scholarly journals TM Electromagnetic Scattering from PEC Polygonal Cross-Section Cylinders: A New Analytical Approach for the Efficient Evaluation of Improper Integrals Involving Oscillating and Slowly Decaying Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Mario Lucido ◽  
Chiara Santomassimo ◽  
Fulvio Schettino ◽  
Marco Donald Migliore ◽  
Daniele Pinchera ◽  
...  
Keyword(s):  
Cross Section ◽  
Electromagnetic Scattering ◽  
Computation Time ◽  
Electric Field Integral Equation ◽  
Analytical Technique ◽  
Electrically Conducting ◽  
Acceleration Technique ◽  
Integral Equation Formulation ◽  
The Matrix ◽  
Improper Integrals

The analysis of the TM electromagnetic scattering from perfectly electrically conducting polygonal cross-section cylinders is successfully carried out by means of an electric field integral equation formulation in the spectral domain and the method of analytical preconditioning which leads to a matrix equation at which Fredholm’s theory can be applied. Hence, the convergence of the discretization scheme is guaranteed. Unfortunately, the matrix coefficients are improper integrals involving oscillating and, in the worst cases, slowly decaying functions. Moreover, the classical analytical asymptotic acceleration technique leads to faster decaying integrands without overcoming the most important problem of their oscillating nature. Thus, the computation time rapidly increases as higher is the accuracy required for the solution. The aim of this paper is to show a new analytical technique for the efficient evaluation of such kind of integrals even when high accuracy is required for the solution.

scholarly journals ANALYSIS OF COMPOSITE DIELECTRIC METAMATERIALS USING INTEGRAL EQUATION TECHNIQUES

2020 ◽  
Author(s):  
John Stevenson
Keyword(s):  
Integral Equation ◽  
Method Of Moments ◽  
Electromagnetic Scattering ◽  
Three Dimensional ◽  
Surface Integral ◽  
Integral Equation Formulation ◽  
The Matrix ◽  
Speed Up ◽  
Fast Multipole Algorithm ◽  
Matrix Vector

We study numerically the electromagnetic scattering properties of three dimensional (3D),arbitrary shaped composite dielectric metamaterials. Using integral equation techniques, we firstderive a surface integral equation formulation which produces well-conditioned matrix equation.To solve the obtained integral equations, we apply a Galerkin scheme and choose the basis andtesting functions as Rao-Wilton-Glisson defined on planar patches. We then develop an algorithmto speed up the matrix-vector multiplications by employing the well-known method of moments(MoM) and the multilevel fast multipole algorithm on personal computer (PC) clusters. Some 3Dnumerical examples are presented to demonstrate the validity and accuracy of the proposedapproach.

scholarly journals Analysis of the Propagation in High-Speed Interconnects for MIMICs by Means of the Method of Analytical Preconditioning: A New Highly Efficient Evaluation of the Coefficient Matrix

2021 ◽  
Vol 11 (3) ◽  
pp. 933
Author(s):  
Mario Lucido
Keyword(s):  
Integral Equation ◽  
Integrated Circuits ◽  
High Speed ◽  
Coefficient Matrix ◽  
Single Step ◽  
Integral Theorem ◽  
Acceleration Technique ◽  
Cauchy Integral Theorem ◽  
Integral Equation Formulation ◽  
High Speed Interconnects

The method of analytical preconditioning combines the discretization and the analytical regularization of a singular integral equation in a single step. In a recent paper by the author, such a method has been applied to a spectral domain integral equation formulation devised to analyze the propagation in polygonal cross-section microstrip lines, which are widely used as high-speed interconnects in monolithic microwave and millimeter waves integrated circuits. By choosing analytically Fourier transformable expansion functions reconstructing the behavior of the fields on the wedges, fast convergence is achieved, and the convolution integrals are expressed in closed form. However, the coefficient matrix elements are one-dimensional improper integrals of oscillating and, in the worst cases, slowly decaying functions. In this paper, a novel technique for the efficient evaluation of such kind of integrals is proposed. By means of a procedure based on Cauchy integral theorem, the general coefficient matrix element is written as a linear combination of fast converging integrals. As shown in the numerical results section, the proposed technique always outperforms the analytical asymptotic acceleration technique, especially when highly accurate solutions are required.

Decomposing the Non-Gaussian Surface in Sum of Gaussian Surfaces

2012 ◽  
Vol 580 ◽  
pp. 170-174
Author(s):  
Zhang Xing Qi ◽  
Zhen Sen Wu ◽  
Zi Wen Yu ◽  
Hai Ying Li
Keyword(s):  
Cross Section ◽  
Electromagnetic Scattering ◽  
Radar Cross Section ◽  
Kirchhoff Approximation ◽  
Munk Function ◽  
The Difference ◽  
Non Gaussian ◽  
Gaussian Surface

The decomposition of the multivariate Non-Gaussian PDF in the sum of a Gaussian PDF instead of the Gram-Charlier series is investigated. Four parameters need to be found by minimizing the integrated square of the difference between Cox-Munk function and its approximation. The backscattering radar cross section (RCS) of the surface is calculated by the Kirchhoff approximation (KA) under different value of k using the formula of decomposition of the Non-Gaussian. The condition of KA satisfying electromagnetic scattering scale from Gaussian and Non-Gaussian surfaces is taken into account by computing the backscattering coefficients in HH and VV polarity.

A Modified Hybrid Integral Equation to Electromagnetic Scattering from Composite PEC-Dielectric Objects Containing Closed-Open PEC Junctions

2021 ◽  
Vol 36 (6) ◽  
pp. 642-649
Author(s):  
Jinbo Liu ◽  
Hongyang Chen ◽  
Hui Zhang ◽  
Jin Yuan ◽  
Zengrui Li
Keyword(s):  
Integral Equation ◽  
Electromagnetic Scattering ◽  
Surface Integral ◽  
Electric Conductor ◽  
Electric Field Integral Equation ◽  
Surface Integral Equation ◽  
Hybrid Integral ◽  
Fast Solution ◽  
Dielectric Objects ◽  
Field Integral

To efficiently analyze the electromagnetic scattering from composite perfect electric conductor (PEC)-dielectric objects with coexisting closed-open PEC junctions, a modified hybrid integral equation (HIE) is established as the surface integral equation (SIE) part of the volume surface integral equation (VSIE), which employs the combined field integral equation (CFIE) and the electric field integral equation (EFIE) on the closed and open PEC surfaces, respectively. Different from the traditional HIE modeled for the objects whose closed and open PEC surfaces are strictly separate, the modified HIE can be applied to the objects containing closed-open junctions. A matrix equation is obtained by using the Galerkin’s method of moments (MoM), which is augmented with the spherical harmonics expansion-based multilevel fast multipole algorithm (SE-MLFMA), improved by the mixed-potential representation and the triangle/tetrahedron-based grouping scheme. Because in the improved SE-MLFMA, the memory usage for storing the radiation patterns of basis functions is independent of the SIE type in the VSIE, it is highly appropriate for the fast solution of the VSIE that contains the HIE. Various numerical experiments demonstrate that during the calculation of composite objects containing closed-open PEC junctions, the application of the modified HIE in the VSIE can give reliable results with fast convergence speed.

scholarly journals Harmonic Modeling of a Diode-Clamped Multilevel Voltage Source Converter for Predicting Uncharacteristic Harmonics

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Tian Hao Huang ◽  
Kuo Lung Lian
Keyword(s):  
Computation Time ◽  
Voltage Source ◽  
Voltage Source Converter ◽  
Voltage Source Converters ◽  
Harmonic Model ◽  
Abcd Matrix ◽  
Truncation Errors ◽  
The Matrix ◽  
Matrix Mapping ◽  
The Time Domain

In response to the growing demand for medium- and high-power trends, multilevel voltage source converters (VSCs) have been attracting growing considerations. One of the widely used VSCs are the diode-clamped multilevel VSC (DCM-VSC). As these converters proliferate, their harmonic impact may become significant. Nevertheless, a harmonic model for the DCM-VSC is currently lacking in the literature. In this paper, the ABCD matrix, mapping the input harmonics to the output harmonics of DCM-VSC, is derived. As the matrix is formulated in the time-domain, the output harmonics are exact and do not suffer from harmonic truncation errors. As the paper will demonstrate, the derived ABCD matrix can be easily applied to a microgrid system and users can easily predict all the uncharacteristic harmonics when a microgrid is subjected to various conditions of imbalance. In addition to all the results being validated with those of PSCAD/EMTDC, the computation time of the proposed method is in contrast much shorter.

scholarly journals GAUSSIAN BEAM ELECTROMAGNETIC SCATTERING FROM PEC POLYGONAL CROSS-SECTION CYLINDERS

2017 ◽  
Vol 79 ◽  
pp. 101-113
Author(s):  
Mario Lucido ◽  
Fulvio Schettino ◽  
Marco Donald Migliore ◽  
Daniele Pinchera ◽  
Gaetano Panariello
Keyword(s):  
Gaussian Beam ◽  
Cross Section ◽  
Electromagnetic Scattering

Gravitational Möller scattering, Lorentz violation and finite temperature

2020 ◽  
Vol 35 (26) ◽  
pp. 2050213
Author(s):  
A. F. Santos ◽  
Faqir C. Khanna
Keyword(s):  
Differential Cross Section ◽  
Cross Section ◽  
Differential Cross ◽  
Electromagnetic Scattering ◽  
Lorentz Violation ◽  
Gravitational Effect ◽  
Energy Scale ◽  
Minimal Coupling ◽  
Moller Scattering ◽  
Thermo Field Dynamics

A formal analogy between the gravitational and the electromagnetic fields leads to the notion of Gravitoelectromagnetism (GEM) to describe gravitation. A Lagrangian formulation for GEM is developed for scattering processes with gravitons as an intermediate state, in addition to photons for electromagnetic scattering. The differential cross section is calculated for gravitational Möller scattering based on GEM theory. This gravitational cross section is obtained for cases where the Lorentz symmetry is maintained or violated. The Lorentz violation is introduced with the non-minimal coupling term. In addition, using the Thermo Field Dynamics formalism, thermal corrections to the differential cross section are investigated. By comparing the electromagnetic and GEM versions, of Möller scattering, it is shown that the gravitational effect may be measured at an appropriate energy scale.

Integration of Immunochemical Methods with Other Analytical Techniques for Pesticide Residue Determination

1995 ◽  
Vol 78 (3) ◽  
pp. 585-591 ◽  
Author(s):  
Anne D Lucas ◽  
Shirley J Gee ◽  
Bruce D Hammock ◽  
James N Seiber
Keyword(s):  
Small Molecules ◽  
Analytical Techniques ◽  
Low Molecular Weight ◽  
Solvent Exchange ◽  
New Techniques ◽  
Analytical Technique ◽  
Residue Determination ◽  
Organic Sample ◽  
Sample Extract ◽  
The Matrix

Abstract The growing volume of literature concerning immunoassay analysis for trace levels of agrochemicals and other low molecular weight contaminants in various matrixes is indicative of the tremendous interest in and utility of this analytical technique. Most immunoassay methods described in the literature analyze compounds directly, for example, a herbicide in water, or involve solvent exchange of an organic sample extract or dilution of an aqueous-based sample to minimize the matrix effect. As immunoassay for small molecules becomes widely accepted and applied, new challenges involving more complex chemicals in more difficult matrixes arise. The integration of “classical” analytical chemistry with immunochemistry can provide new techniques and approaches useful in discovering the movement, mode of action, and ultimate impact of certain chemicals on humans and the environment.

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