Method Of Moments Formulation Research Articles

Near Field Scatter from a Body of Revolution

Better understanding of electromagnetic wave propagation through vegetation and forest environments can be achieved with the aid of modeling and simulation. Specifically, modeling the coherent summation of electromagnetic waves due to both single scatter and multi-scatter effects. To accurately perform simulations in lower frequency bands, S-band and below, the Body of Revolution (BOR) Method of Moments (MoM) must be extended to calculate the scattered electric and magnetic near-fields from BOR in the presence of a plane wave. The near field interactions specifically occur during the various higher order scattering harmonics, i.e. 2nd order and greater harmonics. Additionally, the method must accurately capture scattered fields in the presence of a non-plane wave incident upon BOR. The focus of this study is modeling lossy dielectric BOR that are characteristic of vegetation and forest environments, e.g., cylinders representing tree branches. Although the formal electric and magnetic field scattering definitions are known, this report presents analytical formulations of near field scattering from BOR for this implementation of BOR-MoM. The scattered-field extensions are validated using the commercial software FEKO©, which simulates electromagnetic-wave scattering in 3D using MoM formulation of scattered fields.

A φ-divergence based finite element moment method for the polyatomic ES-BGK Boltzmann equation

Bonafide numerical simulations of transport phenomena in rarefied gases are becoming increasingly important in science and engineering. To enhance the accuracy of the rarefied-gas model, it is important to account for the internal structure of the gas molecules and exceed the standard monatomic description. A suitable model for polyatomic rarefied-gas flows that balances between accuracy and complexity is the polyatomic ES-BGK Boltzmann equation. In this work we consider numerical approximation of the ES-BGK Boltzmann equation based on a Method of Moments (MoM) approximation in the velocity/internal-energy dependence, and DGFEM approximation in the spatial dependence. In the MoM setting, only two moments have to be considered in internal-energy dependence to capture the correct macroscopic gas properties, viz. the thermal conductivity, the adiabatic coefficient and the shear and dilational viscosity. In the presentation of the method, we focus specifically on the evaluation of the integrals in the velocity and intrinsic-variable dependence appearing in the MoM formulation and on linearization of the formulation. We present numerical results for the heat flux between two parallel heated plates, mass flow in a micro-channel, a poly-atomic lid-driven cavity problem, and rarefied-gas flow around a sphere. The computed results are compared with corresponding theoretical and experimental results. The results support the suitability of the FEM-MoM approximation of the ES-BGK Boltzmann equations as a model for predicting transport phenomena in rarefied-gas flows.

The Logarithmically-non-uniform Helix Antenna Mounted Above a Finite Ground Plane

In this paper the influence of ground plane size on the performance characteristics of a thin-wire helical antenna characterized by a logarithmically varying turns spacing, and mounted above a circular ground plane of finite extent, is systematically investigated. The moment-method formulation utilized in the paper involves a wire-grid model for the ground plane as well as explicit expressions, deriving from a vector potential approach, for the radiation fields of this ‘loghelix’. Subsequent computational results obtained for a candidate 8-turn ‘loghelix’ axial-mode ˀantenna using various combinations of ‘logarithmic variation factor’ and ground plane size, very clearly reveal that limiting the size of the ground plane to finite dimensions significantly improves antenna performance. Maximum gain obtainable, for example, emerged as 16.45dBi when a finite ground plane is utilized, as against 13.55dBi for the corresponding antenna, backed by an infinite ground plane. The associated axial ratio performance is characterized by for the finite ground case, and , for the infinite ground plane case. A notable finding of the investigations is that the dip that typically features in the power gain profiles of antenna structures backed by finite ground planes will be eliminated, when ground plane size, relative to antenna size exceeds a certain minimum.

Novel techniques for numerically efficient solution of multiscale problems in computational electromagnetics

AbstractMultiscale problems in numerical electromagnetics are becoming increasingly common with the advent and widespread usage of compact mobile phones, body area networks, small and nano antennas, sensors, high‐speed interconnects, integrated circuits, and complex electronic packaging structures, to name just a few commercial applications. Numerical electromagnetic modeling and simulation of structures with multiscale features are highly challenging due to the fact that electrically small as well as large features are simultaneously present in the model that demands for discretization of the computational domain such that the number of degrees of freedom is very large, thus levying a heavy burden on the computational resources. The multiscale nature of a given problem also exacerbates the challenge of generating very fine meshes that do not introduce instabilities or ill‐conditioned behaviors.In this paper, we present novel techniques for an efficient solution of multiscale problems in the time‐domain. The proposed techniques handle arbitrarily shaped objects with fine features by using the dipole moment–based method of moments (MoM) type formulation in the MoM domain and electrically large objects in the finite‐difference time‐domain (FDTD) domain. Scattered fields in the MoM domain are obtained in closed forms and directly in the time‐domain at the desired observation points on a planar interface, which are combined with the conventional FDTD update equations. The time‐domain scattered fields computed by using the MoM formulations presented herein are stable in their implementation.

Surface-Volume-Surface Electric Field Integral Equation for Solution of Scattering Problems on 3-D Dielectric Objects in Multilayered Media

Generalization of the surface-volume-surface electric field integral equation (SVS-EFIE) for the solution of electromagnetic scattering problems on 3-D dielectric objects embedded in multilayered media is proposed. While having only a single unknown surface current density on the boundary of the scatterer, the SVS-EFIE also features only electric field dyadic Green’s functions in its integral operators. This property in conjunction with Michalski–Zheng’s formulation of the multilayered media electric field Green’s function allows for the formulation of SVS-EFIE in the mixed potential form for the solution of the scattering problems in layered media. In the proposed method of moments (MoM) discretization scheme, the gradient and divergence operators associated with the electric field Green’s function are shifted to the basis and test functions of the discretized integral operators. As a result, the proposed formulation features no derivatives acting on the components of the layered media dyadic Green’s function, hence, substantially alleviating the numerical evaluation of the pertinent Sommerfeld integrals. The proposed MoM formulation scalarizes reaction integrals containing the multilayered media dyadic Green’s function through the use shape function-based definition of the basis and test functions. The resultant MoM integrals feature no singularities stronger than $1/R$ . The validation of the proposed SVS-EFIE formulation and its MoM discretization is performed through a comparison of the computed fields against the fields produced using commercial electromagnetic analysis software.

Accurate Evaluation of Field Interactions Between Cable Harness and Vehicle Body by a Multiple Scattering Method

Interactions between cable harness and vehicle body can be calculated using the full-wave method-of-moments (MoM) formulation. Although the full-wave MoM formulation can help us to calculate these interactions with great accuracy, it can be fairly time consuming when dealing with complex wire structures. On the other hand, the conventional multiconductor transmission-line theory can be used to obtain a simple model of the interactions, but only the effect of the transmission-line (TL)-mode current can be accounted for in this method. Starting with the complete electrical field integral equations, the current on a two-conductor thin wire structure due to incident field illumination can be decomposed into TL and antenna modes. Both modes can be solved using a SPICE solver in the form of Telegrapher's equations. A proposed multiple scattering (MS) method based on a hybrid of TL and surface MoM can then be used to calculate interactions between thin wire structures, such as cable harness, and conductive surfaces, such as vehicle body. A test case shows that wire current computation using the proposed MS method takes less time but reaches the same accuracy compared to the full-wave MoM.

Comparison of iterative solvers for electromagnetic analysis of plasmonic nanostructures using multiple surface integral equation formulations

The electromagnetic behavior of plasmonic structures can be predicted after discretizing and solving a linear system of equations, derived from a continuous surface integral equation (SIE) and the appropriate boundary conditions, using a method of moments (MoM) methodology. In realistic large-scale optical problems, a direct inversion of the SIE–MoM matrix cannot be performed due to its large size, and an iterative solver must be used instead. This paper investigates the performance of four iterative solvers (GMRES, TFQMR, CGS, and BICGSTAB) for five different SIE–MoM formulations (PMCHWT, JMCFIE, CTF, CNF, and MNMF). Moreover, under this plasmonic context, a set of suggested guidelines are provided to choose a suitable SIE formulation and iterative solver depending on the desired simulation error and available runtime resources.

MoM과 PMCHW 적분방정식 융합에 의한 유전체 육면체의 유도전류 계산

In this paper, we analysis the electromagnetic scattering of an arbitrary shape dielectric cube subjected to plane wave incidence in three dimensions. MoM(Method of Moments)in which a surface of a body is divided with small triangular patches and equivalence principle are used to fuse the PMCHW(Poggio, Miller, Chang, Harrington, and Wu) Integral Equations with respect to equivalent currents on a dielectric body. Triangular patch and loop-patch basis functions that is robust in wide frequency ranges are used for MoM formulations. Proposed method is very useful to analysis the induced current of arbitrary dielectric bodies and numerical results for a dielectric cube are presented.

Fast analysis of metallic antennas by parallel moment method implemented on CUDA

In this paper a modeling technique enabling the fast analysis of antenna arrangements built-up from metallic parts is presented in detail. A calculation method which accelerates the solution of integral equations discretized by the Method of Moments have been implemented in a massively parallel computing environment, a general purpose video card (GPU). Rao-Wilton-Glisson edge basis functions are used to expand surface currents, while radiated field is computed using the dipole model. Since the entire computation takes place on the GPU exclusively, the overall computational time could be significantly reduced. To obtain such an acceleration, a novel computational technique is proposed for the filling of the impedance matrix, which takes full advantage of the given platform. Analysis of antenna structures can be made very efficiently using the frequency domain (FD) integral equationformulation, discretizedby the Methodof Moments (MoM) (1). The FD-MoM implementation employing surface patch modeling (2) of the (infinitesimally thin) metal surfaces lacks the incorporation of the surrounding air. This is a major advantage over Finite Element Method (FEM), where the surrounding air is part of the model and therefore must be discretized as well. As the computational complexity (demand) is proportional to the number of discrete geometrical elements constituting the model, in the latter case the Degrees of Freedom (DoF) of the resulting linear equation system to be finally solved is significantly higher than in the preceding one. Furthermore, as the correct behavior for the radiation condition is automatically incorporated in the moment method, there is no need for special termination -by e.g., a Perfectly Matched Layer (PML) or Absorbing Boundary Condition (ABC)- of the problem domain, as in FEM. Unfortunately, the advantagesof MoM are spoiled by its well-known high demands for computational resources in terms of memory capacity and CPU time. Although spectacular reduction techniques like the so-called multi-level fast multiple Method (MLFMM) exist, these can not be applied to all practical problems, hence often the tedious standard MoM formulation is to be utilized. In this paper the acceleration of the standard MoM method is carried out using a massively parallel computing environment, the GPU. Although several similar works have already been published (3,4),

The Complete Surface-Current Distribution in a Normal-Mode Helical Antenna

An investigation of the surface-current distribution in a normal-mode helical antenna (NMHA) is reported. This enables precise prediction of the performance of normal-mode helical antennas, since traditional wire-antenna simulations ignore important details. A Moment-Method formulation was developed, using two geometrically orthogonal basis functions to represent the total nonuniform surface-current distribution over the wire of the helix. Extended basis functions were used to reliably treat the discontinuity of the current at the free ends. A surface kernel was used all over the antenna's structure. The surface-current distribution was computed for different antenna geometries, such as dipoles, loops, and helices. For helices, the currents were investigated for different pitch distances and numbers of turns. It was found that the axially-directed component of the current distribution around the surface of the wire was highly nonuniform, and that there was also a significant circumferential current flow due to inter-turn capacitance, both effects that are overlooked by standard filamentary current representations using an extended kernel. The impedance characteristic showed good agreement with the predictions of a standard filamentary-current code, in the case of applied uniform excitation along the local axis of the wire. However, the power-loss computations of the present technique produce significantly different results compared to those well-established methods when the wires are closely spaced.

Numerically efficient method-of-moments formulation valid over a wide frequency band including very low frequencies

A method of moments (MoM)-based procedure is developed for efficient treatment of scattering problems over a wide frequency band where many of the conventional algorithms often fail. The proposed method uses a type of basis function whose radiated field is expressible in a convenient closed-form. This, in turn, circumvents the need to either employ the Green's function to formulate the problem, or having to deal with the singularities of the same. Furthermore, since the formulation deals with the electric fields generated by the basis functions directly, without involving the vector and scalar potentials typically employed in the conventional MoM formulation, it is possible to use a uniform formulation over a much wider frequency range without having to resort to special basis functions, for example, the loop-stars. Numerical results validating the accuracy and the numerical efficiency of the proposed method both in the near- and in the far-field regions are included in this study.

Physical Bounds and Optimal Currents on Antennas

Physical bounds on the directivity Q-factor quotient and optimal current distributions are determined for antennas of arbitrary shape and size using an optimization formulation. A variational approach offers closed form solutions for small antennas expressed in the polarizability of the antenna structure. Finite sized antennas are solved using Lagrangian parameters in a method of moments formulation. It is also shown that the optimal charge density for a small antenna can be generated by several current densities. Numerical examples for small and large antennas are used to illustrate the results.

Prediction of the molecular and polymer solution properties of LDPE in a high-pressure tubular reactor using a novel Monte Carlo approach

In the present work, a novel kinetic/topology Monte Carlo algorithm is developed for the prediction of molecular, topological and solution properties of highly branched low-density polyethylene (LDPE), produced in a high-pressure multi-zonal tubular reactor. It is shown that the combined kinetic/topology MC algorithm can provide comprehensive information regarding the distributed molecular and topological properties of LDPE (i.e., molecular weight distribution, short- and long-chain branching distributions, joint molecular weight-long chain branching distribution, branching order distribution, seniority/priority distributions, etc.) The molecular/topological results obtained from the MC algorithm are then introduced into a random-walk molecular simulator to calculate the solution properties of LDPE (i.e., the mean radius of gyration, R g , and the branching factor, g) in terms of the chain length of the branched polyethylene. The validity of the commonly applied approximation regarding the random scission of highly branched polymer chains is assessed by a direct comparison of the average molecular properties of LDPE (i.e., number and weight average molecular weights), calculated by the combined kinetic/topology MC algorithm, with the respective predictions obtained by the commonly applied method of moments (MOM). Through this comparison it is demonstrated that the ambiguous implementation of the random scission reaction in the MOM formulation can result in erroneous predictions of the weight average molecular weight and MWD of LDPE. Finally, the effects of two key process parameters, namely, the polymerization temperature profile and the solvent concentration, on the molecular, topological and polymer solution properties of LDPE produced in a multi-zonal tubular reactor are investigated.

Computational Estimates of Electrically Small Antenna High-Contrast Polarizabilities

Polarizability has been shown to be a useful route for the calculation of the directivity-to-quality-factor ratio (D/Q) bound of electrically small antennas of arbitrary shape. We demonstrate that the same integral-equation-based moment method formulation used to determine the radiation patterns and input impedance of such antennas can also be used to estimate its polarizability, and hence D/Q bounds.

PARALLEL MOM-PO METHOD WITH OUT-OF-CORE TECHNIQUE FOR ANALYSIS OF COMPLEX ARRAYS ON ELECTRICALLY LARGE PLATFORMS

A Message Passing Interface (MPI) parallel implementation of a hybrid solver that combines the Method of Moments (MoM) with higher order basis functions and Physical Optics (PO) has been successfully used to solve a challenging problem including a 2160-slot waveguide array on an airplane with a maximum dimension larger than 1000 wavelengths. The block-partitioned scheme for the large dense MoM matrix combined with the process-cyclic scheme for the PO discretized triangles is designed to achieve excellent load balance and high parallel efficiency. To break the limitation of physical memory, the parallel out-of-core technique is introduced to tackle large dense systems generated using the MoM formulation. This research provides a solution with reasonable accuracy for solving large on-board antenna problems but has very low memory usage.

Moment Method Analysis of Corrugated Surfaces Using the Aperture Integral Equation

This communication describes a method of moments formulation to analyze the scattering from corrugated surfaces. The approach is based on the aperture integral equation. Such approach decouples the analysis of the impedance effect of the grooves from the external coupling among grooves and allows us to deal accurately with grooves of any shape. Advantage is taken of the geometrical properties of the problem to solve it efficiently using a conjugate gradient-FFT algorithm.

Efficient, numerically robust characterisation of a large, double-loop antenna array

Arrays of circular, double-loops are treated via a semi-analytical technique, on the basis of a Method of Moments formulation. A Pocklington-type integral equation for the current is derived and discretised via a suitable set of basis functions. The matrix corresponding to the pertinent linear system is found to consist of circulant blocks. The system is therefore analytically solvable, and hence, potential ill-conditioning, encountered in large geometry cases, cannot possibly introduce any numerical instabilities to the calculations. Introduction of a delta gap source as excitation facilitates very efficient computation of the current and input admittance. The algorithm exploits almost exclusively elementary functions and yields results in terms of a set of rapidly convergent series, applicable to extremely large loops. Data for such loops are presented for the first time in literature. The method is expected to lead in the future to very efficient designs of multi-loop arrays.

Determination of the Pole-Singularity Order in Spectral MoM Formulations for Source-Free Planar Periodic Structures

The order of the pole singularities encountered in spectral method of moments formulations for source-free periodic problems is investigated. The solution of the source-free problem is often obtained by searching for the zeros of the Z matrix determinant using an iterative algorithm. During this process, pole singularities of the determinant are encountered and may cause numerical instability. In order to cancel the poles, their order must be known. A rigorous proof of the pole singularity order in the Z matrix determinant is given. The proof is general and holds for any problem which is periodic in at least one of the spatial directions. This knowledge enables to cancel the poles by an appropriate fixed factor with a simple routine.

Implementation of Method of Moments for Numerical Analysis of Corrugated Surfaces With Impedance Boundary Condition

A method of moments formulation is developed to analyze the scattering of corrugated surfaces by using an impedance boundary condition. The numerical analysis of the impedance surface is done using closed-form formulae and accurate numerical integration. The studied formulation greatly decreases the computational resources required to study corrugated structures.

ACCURACY AND COMPLEXITY ASSESSMENT OF SUB-DOMAIN MOMENT METHODS FOR ARRAYS OF THIN-WIRE LOOPS

A direct sub-domain moment-method formulation is presented for the analysis of arrays of thin-wire loops. Curved piecewise sinusoidal basis functions are used for the description of the currents on the loops, while both point matching and reaction matching are examined as testing schemes. Numerical results are provided for representative array structures with the intention to delve into the behavior of the solutions as the number of basis/testing functions grows, but also for the purpose of comparison with well-documented results. Finally, the complexity of the developed codes is estimated and general guidelines are provided for the efficient and accurate analysis of multi-element arrays.