Moments Formulation Research Articles

Characteristic basis function method: A new technique for efficient solution of method of moments matrix equations

AbstractIn this paper, we introduce a novel approach for an efficient solution of matrix equations arising in the method of moments (MoM) formulation of electromagnetic scattering problems. This approach is based on the characteristic basis functions (CBFs), which are used to substantially reduce the matrix size because these bases are not bound by the conventional λ/20 domain discretization. As a result, it is possible to electrically solve large problems with much fewer unknowns than those needed when using conventional RWG basis functions. The accuracy and efficiency of the CBFs are demonstrated in a variety of scattering problems to illustrate the versatility of the approach. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 95–100, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10685

Measuring asphaltenes and resins, and dipole moment in petroleum fluids

AbstractA petroleum fluid can be divided into three types of species: asphaltenes, resins, and oils. Asphaltenes and resins are polar, while the rest of the so‐called oils are either nonpolar or mildly polar. The interaction among these species strongly affect asphaltene precipitation from petroleum fluids. Different measuring methods for asphaltenes in a petroleum fluid give similar results, but different results for the resin content of a petroleum fluid. In addition to the amount affecting precipitation, the polarity of asphaltenes and resins affects precipitation strongly. The Onsager formulation of dipolar moments was used to measure the dipole moment of asphaltenes, resins and the oil species from eight different petroleum fluids from various parts of the world. The dipole moment, a measure of polarity, for resins was measured in this work for the first time. Results showed that resin separated from a petroleum fluid by propane is part of the total resin. Adsorption methods, however, give the total amount of resins. For a given petroleum fluid, asphaltenes had a higher dipole moment than resins. However, resins from one petroleum fluid can have a higher dipole moment than asphaltenes from another petroleum fluid.

MNM: a technique for the iterative solution of matrix equations arising in the method of moments formulation

The advent of the fast multipole method (FMM) and other techniques for carrying out the matrix vector product in an efficient manner, in the context of the method of moments (MoM) formulation, has made it possible for us to take a quantum leap forward towards solving a class of large problems involving perfectly conducting scatterers. Among a plethora of different iterative algorithms available in the literature, the conjugate gradient (CG) and its variants are among the most widely used. The speed with which convergence to the correct solution is achieved in employing this iteration algorithm, is dependent upon the choice of the pre conditioner, as well as the initial guess. The authors focus on introducing a technique the (Maxwell and Markov technique, referred to herein as MNM) for choosing the initial guess. This can help reduce the number of iterations and, consequently the solution time, over the typical choice of a zero initial guess in the context of CG. The application of the method is illustrated via a number of numerical examples that combine the FMM with MNM, to derive the solution of representative electromagnetic scattering problems.

Beam steered reactively loaded printed microstrip loop antennas

Printed microstrip loop antennas loaded with reactive components are analysed to demonstrate the capability of beam steering by reactance adjustment. The geometry of the printed microstrip loop including reactive element loading is represented as a superquadratic function so that the current distribution, hence radiation pattern for various antenna loop shapes, can be calculated using a unified method of moment formulation. The effects of the loop shapes and dielectric substrates on the beam steering capability and input impedance characteristics are investigated. It is found that continuous beam steering can be achieved and that a compromise has to be made between the maximum beam steering and minimum input VSWR. A 1.0GHz experimental verification is provided, which demonstrates that beam steering of 24/spl deg/ can be achieved by control of a single reactive element, while low cross-polarisation (/spl sim/ -20 dB) and VSWR (/spl sim/ 1.7) can be simultaneously maintained.

Physics‐based preconditioner for iterative algorithms in multi‐scatterer and multi‐boundary method of moments formulations

AbstractAn efficient method to solve electromagnetic scattering problems involving several metallic scatterers or bodies composed of dielectric and metallic regions is proposed. So far, the method of moments has successfully been applied to large arrays of identical scatterers when it was combined with preconditioned iterative algorithms to solve for the linear system of equations. Here, the method is generalized to geometries that are composed of several metallic elements of different shapes and sizes, and also to scatterers that are composed of metallic and dielectric regions. The method uses in its core an iterative algorithm, preferably the transpose‐free quasi‐minimum residual (TFQMR) algorithm, and a block diagonal Jacobi preconditioner. For best performance, the blocks for the preconditioner are chosen according to individual scatterers or groups of scatterers for the array case, and according to the electric and magnetic current basis functions for dielectric/metallic scatterers. The iterative procedure converges quickly for an optimally chosen preconditioner, and is robust even for a non‐optimal preconditioner. Reported run times are compared to run times of an efficiently programmed LU factorization, and are shown to be significantly lower. Copyright © 2002 John Wiley & Sons, Ltd.

Invarianceness of Higher Order Centralised Scaled-invariants Undergo Basic Transformations

This paper presents an alternative formulation of invariant moments using higher order centralised scaled-invariants for unequal scaling unconstrained handwritten digits which undergo basic transformations. Basic transformations that are covered in this study includes scaling and rotation embedded into Hu's invariants. Moment invariants have been proposed as pattern sensitive features in classification and recognition applications. Hu was the first to introduce the concept of invariants based on combinations of regular moments using algebraic invariants. In this study, we consider unconstrained handwritten digits of different presentations. Results of computer simulations for digits of unequal scaling are also included verifying the validity of the method proposed.

Prediction of the shielding and resonant behavior of multisection enclosures based on magnetic current modeling

A new method of moments (MoM) formulation is proposed to evaluate the shielding efficiency of metallic rectangular enclosures. To this end, a mixed potential integral equation (MPIE) is formulated for the magnetic currents in the apertures using the exact Green's function of the enclosure. The accuracy of the method is demonstrated by a number of examples. The method allows the quality factor of the resonances to be predicted. Finally, the effect of partitioning the enclosure by metallic planes is also investigated.

454 Simple Multi-integrated Moment Formulation for Hydrodynamics based on CIP-CSL Type Schemes

454 Simple Multi-integrated Moment Formulation for Hydrodynamics based on CIP-CSL Type Schemes

Large deflections of cantilever beams of non-linear elastic material under a combined loading

Large deflection of cantilever beams made of Ludwick type material subjected to a combined loading consisting of a uniformly distributed load and one vertical concentrated load at the free end was investigated. Governing equation was derived by using the shearing force formulation instead of the bending moment formulation because in the case of large deflected member, the shearing force formulation possesses some computational advantages over the bending moment formulation. Since the problem involves both geometrical and material non-linearities, the governing equation is complicated non-linear differential equation, which would in general require numerical solutions to determine the large deflection for a given loading. Numerical solution was obtained by using Butcher's fifth order Runge–Kutta method and are presented in a tabulated form.

Modeling of a cylindrical wire antenna with flat end caps using a rigorous moment method technique

With recent capabilities for accurately and efficiently modeling electrically thicker wire antennas, questions concerning the necessity of including end caps in the model have resurfaced. The finite charge on the ends, which can significantly affect the current distribution, as well as improve convergence and stability of the solution, has been characterized in the past by several approximate models. However, a more in‐depth analysis of a wire antenna with end caps is necessary for completely characterizing the end charge density and understanding its effects on the near‐field behavior and the current distribution of the wire. Such a treatment is especially important for moderately thick wires or resonant structures. A rigorous method of moments formulation is developed in this paper for the analysis of cylindrical wire antennas with flat end caps. Circumferentially invariant axially directed trigonometric current basis functions are assumed on the cylindrical surface, and pulse charge density basis functions are assumed on the end caps. In addition, the formulation introduces a ring charge at the outer boundary of the top and bottom end caps to account for the edge discontinuity. Exact analysis techniques are employed to obtain the solution to the electric field integral equation.

Method of Moments Solutions for a Laminar Flow Aerosol Reactor Model

This study compares the capabilities of the conventional and quadrature methods of moments to describe condensational growth in a well-known laminar flow aerosol reactor model. Governing equations for energy, lower order radial moments of the particle size distribution, and vapor transport are written for a two-dimensional model using both approaches. Conventional and quadrature techniques to obtain closure of the moment equations are applied and compared. The conventional method requires certain approximations to the growth law. These include assumptions that the Kelvin effect is negligible and that the particle growth rate function is linear in particle size. In contrast, restrictive constraints of the conventional method of moments to obtain closure are avoided by applying the quadrature method. Numerical results for the laminar flow aerosol reactor model are obtained for a six moment formulation of the seed particle distribution to illustrate application of the quadrature method to continuous polydisperse distributions. We present the first calculations with the new quadrature method of moments to a two-dimensional aerosol transport and growth model.

Efficient method of moments formulation for large PEC scattering problems using asymptotic phasefront extraction (APE)

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.

Scattering properties of patch antennas loaded with inhomogeneous substrates via a combined spectral domainmoment method

In this paper a combined spectral domain-moment method is proposed in order to investigate the scattering properties of microstrip patch antennas with inhomogeneous substrates. The closed analytical expressions for the spectral dyadic Green's functions for different inhomogeneity profiles both in the rigorous and in the asymptotic form are obtained. A method of moments (MoM) formulation involving these expressions and using roof-top subdomain expansions is developed in order to calculate the radar cross-section for the antennas under analysis. Finally, different rectangular geometry patch shapes are considered (rectangular itself, L-patch, cross-patch, rectangular ring, etc.) and, for all of them, the monostatic radar cross-sections, compared to those obtained by using homogeneous substrates, are improved.

Method of Moments Solutions for a Laminar Flow Aerosol Reactor Model

This study compares the capabilities of the conventional and quadrature methods of moments to describe condensational growth in a well-known laminar flow aerosol reactor model. Governing equations for energy, lower order radial moments of the particle size distribution, and vapor transport are written for a two-dimensional model using both approaches. Conventional and quadrature techniques to obtain closure of the moment equations are applied and compared. The conventional method requires certain approximations to the growth law. These include assumptions that the Kelvin effect is negligible and that the particle growth rate function is linear in particle size. In contrast, restrictive constraints of the conventional method of moments to obtain closure are avoided by applying the quadrature method. Numerical results for the laminar flow aerosol reactor model are obtained for a six moment formulation of the seed particle distribution to illustrate application of the quadrature method to continuous polydisperse distributions. We present the first calculations with the new quadrature method of moments to a two-dimensional aerosol transport and growth model.

Transfer impedance of nonmagnetic conduits of various shapes

Metallic conduits provide mechanical support for cables, and may also protect the cables against interference caused by currents induced by external electromagnetic fields. The conduit transfer impedance Z/sub t/ then is a good measure for the provided protection. We studied Z/sub t/ by means of conformal transformations and of the method of moments in a quasistatic, two-dimensional (2-D) approach. Practical U-, H-, L-, and T-shaped conduits are discussed. Conformal transformations provide simple engineering expressions for the mutual inductance part of Z/sub t/ for cable positions inside the conduit. The method of moments formulation results in useful approximations for the crossover frequencies in Z/sub t/ between DC and high frequency. Measurements on U-shaped conduits confirm the calculations.

Optimal Material Layout in Three-Dimensional Elastic Structures Subjected to Multiple Loads1*

A method is presented for the optimal layout of material in three-dimensional elastic structures subjected to multiple loads. The problem is solved using a moment formulation to characterize optimal anisotropy of the material at each point of the domain. The method has important practical applications, e.g., in design of cross sections of prismatic bars and in optimal design of laminates.

Time moment analysis of first passage time, time lag and residence time problems via Taylor expansion of transmission matrix

Taylor expansion (with respect to the Laplace variable, s) of the transmission matrix, T(s), has been developed for the diffusion transport with position-dependent diffusivity, D(x) and partition coefficient, K(x). First, we find the relation between the expansion coefficients of the matrix elements and the moments of the first passage times by connecting them to Ĵ(s), the Laplace transform of the escaping flux, J(t). The moments can be formulated by repeated integrals of K(x) and [D(x)K(x)]−1 from solving the backward diffusion equation subject to appropriate initial and boundary conditions. In this way, Taylor expansion coefficients of T11(s), T21(s), and T22(s) are expressed in terms of the repeated integrals. Further application of the identity det[T(s)]=1 leads to the Taylor expansion T12(s). With the knowledge of the Taylor expansion of T(s), the formulation of the time moments for diffusion problems with position dependent D(x) and K(x) subject to various initial and boundary conditions is then just a simple, algebraic manipulation. Application of this new method is given to the membrane permeation transport and mean residence time problem.

Galerkin versus razor-blade testing in the method of moments formulation for multiconductor transmission lines

In this paper, the effect of the testing technique in the method of moments (MoM) solution for multiconductor transmission lines is investigated. Two important testing techniques, namely, Galerkin and razor-blade testing, are used and compared. The problem is formulated using the mixed potential integral equation. The analysis shows that the solution of the longitudinal modal current near the edge of the conductor is significantly affected by the testing scheme in the MoM kernel. For the selected expansion functions, razor-blade testing gives more reasonable modal current distribution than Galerkin testing. © 2000 John Wiley & Sons, Inc. Int J RF and Microwave CAE 10: 132–138, 2000.

Galerkin versus razor-blade testing in the method of moments formulation for multiconductor transmission lines

Galerkin versus razor-blade testing in the method of moments formulation for multiconductor transmission lines

Excitation energies and transition moments by the multireference averaged quadratic coupled cluster (MR-AQCC) method

The MR-AQCC (multireference averaged quadratic coupled cluster) and the MR-ACPF (multireference averaged coupled pair functional) methods can be considered as size-extensivity corrected MR-CISD procedures. So far, they have been applied mostly to ground state calculations of a given symmetry. By formulating MR-AQCC and MR-ACPF in terms of a diagonal shift to the Hamiltonian this restriction is removed. In order to compute transition moments, linear response theory (LRT) is used since there is no wavefunction defined within these methods. A LRT-compliant variant of MR-AQCC and MR-ACPF is developed which allows a consistent formulation of transition energies and moments. In calculations on CH2, CH+ and C2 (where full CI results are available) it is shown that MR-AQCC brings about a substantial improvement for excitation energies and transition moments as compared to MR-CISD.