Fast Converging Cfie-Mom Analysis of Electromagnetic Scattering From Pec Polygonal Cross-Section Closed Cylinders

Lucido, Mario; Murro, Francesca Di; Panariello, G.; Santomassimo, Chiara

doi:10.2528/pierb17011803

Cited by 3 publications

(2 citation statements)

References 45 publications

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“…This is what happens when: (1) the Galerkin scheme is adopted, and (2) the selected expansion functions are orthonormal eigenfunctions of a suitable operator containing the most singular part of the integral operator at hand. Such an approach, appropriately called method of analytical preconditioning, is very effective, as clearly shown in the literature devoted to the study of the scattering, propagation, and radiation problems [23][24][25][26][27][28][29][30][31][32][33]. Another way to obtain a guaranteed-convergence consists in solving numerically the singular integral equation by means of a Nyström-type discretization scheme taking into account the singularity of the integral equation and the behavior of the unknowns at the edges [34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Scattering from a Two Stacked Thin Resistive Disks Resonator by Means of the Helmholtz–Galerkin Regularizing Technique

Lucido

2021

Applied Sciences

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In this paper, the scattering of a plane wave from a lossy Fabry–Perót resonator, realized with two equiaxial thin resistive disks with the same radius, is analyzed by means of the generalization of the Helmholtz–Galerkin regularizing technique recently developed by the author. The disks are modelled as 2-D planar surfaces described in terms of generalized boundary conditions. Taking advantage of the revolution symmetry, the problem is equivalently formulated as a set of independent systems of 1-D equations in the vector Hankel transform domain for the cylindrical harmonics of the effective surface current densities. The Helmholtz decomposition of the unknowns, combined with a suitable choice of the expansion functions in a Galerkin scheme, lead to a fast-converging Fredholm second-kind matrix operator equation. Moreover, an analytical technique specifically devised to efficiently evaluate the integrals of the coefficient matrix is adopted. As shown in the numerical results section, near-field and far-field parameters are accurately and efficiently reconstructed even at the resonance frequencies of the natural modes, which are searched for the peaks of the total scattering cross-section and the absorption cross-section. Moreover, the proposed method drastically outperforms the general-purpose commercial software CST Microwave Studio in terms of both CPU time and memory occupation.

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Section: Introductionmentioning

confidence: 99%

Analysis of the Scattering from a Two Stacked Thin Resistive Disks Resonator by Means of the Helmholtz–Galerkin Regularizing Technique

Lucido

2021

Applied Sciences

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“…However, for such first-kind weakly-singular or hyper-singular integral equations, the convergence of discretization schemes cannot be guaranteed, and the sequence of condition numbers of truncated system is divergent due to the unboundedness of the integral operator or of its inverse [1]. In order to overcome these problems, a general approach, detailed in [2], has been extensively applied to the analysis of propagation, radiation and scattering problems [3][4][5][6][7][8][9][10][11][12][13][14][15][16], combining analytical regularization and discretization of the integral operator in a single step. By means of Galerkin method with a complete set of basis functions that makes the most singular part of the integral operator invertible with a continuous two-side inverse, the integral equation at hand is recast as a matrix equation at which Fredholm alternative can be applied [17].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic Scattering From a Zero-Thickness Pec Disk: A Note on the Helmholtz-Galerkin Analytically Regularizing Procedure

Lucido¹,

Murro²,

Panariello³

2017

PIER Letters

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Recently, a new analytically regularizing procedure, based on Helmholtz decomposition and Galerkin method, has been proposed to analyze the electromagnetic scattering from a zero-thickness perfectly electrically conducting disk. The convergence of the discretization scheme is guaranteed and of exponential type, i.e., few expansion functions are needed to achieve highly accurate solutions. However, it leads to the numerical evaluation of improper integrals of asymptotically oscillating and slowly decaying functions. Asymptotic acceleration techniques allow to obtain faster decaying integrands without overcoming the problem of the oscillating nature of the integrands themselves, i.e., the convergence of the integrals becomes slower and slower as the accuracy required for the solution is higher. In this paper, by means of algebraic manipulations and a suitable integration procedure in the complex plane, an alternative expression for the scattering matrix coefficients involving only fast converging proper integrals is devised. As shown in the numerical results section, the proposed technique is very effective and drastically outperforms the classical analytical asymptotic acceleration technique.

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Electromagnetic Scattering from a Graphene Disk: Helmholtz-Galerkin Technique and Surface Plasmon Resonances

Lucido

2021

Mathematics

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The surface plasmon resonances of a monolayer graphene disk, excited by an impinging plane wave, are studied by means of an analytical-numerical technique based on the Helmholtz decomposition and the Galerkin method. An integral equation is obtained by imposing the impedance boundary condition on the disk surface, assuming the graphene surface conductivity provided by the Kubo formalism. The problem is equivalently formulated as a set of one-dimensional integral equations for the harmonics of the surface current density. The Helmholtz decomposition of each harmonic allows for scalar unknowns in the vector Hankel transform domain. A fast-converging Fredholm second-kind matrix operator equation is achieved by selecting the eigenfunctions of the most singular part of the integral operator, reconstructing the physical behavior of the unknowns, as expansion functions in a Galerkin scheme. The surface plasmon resonance frequencies are simply individuated by the peaks of the total scattering cross-section and the absorption cross-section, which are expressed in closed form. It is shown that the surface plasmon resonance frequencies can be tuned by operating on the chemical potential of the graphene and that, for orthogonal incidence, the corresponding near field behavior resembles a cylindrical standing wave with one variation along the disk azimuth.

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Fast Converging Cfie-Mom Analysis of Electromagnetic Scattering From Pec Polygonal Cross-Section Closed Cylinders

Cited by 3 publications

References 45 publications

Analysis of the Scattering from a Two Stacked Thin Resistive Disks Resonator by Means of the Helmholtz–Galerkin Regularizing Technique

Analysis of the Scattering from a Two Stacked Thin Resistive Disks Resonator by Means of the Helmholtz–Galerkin Regularizing Technique

Electromagnetic Scattering From a Zero-Thickness Pec Disk: A Note on the Helmholtz-Galerkin Analytically Regularizing Procedure

Electromagnetic Scattering from a Graphene Disk: Helmholtz-Galerkin Technique and Surface Plasmon Resonances

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