Traditional Method Of Moments Research Articles

An electromagnetic scattering reanalysis method for partial geometry modifications

AbstractThis work proposes an effective and accurate method for solving the partial geometry modification problem of original scattering. The current and scattering characteristics after structure modification can be efficiently calculated by using the information of the initial impedance matrix. These modifications include adding geometry or moving and rotating different parts of geometry. Although the changes in each impedance matrix are local for partial modified geometries, the associated computational cost is high because the whole analysis is iterative. By combining the binomial series method and the reduced basis method, the proposed method can effectively evaluate the scattering field without solving the inverse impedance matrix of the modified geometry. The proposed algorithm has a computational cost of O(n2), which is much smaller than O(n3) of the traditional method of moments (MoM), where n is the number of unknowns. Through several examples, the traditional MoM and the proposed method are compared, and the efficiency and accuracy of the proposed method are proved.

Spatial Characteristics of the Fungus Powdery Mildew (Erysiphe neolycopersici) on Tomatoes and its Spread in Industrial Greenhouses

In regions with cool temperate climates, tomatoes are grown on an industrial scale in large greenhouses. There the crops are susceptible to infection by powdery mildew, the fungus Erysiphe neolycopersici, which is introduced largely as fungal spores from outside the greenhouses and spread by wind within them. We have monitored the spread of the disease and mapped its distribution in four commercial greenhouses throughout the growing season to understand its aetiology. We modelled the patterns of infection geostatistically, each comprising a deterministic long-range trend plus a short-range spatially correlated random residual. We identified three main kinds of pattern; one consisted of a constant plus a spatially correlated residual, second comprised a linear trend throughout the greenhouse plus a correlated random residual, and third, the trend had the form of a bell akin to a Gaussian surface plus, again, a correlated random residual. Here, we show three examples of these distributions and the detail of their geostatistical analysis using both the traditional method of moments (MoM) estimation of variograms and residual maximum likelihood (REML) to separate the deterministic and random components. The analytical modelling is followed by ordinary punctual kriging in the first case, by universal kriging in the second, and by regression kriging in the third case to display the infection as isarithmic ("contour") maps. We interpret the first form of distribution as arising from numerous foci as spores landed on the leaves from various sources spread by air currents and the movement of workers along the paths through the greenhouse. In the second case, the disease seemed to have spread from an infection introduced through the main door in one corner of the greenhouse and spread from there by the workers and air currents. The third infection arose near the centre of the greenhouse by the main path and spread outwards from there. In all three examples, the main pathways seemed important routes along which the fungus spread.

Fast Analysis of Bistatic Scattering Problems for Three-Dimensional Objects Using Compressive Sensing and Characteristic Modes

In this letter, a combination of characteristic mode (CM) and compressive sensing (CS) is utilized to accelerate the solution of bistatic scattering problems of three-dimensional (3-D) objects. The surface induced currents discretized by Rao–Wilton–Glisson basis functions are successfully sparsely transformed by CM basis functions based on domain decomposition. Different from the dense matrix equation of traditional method of moments (MoM), a low-rank CS model with smaller size is constructed in the proposed method, wherein the induced currents can be reconstructed efficiently. Due to partially filling of the impedance matrix and efficient recovery algorithm, the time cost in the proposed method is reduced dramatically. Last, the results from several numerical simulations validate the efficiency and accuracy of the proposed method.

PMCHWT Solver Accelerated by Adaptive Cross Approximation for Efficient Computation of Scattering from Metal Nanoparticles.

An accelerated algorithm that can efficiently calculate the light scattering of a single metal nanoparticle was proposed. According to the equivalent principle, the method of moment (MoM) transforms the Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT) integral equations into linear algebraic equations, which are solved by the flexible generalized minimal residual solver (FGMRES). Each element of near field MoM impedance matrix was described by Rao–Wilton–Glisson (RWG) basis functions and calculated by double surface integrals. Due to the low-rank property, the adaptive cross approximation (ACA) algorithm based on the octree data structure was applied to compress the MoM impedance matrix of far field action leading to the significant reduction of solution time and memory. Numerical results demonstrated that the proposed method is both accurate and efficient. Compared with the traditional MoM, the ACA algorithm can significantly reduce the impedance matrix filling time and accelerate the scattering field’s computation from actual metal nanoparticles using PMCHWT integral equations.

Fast and Accurate Prediction of Light Scattering from Plasmonic Nanoarrays in Multiple Directions.

The method of moments (MoM) is an efficient electromagnetic numerical method for the accurate prediction of light scattering from plasmonic nanostructures. In practice, the light-scattering properties in different incident directions are often concerning. However, traditional MoM generally resorts to the iterative method, which suffers from the problems of convergence rate and redundant computations for multiple incident excitations. Nanoarray structures will further aggravate these problems due to a large number of unknowns. In this article, an efficient numerical method based on MoM and a hierarchical matrix (H-matrix) algorithm is proposed to solve these problems. Numerical experiments demonstrate the efficiency and accuracy of the proposed method for the prediction of light scattering from plasmonic nanoarrays in multiple directions.

Accurate Nyström Solution for Electromagnetic Scattering by Zero-Thickness Conducting Objects

A Nystrom method is proposed to solve the electromagnetic (EM) scattering by zero-thickness conducting objects. The problem is formulated through the electric field integral equation (EFIE) so that the current density on the two opposite sides can be summed up and assigned to one of sides. Since the dominant component of current density near a boundary tends to be infinite, it is challenging to accurately model and more robust singularity treatment is required. The Nystrom method has presented certain merits compared with the traditional method of moments (MoM), but has seldom been used to solve such problems. In this paper, efficient analytical formulas are derived to evaluate singular integrals so as to facilitate the implementation of Nystrom method and a CPU parallelization scheme is used to accelerate the matrix filling process. Two numerical examples are provided to demonstrate the approach.

A differential evolution algorithm for estimating mobile channel parameters [formula omitted

The statistical modeling of mobile radio signals requires the estimation of parameters that describe the probability distribution that hypothetically models this channel, so that this probabilistic model guarantees a good adjustment to the experimental data. This article proposes the use of differential evolution (DE) algorithms for estimating parameters of the α−η−μ fading channel, and to compare these to the traditional method of moments (MM) and maximum likelihood estimation (MLE) method. These traditional parameter estimation methods use nonlinear numerical methods, and the solution, if found, may be the optimal value, an approximation of the optimal value, or a local maximum. The authors demonstrate through comparative experiments using the MM and the MLE method that the DE algorithm for the proposed estimation demands a lower run time. In addition, it presents the error performance measured by the mean square error (MSE), near or above, as well as high robustness measured by the statistical analysis. Essentially, this algorithm always finds acceptable physical estimations with a good goodness of fit to experimental data. This estimating DE algorithm along with its proposed fitness function are original contributions of this paper. The received signal samples, used in the experiments of this paper, were randomly generated by the α−η−μ fading simulator, which is another contribution of this paper. This proposed α−η−μ fading simulator is based on the Clarke and Gans fading model and expands the generation range of current simulators, from μ integer multiples of 0.5, to μ integer multiples of 0.25.

A regularized method of moments for three-dimensional time-harmonic electromagnetic scattering

A regularized method of moments based on the modified fundamental solution of the Helmholtz equation is proposed in this article. The regularized method of moments uses the origin intensity factor technique which is free of mesh and integration to deal with the singularity at origin of the basis function. Thus, the time-consuming singular integration can be avoided. In addition, the non-uniqueness at internal resonance is also fixed using the constructed modified fundamental solution. In comparison with the traditional method of moments, the regularized method of moments can reduce the computational time by half, while the stability and accuracy stay about the same. Numerical experiments demonstrate that the regularized method of moments can accurately and efficiently compute the radar cross section of perfect conducting scatter in all frequency ranges.

A novel solver for simulation of flows from continuum regime to rarefied regime at moderate Knudsen number

A novel and simple solver for simulation of flows from continuum regime to rarefied regime at moderate Knudsen number is developed in this work. The present solver combines good features of gas kinetic flux solver (GKFS), discrete velocity method (DVM) and the moment method. Like the GKFS, in the present solver, the macroscopic governing equations are discretized by finite volume method and the numerical fluxes at cell interfaces are evaluated by the local solution of Boltzmann equation. To get the local solution of Boltzmann equation, the initial distribution function is reconstructed with the help of Grad's distribution function, which is inspired from the moment method. For the high order moments in Grad's distribution function, they are computed directly by the moments of distribution function, which is inspired from DVM. In principle, the present solver only needs to discretize the physical space and solves the governing equations resulted from conservation laws of mass, momentum and energy. Thus, its governing equations are much simpler than those of the moment method. To validate the proposed solver, some test examples covering continuum regime and rarefied regime are simulated. Numerical results showed that the present solver can give accurate prediction in the continuum regime and reasonable results as the traditional moment method in the rarefied regime at moderate Knudsen number.

Efficient RCS Computation Over a Broad Frequency Band Using Subdomain MoM and Chebyshev Approximation Technique

The analysis of the target’s broadband electromagnetic scattering characteristics plays an important role in radar stealth and recognition areas. The traditional method of moments (MoM) needs to calculate the currents at each frequency point when analyzing the target. With the increase of the target electrical size and complexity, the radar cross section (RCS) of the target changes drastically with frequency, it is necessary to calculate the accurate frequency response with a small frequency interval, which is very time-consuming in calculation and not feasible. This paper proposes to combine the subdomain method of moments (SMoM) with the Chebyshev approximation technique (CAT) to efficiently analyze the electromagnetic scattering of arbitrary shaped objects over a broad frequency band. In the SMoM technique, the whole object can be divided into several regions, each of which can be independently solved by the method of moments (MoM). The CAT technique is employed to expand the unknown current coefficients into a Chebyshev series for achieving fast frequency sweeping. Instead of direct point-by-point simulations, it is only necessary to calculate the currents by SMoM at several Chebyshev-Gauss frequency sample points. Furthermore, the Chebyshev series are matched via the Maehly approximation to a rational function to improve the accuracy. Numerical examples show that the hybrid technique can greatly reduce the computation time without loss of accuracy.

Resummed hydrodynamic expansion for a plasma of particles interacting with fields

A novel description of kinetic theory dynamics is proposed in terms of resummed moments that embed information of both hydrodynamic and non-hydrodynamic modes. The resulting expansion can be used to extend hydrodynamics to higher orders in a consistent and numerically efficient way; at lowest order it reduces to an Israel-Stewart-like theory. This formalism is especially suited to investigate the general problem of particles interacting with fields. We tested the accuracy of this approach against the exact solution of the coupled Boltzmann-Vlasov-Maxwell equations for a plasma in an electromagnetic field undergoing Bjorken-like expansion, including extreme cases characterized by large deviations from local equilibrium and large electric fields. We show that this new resummed method maintains the fast convergence of the traditional method of moments. We also find a new condition, unrelated to Knudsen numbers and pressure corrections, that justifies the truncation of the series even in situations far from local thermal equilibrium.

Efficient Characteristic Mode Analysis for Radiation Problems of Antenna Arrays

The analysis for large-scale antenna arrays is a hot topic for design and optimization. In this paper, an efficient method for analyzing antenna arrays by using characteristic mode (CM) is proposed. In order to analyze common antennas composing of conductor and dielectric, the theory of CM is first introduced into the volume-surface integral equation. An auxiliary general eigen-equation is established to make the modes orthogonal. Furthermore, a source mode (SM) is constructed to modify the accuracy when using CMs to expand the currents excited by a delta gap source for antenna problems. To demonstrate the influence of antenna structures and excitations on the CM and SM, three antennas are analyzed and only a few modes are required to achieve a good accuracy. Due to the periodicity of antenna arrays, CMs can be served as entire-domain basis functions defined on one antenna element and reused to reduce the unknowns in the method of moments (MoM). Numerical results have shown that the proposed method can have a good agreement with the traditional MoM. Meanwhile, both the memory requirements and computational time of the proposed method can be significantly reduced.

Bilateral sparse transform for fast solving EM scattering problems by compressed sensing

Rapid and accurate calculation of electromagnetic (EM) scattering problems over a wide incident angle range is always a difficult task which requires repeated numerical computation as the incident angle changes. Aiming at this subject, a solution that introduces compressed sensing into traditional method of moments is described, and the bilateral sparse transform method is first proposed to form a new scheme, in which the effectiveness is improved greatly since the total number of measurements required is reduced drastically as compared with the traditional unilateral sparse transform method. The basic principle is analysed in detail and the high effectiveness of bilateral sparse transform is verified by numerical results.

CFD modeling of particle dispersion and deposition coupled with particle dynamical models in a ventilated room

Two dynamical models, the traditional method of moments coupled model (MCM) and Taylor-series expansion method of moments coupled model (TECM) for particle dispersion distribution and gravitation deposition are developed in three-dimensional ventilated environments. The turbulent airflow field is modeled with the renormalization group (RNG) k–ε turbulence model. The particle number concentration distribution in a ventilated room is obtained by solving the population balance equation coupled with the airflow field. The coupled dynamical models are validated using experimental data. A good agreement between the numerical and experimental results can be achieved. Both models have a similar characteristic for the spatial distribution of particle concentration. Relative to the MCM model, the TECM model presents a more close result to the experimental data. The vortex structure existed in the air flow makes a relative large concentration difference at the center region and results in a spatial non-uniformity of concentration field. With larger inlet velocity, the mixing level of particles in the room is more uniform. In general, the new dynamical models coupled with computational fluid dynamics (CFD) in the current study provide a reasonable and accurate method for the temporal and spatial evolution of particles effected by the deposition and dispersion behaviors. In addition, two ventilation modes with different inlet velocities are proceeded to study the effect on the particle evolution. The results show that with the ceiling ventilation mode (CVM), the particles can be better mixed and the concentration level is also higher. On the contrast, with the side ceiling ventilation mode (SVM), the particle concentration has an obvious stratified distribution with a relative lower level and it makes a much better environment condition to the human exposure.

Measurement with random sampling for solving EM scattering problems over a wide angle by compressed sensing

Rapid calculation of electromagnetic (EM) scattering problems over a wide incident angle is always a difficult task for computational electromagnetics (CEMs). As a new kind of excitations which include plenty of information about incident angles was constructed, a fast method by applying compressed sensing in conjugation with traditional method of moments has been proposed. Random sampling is firstly taken into the process of linear measurement to simplify the construction of the new excitations and accelerate the recovery of unknown induced currents. The basic principle is elaborated in detail, and the effectiveness of the proposed method is validated with numerical results.

Quasi-Periodic Array Modeling Using Reduced Basis From Elemental Array

Quasi-periodic arrays have appeared in many electromagnetic devices, such as reflectarray antennas, metasurfaces, and nanoparticle arrays. In these devices, elements with similar configuration are positioned on a periodic lattice. The entire array is usually a large multiscale structure. Therefore, efficient modeling of quasi-periodic arrays can be very challenging due to the loss of periodicity and the multiscale feature in the array. In this work, based on the similarity among elements, we apply the reduced basis method to integral equation solvers to model wave interaction with quasi-periodic arrays. The matrix equation can be constructed through interpolation instead of matrix assembling as traditional method of moments. A linear transform is used to reduce the sampling in interpolation from two to one dimension. Furthermore, the reduced basis can also be generated from elemental arrays to take the mutual coupling between elements into the basis set. Numerical examples show that both the computation and memory efficiency are improved compared with direct modeling using method of moments.

A Mixed Approach for Solving Volume-Surface Integral Equations in the Analysis of Microstrip Antenna and Packaging Structures

Electromagnetic analysis for microstrip antenna and packaging structures is formulated by volume-surface integral equations (VSIEs). The conducting microstrip and ground are described with SIEs, while the dielectric substrate is governed by volume integral equations (VIEs), and they are coupled to each other to form VSIEs. Using VIEs instead of SIEs for dielectric substrate can improve the conditioning of system matrix related to the multiscale property of antenna and packaging structures. The VSIEs are usually solved by the method of moments (MoM) with well-designed basis functions defined over conforming meshes, resulting in much inconvenience of implementation. We propose a mixed approach to solve the VSIEs by combining the traditional MoM for the conducting part and a point-matching scheme for the dielectric part together. The approach uses cuboids to discretize the dielectric substrate and does not require conforming meshes between the conducting and dielectric parts. Also, the approach considers the thickness of metallic microstrip and ground, which is usually neglected. Typical numerical examples are presented to demonstrate the proposed approach, and its effectiveness has been verified.

Compressive Sensing for Monostatic Scattering From 3-D NURBS Geometries

Compressive sensing (CS) proposes to capture compressible signals at a rate significantly smaller than the Nyquist–Shannon rate, yet allows accurate signal reconstruction. CS exploits the fact that the signal of interest is compressible by a known transform (e.g., Fourier, Wavelet, etc.) and it employs nonadaptive linear projections that preserve the structure of the signal. Approximate reconstruction is then obtained from these measurements by solving an optimization problem. In this paper, a new method that introduces ideas from CS to the method of moments (MoM) is proposed to solve electromagnetic monostatic scattering from conducting bodies of arbitrary shape efficiently modeled by nonuniform rational B-spline (NURBS) surfaces. The new method is applied to obtain monostatic induced currents and radar cross section values of several objects modeled with NURBS surfaces. The efficiency and accuracy of the new method are verified by comparing it against the multilevel fast multipole algorithm and the traditional MoM. The influences of the structure of the sparse basis functions and the number of measurements on the recovery error are also investigated.

On the Treatment of Arbitrary Boundary Conditions Using a Fast Direct <inline-formula> <tex-math notation="LaTeX">${\mathcal {H}}$ </tex-math> </inline-formula>-Matrix Solver in MoM

This communication adapts the formalism of hierarchical ( ${\mathcal {H}}$ -) matrices to the direct solution process (LU decomposition) of the method of moments (MoM) in the frequency domain. A novel clustering approach based on physical constraints is presented and extended to treat dielectric bodies as well as arbitrary boundary conditions. Comparisons with other numerical methods are provided. The analyses show a considerable speedup of the computation times and a significant reduction of required memory compared with the traditional MoM solution process, especially for highly resonant structures where iterative solvers like the multilevel fast multipole algorithm show poor convergence.

Fast computation of monostatic radar cross section using compressive sensing and ACA-accelerated block LU factorization method

Compressive sensing (CS) technique in conjunction with adaptive cross approximation (ACA) algorithm is applied to calculate the monostatic radar cross section with many required sampling angles based on block LU factorization method. CS technique is used to construct a new excitation matrix and reduce the number of right-hand side. ACA algorithm is applied to all steps of the solution including impedance matrix filling, block LU solve, and excitation matrix compression to accelerate the computation process and reduce the memory consumption. Finally, the real-induced currents can be recovered by the orthogonal matching pursuit algorithm or compressive sampling matching pursuit algorithm, which have relatively low computational complexity than computation by the traditional method of moments (MoM). Numerical results are presented to validate the efficiency and accuracy of this method through comparison with the traditional MoM and other rigorous solutions.