Plane wave scattering from a partially coated air platform using a non-overlapping surface integral equation domain decomposition method

Printed circuits in bounded media encompass a wide range of practical structures such as discontinuities in waveguides, planar circuits embedded in shielded multilayered media or even two-dimensional printed periodic structures. The Electromagnetic (EM) modeling of printed circuits in layered bounded media is performed via an Integral Equation (IE) technique. Green's functions (GFs) are specially defined to satisfy both the Boundary Conditions (BCs) imposed by the layered media and by the transverse boundary enclosing the entire structure. Finally, a system of IEs on the equivalent sources can be solved numerically by means of the Method of Moments (MoM). Each of the problems enumerated above has already been solved by other authors using IE-MoM techniques. Nevertheless, our formulation introduces a unified approach applicable to all the aforementioned problems. Due to the symmetry presented by a bounded layered media, the GF problem can be reduced into a two-dimensional transverse boundary problem and a one-dimensional transmission line problem in the normal direction. Both problems can be treated independently. This thesis proposes and fully develops an efficient technique that encompasses different laterally bounded multilayered problems with a seamless transition between them. The method is based on a modal representation of the transverse boundary problem and on the expansion of the equivalent surface currents by zero-curl & constant-charge Basis Functions (BFs). It offers a unified and versatile approach that, on one hand eliminates redundancy in the formulation and on the other hand simplifies each particular problem to the evaluation of constant coefficients or basic line integrals. Analytical solutions can be found for the combination of linear subsectional basis functions in rectangular and circular Perfect Electric Conductor (PEC) boundaries as well as for periodic lattices. This thesis then solves the problem of transmission line model in the longitudinal direction by proposing an efficient algorithm that guarantees numerical stability under a variety of known critical conditions where other already known formulations fail. In addition, it introduces alternate equivalent expressions of this formulation that allow new interpretations of the problem. Due to its practical interest, the method is applied for the EM modeling of multilayered boxed printed circuits. This motivated the implementation of a dedicated software tool for the efficient analysis of these topologies including losses. Extensive numerical experiments have been carried out to assess the validity of the aforementioned theory and some properties of test-structures (losses, mesh, etc).

BACKGROUND: Acromioclavicular (AC) joint dislocation is most frequently encountered in contact sports and is far more common in males. Grade-III AC dislocation involves complete loss of contact between the clavicle and acromion secondary to the total disruption of both the AC and coracoclavicular ligaments, with loss of vertical and horizontal stability, respectively. The use of hook plate on open reduction and internal fixation of the AC joint dislocation had a little adverse effect on shoulder function and is an effective method for the treatment of AC joint dislocation. Hence, this retrospective study was carried out to assess the clinical and functional outcome of AC joint injuries treated with hook plate.\nAIM: The aim of this study is to assess and document the clinical and functional outcome of AC joint dislocation with or without lateral end clavicle fracture treated with hook plate.\nMATERIALS AND METHODS: This retrospective study of patients with Rockwood Type III AC joint disruption (dislocation) who were treated in our hospital. During the period from July 2013 to July 2018, a total of 33 patients with Type III AC joint disruption with or without associated lateral end clavicle fractures were included in this study, with 26 males and 7 females. The functional outcome was assessed using the CONSTANT scoring system during follow-up after hook plate fixation at 4 weeks, 3 months, 6 months, and 12 months.\nRESULTS: Thirty three patients with AC joint disruption were participated in the study after meeting the inclusion and exclusion criteria. There were 26 males (78.8%) and 7 females (21.2%) with a mean age of 44.7 years, eight patients had an associated lateral end clavicle fracture. All the patients were fixed with hook plate were followed up for a period of 1 year postoperatively. The mean Constant score improved progressively from a preoperative score of 44.5 to postoperative score of 68.3 at 4 weeks, 77.9 at 3 months, 89.4 at 6 months, and 93.3 at 12 months.\nCONCLUSIONS: In the current study, we conclude that the surgical and functional outcomes after AC joint stabilization with or without lateral end clavicle fractures using hook plate fixation yield satisfactory results. The hook plate also provides good horizontal, rotational, and vertical stability. Furthermore, the maintenance of reduction by the hook plate was significantly superior compared to the other modes of treatment. The hook plate also facilitates early mobilization and prevents stiffness of the shoulder joint.

Dislocation of the acromioclavicular (AC) joint is a common injury seen in young adults. The objective is to describe a surgical technique that can restore the horizontal and vertical stability of the AC joint. This is a surgical technique with anatomical and biological reconstruction of the CC and AC ligaments, using an allograft. Two bone tunnels are made in the clavicle, passing the lateral end of the graft below the acromion; then the two ends are fixed with 2 bio-absorbable screws, restoring vertical and horizontal stability. This procedure allows to restore the vertical and horizontal stability of the AC joint. Follow up studies are required to report functional and radiological results, in order to ensure advantages compared to existing techniques.

Electromagnetic (EM) scattering from perfect electric conductor (PEC) object embedded between two rough interfaces is investigated utilizing method of moments (MoM) for both TE and TM polarizations. Theoretical formulations of EM scattering model considered in this paper is presented and the total fields and their derivatives are solved numerically by employing MoM. The rough surfaces are modeled as realizations of a Gaussian random process with the Gaussian spectrum, while the tapered incident wave is chosen to reduce the truncation error. The influences of characteristic parameters of the rough surfaces, the relative permittivity of the medium, as well as the average height between the two rough surfaces, on the bistatic scattering coefficient (BSC) are discussed.

The electromagnetic radiation and scattering from a body of revolution (BOR) of arbitrary shape have been widely discussed during several decades. The objects can contain perfect electric conductor (PEC), homogeneous dielectric bodies, coated conducting bodies and combined dielectric and conducting bodies [1][2]. The traditional method used to solve BOR with integral equations is the Method of Moments (MoM). And the computational time consumed in solving the integral equation of the BOR problem depends on the evaluation of modal Green's function (MGF), which is a time consuming process. Some research has been done to reduce this computational complexity. For example, Abdelmageed used spherical Bessel function to expansion to evaluate the MGF [3]. In this work, we extend the fast inhomogeneous plane wave algorithm (FIPWA) [4][5] to accelerate the computation of the MoM for composite homogeneous dielectric and conducting bodies of revolution. PMCHW [6] (Poggio-Miller-Chang-Harrington-Wu) equations and electric field integral equation are used for solving the homogeneous dielectric and conducting objects, respectively. Both the memory requirement and CPU time are reduced for large-scale BOR problems. Numerical results are given to demonstrate the validity and efficiency of the FIPWA.

A non-overlapping Schwarz domain decomposition method with high-order finite elements for flow acoustics

Efficient analysis of electromagnetic-wave responses from electrically large complex objects is a crucial but difficult topic in many applications of electromagnetic engineering. Among various numerical methods, the Method of Moments (MoM) solves for surface- or volume-distributed equivalent currents, which are expanded in terms of basis functions. In this paper, the traveling-wave phase variation has been incorporated into the basis functions to enhance their capability of describing the equivalent surface currents induced over surfaces of perfect electric conductors (PECs). A rigorous derivation is first given as physical insight, to show that the induced surface current is composed of a traveling-wave term and several standing-wave terms. A phase-extracted basis function (PEBF) is then proposed to describe the traveling current wave, and is applied in solving the electromagnetic scattering from three-dimensional (3D) PEC objects with smooth surfaces. By hybridizing the phase-extracted basis function with higher-order hierarchical basis functions, a moving standing-wave (MSW) basis function is further introduced to describe both the traveling-wave and the standing-wave terms in the induced surface current. It is shown from several numerical examples that the moving standing-wave basis function has excellent performance for solving electromagnetic scattering from three-dimensional PEC objects with both smooth and non-smooth surfaces, as well as for three-dimensional PEC cavities. After that, the unique properties of the phase-extracted basis function are utilized in the “sparsification” of the MoM matrix, and in the fast calculation of wideband responses. With the aid of the phase-extracted basis function and the moving standing-wave basis functions, the total memory requirements and the computational time can be significantly reduced, while numerical solutions can be obtained with good accuracy. The advantages of the phase-extracted basis functions and the moving standing-wave basis functions in predicting electromagnetic scattering from electrically large complex objects are summarized before the conclusions are drawn.

Numerical methods to analyze waveguides have been investigated long time, and many methods are proposed.We have proposed two types of integral equations, boundary integral equation and volume integral equation, to analyze two-dimensional slab waveguides.Each integral equation is solved by the boundary element method or the method of moments, combined with equations that is derived with the orthogonality of modes [1], [2].To validate the proposed methods, we analyzed two-port slab waveguides such as step waveguide, triangular rib waveguide, gap waveguide, and grating waveguide.The numerical results were in good agreement with those of published papers.

A method is introduced for reducing the exorbitant dependence on computer storage and solution time in the method of moments (MoM) for electrically large electromagnetic (EM) scattering problems. The unknown surface currents on large, smooth parts of a perfect electrical conductor (PEC) scatterer are expressed by an efficient set of linearly phased surface current basis functions. The phasefront characteristics of the surface currents are numerically extracted from known current samples obtained from a lower-frequency solution of the same configuration. The use of such basis functions for efficiently representing the surface currents that are constructed in terms of linearly phased currents at higher frequencies is justified by considering the form of the surface currents predicted by high-frequency asymptotic ray methods. The procedure for extracting the current phasefronts is purely numerical, obviating computationally expensive and nonrobust operations such as ray-tracing, and thus, is amenable to general purpose scattering codes. The new MoM with linearly phased basis functions is shown to greatly relieve the storage and solution time of the conventional MoM while accurately reproducing the induced surface currents and scattered fields of some chosen targets.

Two sets of integral equations are obtained for electromagnetic (EM) scattering by isotropic two-dimensional chiral bodies embedded in free space which can be attached to a perfect electric conducting (PEC) body. For the special case of homogeneous chiral media, integral equations (IEL) are obtained in terms of only line integrals involving the free-space and chiral media Green's functions. For the more general case where the chiral media is inhomogeneous, the integral equations (IESL) are expressed in terms of a combination of surface and line integrals involving only the free-space Green's function. To validate the results obtained here, the two sets of integral equations are solved by means of the moment method technique. In fact, the IEL equations are solved exactly for two canonical geometries, whereas the IESL equations are approximately solved and compared with an exact eigenfunction solution.

A battery track engineering vehicle faces challenges such as derailment and other safety concerns when navigating an R20m minimum radius curve, primarily owing to its low vertical and horizontal stabilities. To address these issues, a methodology integrating genetic optimization algorithms with a rigid and flexible coupled multi-body dynamics simulation is proposed to optimize the primary suspensions of the bogie of the vehicle. Initially, a multi-objective optimization model combining rigid and flexible coupled multi-body dynamics of battery track engineering vehicles with a genetic optimization algorithm was formulated. Subsequently, the optimal Latin hypercube design was applied to analyze the sensitivity of vertical and horizontal stability to various suspension parameters. Finally, a non-dominated sorting genetic algorithm (NSGA-II) and an archive-based micro genetic algorithm (AMGA) were applied to optimize the primary suspensions to enhance stability. Consequently, a set of optimal suspension parameter combinations was obtained. A notable enhancement was observed in the lateral stability of the optimized battery track engineering vehicles by 23.33% and in the vertical stability by 3.5% when traversing the R20m minimum radius curve, thereby establishing a theoretical foundation for further improving the running safety of railway vehicles and resolving the shortcomings of less research on the smallest radius curve.

High angle-of-attack flight regime research is currently being conducted for modern fighter aircraft at the NASA Ames Research Center's Dryden Flight Research Facility. This flight regime provides enhanced maneuverability to fighter pilots in combat situations. Flight research data are being acquired to compare and validate advanced computational fluid dynamic solutions and wind-tunnel models. High angle-of-attack flight creates unique aerodynamic phenomena including wing rock and buffet on the airframe. These phenomena increase the level of excitation of the structural modes, especially on the vertical and horizontal stabilizers. With high gain digital flight-control systems, this structural response may result in an aeroservoelastic interaction. A structural interaction on the X-29A aircraft was observed during high angle-of-attack flight testing. The roll and yaw rate gyros sensed the aircraft's structural modes at 11, 13, and 16 Hz. The rate gyro output signals were then amplified through the flight-control laws and sent as commands to the flaperons and rudder. The flight data indicated that as the angle of attack increased, the amplitude of the buffet on the vertical stabilizer increased, which resulted in more excitation to the structural modes. The flight-control system sensors and command signals showed this increase in modal power at the structural frequencies up to a 30 degree angle-of-attack. Beyond a 30 degree angle-of-attack, the vertical stabilizer response, the feedback sensor amplitude, and control surface command signal amplitude remained relatively constant. Data are presented that show the increased modal power in the aircraft structural accelerometers, the feedback sensors, and the command signals as a function of angle of attack. This structural interaction is traced from the aerodynamic buffet to the flight-control surfaces.

We present scattering computations performed with a newly developed stable hybridization of the finite element method (FEM) and the finite-difference time-domain (FDTD) scheme, which is based on Nitsche's method. This hybrid has not been tested on scattering problems previously, and here we compute the radar cross-section (RCS) for three different targets: (i) the perfect electric conducting (PEC) sphere, (ii) the NASA almond, and (iii) a generic aircraft called RUND. In order to assess the discretization errors associated with the hybrid, we provide comparisons with established results and techniques: (i) the Mie-series for the PEC sphere, (ii) the method of moments (MoM) implemented in the commercial code FEKO, and (iii) a stable FEM–FDTD hybrid that exploits pyramids and a curl-conforming representation of the electric field. The bistatic RCS for the PEC sphere shows second order convergence towards the analytical solution and a relative error of 2% is achieved for about 20 points per wavelength. The NASA almond has a low monostatic RCS in its horizontal plane, which makes it a good benchmark problem for scattering computations. It features a sharp tip and, as a consequence, the order of convergence for the RCS is lowered. Given a careful convergence study for the NASA almond, we achieve a highly accurate monostatic RCS by means of extrapolation and this result is state-of-the-art in the open literature.

The boundary integral equations (BIEs), in their original forms, which govern the electromagnetic (EM) wave scattering in three-dimensional space contain at least a hypersingularity (1/R/sup 3/) or a Cauchy-singularity (1/R/sup 2/), usually both. Thus, obtaining reliable numerical solutions using such equations requires considerable care, especially when developing systematic numerical integration procedures for realistic problems. Regularized BIEs for the numerical computation of time-harmonic EM scattering fields due to arbitrarily-shaped scatterers are introduced. Two regularization approaches utilizing an isolation method plus a mapping are presented to remove all singularities prior to numerical integration. Both approaches differ from all existing approaches to EM scattering problems. Both work for integral equations initially containing either hypersingularities or Cauchy-singularities, without the need to introduce surface divergences or other derivatives of the EM fields on the boundary. Also, neither approach is limited to flat surfaces nor flat-element models of curved surfaces. The Muller linear combination of the electric- and magnetic-field integral equations (EFIE) and (MFIE) is used to avoid the resonance difficulty that is usually associated with integral equation-based formulations. Some preliminary numerical results for EM scattering due to single and multiple dielectric spheres are presented and compared with analytical solutions.

In this paper, an optimization technique combining non-conformal integral equation domain decomposition method (IE-DDM) and particle swarm optimization (PSO) is presented for the design of antenna on platform. The antenna and the platform can be decomposed into different closed sub-domains according to design requirements and the DDM is used to compute the scattering from antenna on platform. Meanwhile PSO is used to find the best antenna location. Numerical example is presented to demonstrate the efficiency of the present method.