Conventional Method Of Moments Research Articles

Composite electromagnetic scattering from an object situated above rough surface.

A highly efficient hybrid method combining physical optics (PO) with physical optics is adopted to analyze the electromagnetic (EM) scattering from a perfectly electric conducting object situated above the conducting rough surface. The PO method is applied to solve the scattering of an object and the underlying rough surface, respectively. And the Huygens equivalence principle and multipath scattering strategy are employed to deal with the mutual interactions between object and rough surface. To validate the efficiency of our present method, the EM scattering of the composite model by the hybrid PO-PO method for different polarizations is calculated and compared with those using the conventional method of moments as well as computational time and memory requirements. The distribution of induced surface currents on the object and rough surface are illustrated for different scattering paths. Finally, the influence of some parameters on the composite scattering is investigated and discussed in detail.

PO–PO method for electromagnetic backscattering from a 2D arbitrary dielectric‐coated conducting target located above a 1D randomly rough surface: horizontal polarisation

This study proposes and validates a new physical optics–physical optics (PO–PO) method based on the reciprocity theorem to calculate the electromagnetic backscattering from a two-dimensional (2D) dielectric-coated conducting target located above a 1D dielectric randomly rough surface. To avoid the artificial reflection from two endpoints of rough surface, the tapered plane wave proposed by Thorsos in 1988 is introduced as the incident wave. The results obtained from the author's method, for horizontal polarisation, show a good agreement with the numerical results derived from the conventional method of moments in a special case of a perfectly electric conducting target located above a dielectric rough surface. Finally, the influence of some parameters related to the coating material on the composite scattering is investigated and discussed in detail.

Scattering analysis of curved FSS using Floquet harmonics and asymptotic waveform evaluation technique

In this paper, we present the scattering characteristics of infinite and finite array using method of moment (MoM) with Floquet harmonics and asymptotic waveform evaluation (AWE) technique. First, infinite cylindrical dipole array is analyzed using the MoM with entire domain basis function and cylindrical Floquet harmonics. To provide the validity of results, we fabricated the cylindrical dipole array and measured the transmission characteristics. The results show good agreements. Second, we analyzed the scattering characteristics of finite array. A large simulation time is needed to obtain the scattering characteristics of finite array over wide frequency range because Floquet harmonics can`t be applied. So, we used the MoM with AWE technique using Taylor series and Pade approximation to overcome the shortcomings of conventional MoM. We calculated the radar cross section (RCS) as scattering characteristics using the proposed method in this paper and the conventional MoM for finite planar slot array, finite spherical slot array, and finite cylindrical dipole array, respectively. The compared results agree well and show that the proposed method in this paper is good for electromagnetic analysis of finite FSS.

Electromagnetic scattering from a PEC object above a dielectric rough sea surface by a hybrid PO–PO method

In this paper, the electromagnetic scattering from a perfectly electric conducting object above a dielectric sea surface is investigated by an efficient hybrid method combining physical optics (PO) with physical optics (PO). Both the scatterings of an object and the underlying sea surface are calculated by the PO method and the mutual couplings between them are solved by the equivalence principle and multi-path scattering strategy. In numerical simulations, the monostatic and bistatic normalized radar cross-section of the composite model is computed by the proposed method and is compared with that by the conventional method of moments. The results show the hybrid PO–PO method has a good accuracy, presence of PO and can greatly reduce the computational time and memory requirement.

Improved method for calculating neoclassical transport coefficients in the banana regime

The conventional neoclassical moment method in the banana regime is improved by increasing the accuracy of approximation to the linearized Fokker-Planck collision operator. This improved method is formulated for a multiple ion plasma in general tokamak equilibria. The explicit computation in a model magnetic field shows that the neoclassical transport coefficients can be accurately calculated in the full range of aspect ratio by the improved method. The some neoclassical transport coefficients for the intermediate aspect ratio are found to appreciably deviate from those obtained by the conventional moment method. The differences between the transport coefficients with these two methods are up to about 20%.

ELECTROMAGNETIC INTERACTIONS ANALYSIS BETWEEN TWO 3-D SCATTERERS USING THE E-PILE METHOD COMBINED WITH THE PO APPROXIMATION

In this paper, the electromagnetic scattering from two scatterers is analyzed from a rigorous integral formulation solved by the method of moments (MoM). G. Kubicke has recently developed the E- PILE (Extended Propagation-Inside-Layer Expansion) method to calculate the scattering from an object above a rough surface for a two-dimensional problem. This method allows us to calculate separately and exactly the interactions between the object and the rough surface. The purpose of this paper is to extend the E-PILE method to a three-dimensional problem. Such a 3-D problem involves a large number of unknowns and can not be solved easily with a conventional method of moments by using a direct LU inversion. Thus to solve this issue, the E-PILE method is combined with the physical optics (PO) approximation to calculate the local interactions on both the object and the rough surface. By using this hybrid method, the requirements of memory and CPU time can be reduced signiflcantly.

Improved modal method of moments technique to compensate the effect of wall dimension in shielding effectiveness evaluation

In the conventional modal method of moments (MoM) method, when shielding effectiveness (SE) of a rectangular enclosure is the goal, it is assumed that the incident wave is reflected from an infinite wall. This assumption makes the results inaccurate specifically at low frequencies where the wall size is not large compared to the illumination wavelength. In this study, the mentioned reflected wave is corrected by considering the reflection from a box without any aperture. To obtain the reflected wave from the box, an induced electric current on the metallic surface is assumed. Using Rao Wilton Glisson basis functions along with free space Green's function, the unknown electric currents and consequently the reflected wave are calculated. The results are compared with full wave numerical methods. A very good agreement is observed between the results and it is shown that for lower frequencies the proposed method has more accuracy rather than the modal MoM itself specifically for an enclosure with a very large aperture.

심음 포락선의 3차 모멘트를 이용한 심음의 주성분 검출

심음도(PCG, Phonocardiogram) 분석을 이용하여 심장의 판막과 관련된 질환을 진단하기 위해서는 먼저 심음 분할을 위해 심음의 주성분인 S1과 S2를 정확하게 찾아야 한다. 본 논문에서는 심음포락선의 모멘트 특성을 분석하고 이를 심음 분할에 적용하였다. 기존의 2차 모멘트를 이용한 심음 분할의 문제점을 분석하고, 심잡음이 있더라도 심음 주성분의 검출이 용이한 3차 모멘트에 기반한 방법을 제안하였다. 심음포락선은 심음 신호의 단구간 에너지를 이용하였으며, 3차 모멘트 궤적의 기울기 정보를 이용하여 심음 주성분을 검출하고 지속시간을 게이팅(gating) 하였다. 다양한 심잡음이 포함된 심음 신호에 대한 실험을 통해 제안한 방법이 기존의 2차 모멘트 기법보다 심잡음의 영향을 적게 받고 심음 주성분의 구간을 정확하게 검출 할 수 있음을 보였다. To diagnose the cardiac valve abnormalities using analysis of phonocardiogram, first of all, accurate detection of S1, S2 components is needed for heart sound segmentation. In this paper, a new method that uses the third moment characteristics of an envelope of the PCG is proposed for accurate detection of S1 and S2 components of the heart sound with cardiac murmurs. The envelope of the PCG is obtained from the short-time energy profile, and its third moment profile with slope information is used for accurate time gating of the S1, S2 components. Experimental results have shown that the proposed method is superior to the conventional second moment method for detection of S1 and S2 regions from the heart sound signals with cardiac murmurs.

Hybrid method of scattering from a dielectric target above a rough surface: TM case

A hybrid method, combining analytic Kirchhoff approximation (KA) and numerical method of moment (MoM), is developed to solve the 2D scattering problem of a dielectric target with arbitrary cross section above a moderate perfect electric conductor (PEC) rough surface under TM-polarized tapered wave incidence. Consider the target as the MoM region and the rough surface as the KA region, the induced current on the rough surface is obtained through the KA method, which depends on the incident tapered wave and the field illuminating by current distribution on the target, leaving only unknowns on the target region. In order to reduce the computational costs further, the rough surface is truncated to speed up computation of the scattering contribution from the rough surface to the target. Compared with the conventional MoM, the hybrid method is very efficient to solve the composite scattering problem of target above rough surface, especially for long underlying rough surface. Simulation results validate the effectiveness and accuracy of the hybrid method.

Nonlinear Magnetostatic Analysis by Unified BIE Utilizing Potential Gap Due to Loop Currents

Since the line loop current is equivalent to the double layer charge, it gives an integral form of scalar potential. The segmental loop current on the interface between magnetic materials produces a potential gap, which works to give a boundary integral equation (BIE). By virtue of another potential gap due to a fictitious circulating current along the contour of cut-surface in the material, the excitation potential becomes single valued and the BIE becomes applicable to generic problems without any restriction. Regarding the nonlinear magnetic material as composed of segmental materials with different values of permeability, we get the same BIE for the nonlinear analysis as for the linear analysis. In order to check the adequacy and effectiveness of the nonlinear BIE, we solve a typical magnetostatic problem and compare the computed results with those by the conventional magnetic moment method.

Four-parameter Weibull probability distribution model for weakly non-linear random variables

The use of multi-parameter distribution functions that incorporate empirically derived parameters to more accurately capture the nature of data being studied is investigated. Improving the accuracy of these models is especially important for predicting the extreme values of the non-linear random variables. This study was motivated by problems commonly encountered in the design of offshore systems where the accurate modeling of the distribution tail is of significant importance. A four-parameter Weibull probability distribution model whose structural form is developed using a quadratic transformation of linear random variables is presented. The parameters of the distribution model are derived using the method of linear moments. For comparison, the model parameters are also derived using the more conventional method of moments. To illustrate the behavior of these models, laboratory data measuring the time series of wave run-up on a vertical column of a TLP structure and wave crests interacting in close proximity with an offshore platform are utilized. Comparisons of the extremal predictions using the four-parameter Weibull model and the three-parameter Rayleigh model verify the ability of the new formulation to better capture the tail of the sample distributions.

A New Method of Moments for the Bimodal Particle System in the Stokes Regime

The current paper studied the particle system in the Stokes regime with a bimodal distribution. In such a system, the particles tend to congregate around two major sizes. In order to investigate this system, the conventional method of moments (MOM) should be extended to include the interaction between different particle clusters. The closure problem for MOM arises and can be solved by a multipoint Taylor-expansion technique. The exact expression is deduced to include the size effect between different particle clusters. The collision effects between different modals could also be modeled. The new model was simply tested and proved to be effective to treat the bimodal system. The results showed that, for single-modal particle system, the results from new model were the same as those from TEMOM. However, for the bimodal particle system, there was a distinct difference between the two models, especially for the zero-order moment. The current model generated fewer particles than TEMOM. The maximum deviation reached about 15% for m0 and 4% for m2. The detailed distribution of each submodal could also be investigated through current model.

Analysis of Finite Conformal Frequency Selective Surfaces via the Characteristic Basis Function Method and Spectral Rotation Approaches

An efficient characteristic basis function (CBF)-based method is proposed to analyze conformal frequency selective surfaces (FSS) that are not amenable to analysis by using conventional numerical methods typically used to model infinite, planar, and doubly periodic FSSs. The technique begins by employing the CBFs to describe the currents induced on the elements. The reaction integrals needed to derive the reduced matrix elements are computed either in the spatial domain, or spectral domain, depending on the separation distance between the blocks, so as to make the process numerically efficient. The spectral domain integrals are evaluated by making use of the spectral rotation (SR) on the spectra of the CBFs to alleviate the computational burden to be associated with full three-dimensional (3-D) Fourier transform, which is required in the conventional spectral domain approach applied to nonplanar geometries. Numerical results from the new method have good agreement with the fully spatial characteristic basis function method (CBFM) and the conventional method of moments (MoM). However, the required central processing unit (CPU) time is greatly reduced.

BLOCK MATRIX PRECONDITIONER METHOD FOR THE ELECTRIC FIELD INTEGRAL EQUATION (EFIE) FORMULATION BASED ON LOOP-STAR BASIS FUNCTIONS

In this paper, electromagnetic scattering problems are analyzed using an electric fleld integral equation (EFIE) formulation that is based on loop-star basis functions so as to avoid low-frequency instability problems. Moreover, to improve the convergence rate of iterative methods, a block matrix preconditioner (BMP) is applied to the EFIE formulation based on loop star-basis functions. Because the matrix system resulting from the conventional method of moments is a dense matrix, a sparse matrix version of each block matrix is constructed, followed by the inversion of the resultant block sparse matrix using incomplete factorization. Numerical results show that the proposed BMP is e-cient in terms of computation time and memory usage.

Volume Integral Equation Analysis of Thin Dielectric Sheet Using Sinusoidal Macro-Basis Functions

In this letter, we present an improvement over the conventional thin dielectric sheet (TDS) formulation for the analysis of thin dielectric sheets. Our focus is to address the problem of scattering from thin penetrable scatterers by developing a volumetric formulation based on the use of macro-basis functions. The electric fields produced by the source basis functions are derived directly, bypassing the summation of scalar and vector potentials. The latter results in a considerable time advantage in comparison to the conventional method of moments (MoM) solution of the volume electric field integral equation (V-EFIE), while the accuracy remains comparable. In contrast to the TDS formulation, both tangential and normal currents are employed so that problems with high and low permittivity, as well as those involving grazing incident angles, can be accurately analyzed. Several examples are reported that show excellent agreement with conventional techniques and demonstrate the effectiveness of the new approach.

Wide-band scattering of 1-D dispersive soil surface by the ADE-FDTD algorithm

In this paper, a wide-band scattering of one-dimensional (1-D) soil surface with exponential spectrum is investigated by the finite-difference time-domain (FDTD) algorithm with pulsed wave excitation. Soil is regarded as isotropic and dispersive media, and it satisfies the two-pole Debye model. And the auxiliary differential equation (ADE) technique is incorporated into the FDTD scheme to deal with the dispersive soil. To ensure the validity of our present method, the wide-band scattering of dispersive soil surface by the ADE-FDTD method is computed and compared with the result by the conventional method of moments (MOM), which requires an individual calculation for every frequency point of interest. Finally, the scattering characteristic of dispersive soil surface is analyzed for different parameters in detail.

A True Domain Decomposition Procedure Based on Method of Moments to Handle Electrically Large Bodies

A true domain decomposition method to obtain numerical solution involving electrically large bodies using the method of moments (MOM) formulation is the subject matter of the present work. The electrically large body is initially divided into smaller sub-structures. By defining a set of new basis functions adaptively, utilizing the primary basis functions, a solution scheme is developed which completely eliminates the interaction of one substructure with the rest of the body. This procedure enables to solve each substructure independently and involves no iterative solution as a final step. The present method is conceptually simple and applicable to any MOM solution. Further, the method can easily handle multiple right-hand side vectors much the same way as the conventional MOM solution. A few representative numerical examples are presented to illustrate the applicability of the new method.

A Computationally Efficient Technique for Prototyping Planar Antennas and Printed Circuits for Wireless Applications

In this paper, we present a novel procedure for an efficient and accurate electromagnetic simulation of microstrip circuits and printed antennas etched in layered media. The proposed approach, based on a new algorithm referred to herein as the equivalent medium approach (EMA), is applied for a rapid design of the preliminary desired circuit prototype. The illustrated technique yields reliable results and reduces the computational time in comparison with the conventional method of moments (MoM). Some examples that demonstrate the accuracy and the efficiency of the described procedure are included.

Efficient Iterative Method of Moments—Physical Optics Hybrid Technique for Electrically Large Objects

The conventional hybrid method of moments (MoM)-physical optics (PO) technique provides a possible way to handle electrically large objects with affordable computer memory. However, its efficiency is not very good because the evaluation of the PO contribution to the MoM impedance matrix is very time-consuming. An efficient implementation of the iterative MoM-PO hybrid technique is presented in this paper to avoid the calculation of the PO contribution in matrix form. For electrically large objects, the proposed efficient iterative MoM-PO (EI-MoM-PO) method can greatly reduce the computational time and maintain the same or better accuracy with the same number of unknowns compared with the conventional MoM-PO method. Several examples of large-scale structures are analyzed by the EI-MoM-PO method, the conventional MoM-PO method, and the multilevel fast multipole algorithm. The excellent efficiency and accuracy are achieved by the proposed EI-MoM-PO technique.

Frequency response of 1D dispersive sea surface by the ADE-FDTD algorithm

The frequency response of a one-dimensional (1D) sea surface was investigated using the finite-difference time-domain (FDTD) algorithm with pulsed wave excitation. Where the sea water is regarded as an isotropic and dispersive medium, it satisfies the single-pole Debye model. The auxiliary differential equation (ADE) technique is incorporated into the FDTD scheme to deal with the dispersive sea surface. To ensure the feasibility of our present method, the frequency response of dispersive sea surface by the ADE-FDTD method is compared with the result by the conventional method of moments (MOM), which requires an individual calculation for every frequency point of interest. Finally, the scattering characteristic of dispersive sea water is investigated for different wind speed, temperature, and salinity. The representative far zone scattered field versus time is also analyzed.