogeneous bodies. Here, the performance of the proposed FEBI method is assessed through comparison with reference numerical results and its practical significance is demonstrated through CO 2 plume monitoring scenarios.

97 MATHEMATICS AND COMPUTING↗

Numerical methods for analyzing electromagnetic scattering

Numerical methods to analyze electromagnetic scattering are presented. The dispersions and attenuations of the normal modes in a circular waveguide coated with lossy material were completely analyzed. The radar cross section (RCS) from a circular waveguide coated with lossy material was calculated. The following is observed: (1) the interior irradiation contributes to the RCS much more than does the rim diffraction; (2) at low frequency, the RCS from the circular waveguide terminated by a perfect electric conductor (PEC) can be reduced more than 13 dB down with a coating thickness less than 1% of the radius using the best lossy material available in a 6 radius-long cylinder; (3) at high frequency, a modal separation between the highly attenuated and the lowly attenuated modes is evident if the coating material is too lossy, however, a large RCS reduction can be achieved for a small incident angle with a thin layer of coating. It is found that the waveguide coated with a lossy magnetic material can be used as a substitute for a corrugated waveguide to produce a circularly polarized radiation yield.

Lee, S. W.↗

A Continuous-Discontinuous Galerkin Method for Electromagnetic Simulations Based on an All-Frequency Stable Formulation

In this paper, a potential-based partial-differential formulation, called the all-frequency stable formulation, is presented for the accurate and robust simulation of electromagnetic problems at all frequencies. Due to its stability from (near) dc to microwave frequencies, this formulation can be applied to simulate wide-band and multiscale problems without encountering the infamous low-frequency breakdown issue or applying basis function decompositions such as the tree-cotree splitting technique. To provide both efficient and flexible numerical solutions to the electromagnetic formulation, a mixed continuous-discontinuous Galerkin (CDG) method is proposed and implemented. In regions with homogeneous media, the continuous Galerkin method is employed to avoid the introduction of duplicated degrees of freedom (DoFs) on the elemental interfaces, while on the interfaces of two different media, the discontinuous Galerkin method is applied to permit the jump of the normal components of the electromagnetic fields. Numerical examples are provided to validate and demonstrate the proposed numerical solver for problems in a wide electromagnetic spectrum.

Yan, Su↗

Apparatus and Methods for Mitigating Electromagnetic Emissions

Apparatus, methods, and other embodiments associated with mitigation of magnetic fields are described herein. In an embodiment, a method for mitigating an electromagnetic field includes positioning a mitigating coil around a linear alternator of linear motor so that the mitigating coil is coaxially located with an alternator coil; arranging the mitigating coil to generate a field to mitigate an electromagnetic field generated by the alternator coil; and passing an induced current from the alternator coil through the mitigating coil.

Geng, Steven M.↗

Apparatus and Methods for Mitigating Electromagnetic Emissions

Apparatus, methods, and other embodiments associated with mitigation of magnetic fields are described herein. In an embodiment, a method for mitigating an electromagnetic field includes positioning a mitigating coil around a linear alternator of linear motor so that the mitigating coil is coaxially located with an alternator coil; arranging the mitigating coil to generate a field to mitigate an electromagnetic field generated by the alternator coil; and passing an induced current from the alternator coil through the mitigating coil.

Geng, Steven M.↗

The finite-difference time-domain (FD-TD) method for electromagnetic scattering and interaction problems

The formulation and recent applications of the finite-difference time-domain (FD-TD) method for the numerical modeling of electromagnetic scattering and interaction problems are considered. It is shown that improvements in FD-TD modeling concepts and software implementation often make it a preferable choice for structures which cannot be easily treated by conventional integral equations and asymptotic approaches. Recent FD-TD modeling validations in research areas including coupling to wires and wire bundles in free space and cavities, scattering from surfaces in relativistic motion, inverse scattering, and radiation condition theory, are reviewed. Finally, the advantages and disadvantages of FD-TD, and guidelines concerning when FD-TD should and should not be used in high-frequency electromagnetic modeling problems, are summarized.

Taflove, A.↗

An Implicit Characteristic Based Method for Electromagnetics

An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the characteristic differencing enables a two-factor approximate factorization that retains its unconditional stability in three space dimensions, and it does not require solution of tridiagonal systems. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both uniform and nonuniform grids. The explicit Finite Difference Time Domain Method (FDTD) algorithm is used as a convenient reference algorithm for comparison. The one-dimensional results indicate that for low frequency problems on a highly resolved uniform or nonuniform grid, this LU/AF algorithm can produce accurate solutions at Courant numbers significantly greater than one, with a corresponding improvement in efficiency for simulating a given period of time. This approach appears promising for development of dispersion optimized LU/AF schemes for three dimensional applications.

Beggs, John H.↗

Further evaluation of the constrained least squares electromagnetic compensation method

Technologies exist for construction of antennas with adaptive surfaces that can compensate for many of the larger distortions caused by thermal and gravitational forces. However, as the frequency and size of reflectors increase, the subtle surface errors become significant and degrade the overall electromagnetic performance. Electromagnetic (EM) compensation through an adaptive feed array offers means for mitigation of surface distortion effects. Implementation of EM compensation is investigated with the measured surface errors of the NASA 15 meter hoop/column reflector antenna. Computer simulations are presented for: (1) a hybrid EM compensation technique, and (2) evaluating the performance of a given EM compensation method when implemented with discretized weights.

Smith, William T.↗

Investigation of finite element: ABC methods for electromagnetic field simulation

The mechanics of wave propagation in the presence of obstacles is of great interest in many branches of engineering and applied mathematics like electromagnetics, fluid dynamics, geophysics, seismology, etc. Such problems can be broadly classified into two categories: the bounded domain or the closed problem and the unbounded domain or the open problem. Analytical techniques have been derived for the simpler problems; however, the need to model complicated geometrical features, complex material coatings and fillings, and to adapt the model to changing design parameters have inevitably tilted the balance in favor of numerical techniques. The modeling of closed problems presents difficulties primarily in proper meshing of the interior region. However, problems in unbounded domains pose a unique challenge to computation, since the exterior region is inappropriate for direct implementation of numerical techniques. A large number of solutions have been proposed but only a few have stood the test of time and experiment. The goal of this thesis is to develop an efficient and reliable partial differential equation technique to model large three dimensional scattering problems in electromagnetics.

Chatterjee, A.↗

Low-Frequency Electromagnetic Exploration for Groundwater on Mars

Water with even a small amount of dissolved solids has an electrical conductivity orders of magnitude higher than dry rock and is therefore a near-ideal exploration target on Mars for low frequency, diffusive electromagnetic methods. Models of the temperature- and frequency-dependent electrical properties of rock-ice-water mixtures are used to predict the electromagnetic response of the Martian subsurface. Detection of ice is difficult unless it is massively segregated. In contrast, liquid water profoundly affects soundings, and even a small amount of adsorbed water in the cryosphere can be detected. Subcryospheric water is readily distinguishable at frequencies as low as 100 Hz for fresh water to 10 mHz for brines. These responses can be measured using either natural or artificial sources. Ultra low frequency signals from solar wind and diurnal-heating perturbations of the ionosphere are likely, and disturbances of regional crustal magnetic fields may also be observable. Spherics, or extremely to very low frequency signals from lightning discharge, would provide optimal soundings; however, lightning may be the least likely of the possible natural sources. Among the active techniques, only the time-domain electromagnetic (TDEM) method can accommodate a closely spaced transmitter and receiver and sound to depths of hundreds of meters or more. A ground- or aircraft-based TDEM system of several kilograms can detect water to a depth of several hundred meters, and a system of tens of kilograms featuring a large, fixed, rover- or ballistically deployed loop can detect water to several kilometers depth.

Grimm, Robert E.↗

Induced Polarization of Clayey Rocks and Soils: Non‐Linear Complex Conductivity Models

Abstract The past decades have witnessed the increased applications of induced polarization (IP) method in the critical zone studies with ubiquitous clay minerals. Although IP outperforms traditional electrical and electromagnetic methods through its unique ability to measure quadrature conductivity, the nonlinearity that quadrature conductivity behaves with salinities and frequencies greatly tortures IP practitioners, as (a) salinity‐dependency makes the quadrature conductivity a varyingly unstable parameter to quantitatively estimate hydraulic properties and clay content; (b) frequency‐dependent Cole‐Cole and Debye/Warburg decomposition models, although mathematically sound, physically mingle the properties of pore water and clay minerals and are empirical in nature. From basic principles, we demonstrate that quadrature conductivity remains a hybrid property involving both clay and water, and develop relevant models to distinguish them. Our models are validated by theories, experiments, simulations, and comparisons, all of which proclaim considerable advantages over previous models and offer the prospect of quantitative applications.

58 GEOSCIENCES↗

The Importance of Nightside Magnetometer Observations for Electromagnetic Sounding of the Moon

Understanding the structure and composition of the lunar interior is a fundamental goal in furthering our knowledge of the formation and subsequent evolution of the Earth-Moon system. Among various methods, electromagnetic sounding is a valuable approach to constraining lunar interior structure. Recent analyses of plasma and field observations provide a wealth of understanding about the dynamics of the lunar plasma environment. To perform Time Domain EM (TDEM) Sounding at the Moon, the first step is to characterize the dynamic plasma environment, and to be able to isolate geophysically induced currents from concurrently present plasma currents. The TDEM Sounding transfer function method focuses on analysis of the nightside observations when the Moon is immersed in the solar wind. This method requires two simultaneous observations: an upstream reference measuring the pristine solar wind, and one downstream at or near the lunar surface. This method was last performed during Apollo and assumed the induced fields on the nightside of the Moon expand as in an undisturbed vacuum within the wake cavity. Our results indicate that EM sounding of airless bodies in the solar wind must be interpreted via self-consistent plasma models in order to untangle plasma and induced field contributions, with implications not only at the Moon but at all airless bodies exposed to the solar wind. Nightside TDEM sounding has the capability to advance the state of knowledge of the field of lunar science. This requires magnetometer operations to withstand the harsh conditions of the lunar night.

Haviland, H. Fuqua↗

Radiative cooling textiles using industry-standard particle-free nonporous micro-structured fibers

Abstract Thermal radiation is a major dissipative pathway for heat generated by the human body and offers a significant thermoregulation mechanism over a wide range of conditions. We could use this in garment design to enhance personal cooling, which can improve the wearing comfort of garments or even result in energy savings in buildings. At present, however, radiative cooling has received insufficient attention in commercial design and production of textiles for wearable garments. Textiles that efficiently transmit the radiative heat were recently demonstrated, but either do not utilize standard weaving and knitting processes for wearable garments or require substantial process modifications. Here, we demonstrate the design and implementation of large-scale radiative cooling textiles for localized cooling management and enhanced thermal comfort using industry-standard particle-free nonporous micro-structured fibers that are fully compatible with standard textile materials and production methods. The micro-structured fibers, yarns and fabrics are part of a hierarchical photonic structure design that renders the textiles highly infrared transparent (up to > 0.8) while assuring visual opacity (up to 0.99). We design radiative cooling textiles with first-principles electromagnetic methods and fabricate them using commercial textile materials and formation facilities. Our “fabless” approach is confirmed by very good quantitative agreement between design and measurements. The resulting fabrics exhibit wearability properties expected of wearable textiles, and lower skin temperature by ≥ 3 °C compared to conventional textiles, which offers the potential for > 30 % energy savings in buildings and increases wearing comfort by significantly reducing the reliance on latent heat dissipation for thermoregulation.

Catrysse, Peter B.↗