Editorial

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Open AccessEditorial

Analytical Methods in Wave Scattering and Diffraction Volume I

by Nikolaos L. Tsitsas

Mathematics 2023, 11(4), 954; https://doi.org/10.3390/math11040954 - 13 Feb 2023

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Boundary value problems (BVPs) pertaining to scattering and radiation by devices that support novel wave phenomena are of primary importance in applied and computational mathematics, computational physics and engineering [...] Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)

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16 pages, 2036 KiB

Open AccessArticle

Analysis of Electromagnetic Scattering from Large Arrays of Cylinders via a Hybrid of the Method of Auxiliary Sources (MAS) with the Fast Multipole Method (FMM)

by Eleftherios Mastorakis, Panagiotis J. Papakanellos, Hristos T. Anastassiu and Nikolaos L. Tsitsas

Mathematics 2022, 10(17), 3211; https://doi.org/10.3390/math10173211 - 05 Sep 2022

Cited by 4 | Viewed by 1263

Abstract

The Method of Auxiliary Sources (MAS) is an established technique for the numerical solution of electromagnetic (EM) scattering and radiation problems. This paper presents a hybrid of MAS with the Fast Multipole Method (FMM), which provides a strategy for reducing the computational cost [...] Read more.

The Method of Auxiliary Sources (MAS) is an established technique for the numerical solution of electromagnetic (EM) scattering and radiation problems. This paper presents a hybrid of MAS with the Fast Multipole Method (FMM), which provides a strategy for reducing the computational cost and for solving large-scale problems without notable accuracy loss (and in a reasonable time). The hybrid MAS-FMM scheme is applied to the problem of EM scattering from an arbitrarily large array of lossless/lossy dielectric cylinders. Numerical results are presented to verify the MAS and MAS-FMM schemes, as well as to illuminate the improvements stemming from the proposed hybridization (especially the ones regarding the associated complexity and computational cost). A few concluding remarks offer a summary of this work, along with a list of possible future extensions. Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)

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18 pages, 4387 KiB

Open AccessArticle

Q Factor Enhancement of Open 2D Resonators by Optimal Placement of a Thin Metallic Rod in Front of the Longitudinal Slot

by Elena D. Vinogradova and Paul D. Smith

Mathematics 2022, 10(15), 2774; https://doi.org/10.3390/math10152774 - 04 Aug 2022

Cited by 3 | Viewed by 916

Abstract

A rigorous approach was employed for the accurate evaluation of the electromagnetic interaction between a thin metallic rod and a two-dimensional (2D) slotted cavity. The problem was posed as a classical boundary value problem for the Helmholtz equation in which a 2D slotted [...] Read more.

A rigorous approach was employed for the accurate evaluation of the electromagnetic interaction between a thin metallic rod and a two-dimensional (2D) slotted cavity. The problem was posed as a classical boundary value problem for the Helmholtz equation in which a 2D slotted open cavity is bounded by an arbitrary but otherwise smooth contour with a longitudinal slit. Using the method of analytical regularization, the problem was transformed to well-conditioned coupled infinite systems of linear algebraic equations for the Fourier coefficients in the expansions of induced surface currents on the rod and slotted cavity. When truncated to finite size, their solutions exhibit fast convergence to the exact solution as the order is increased. This feature makes it possible to investigate the spectral and scattering characteristics of the coupled cavity and rod to within any desired accuracy. In this paper, the complex eigenvalues for a slotted cavity in the presence of a thin rod and the dependence upon their relative location were investigated, particularly to find where there is significant or optimal enhancement of the

Q

factor. Such optimisation may be exploited in the design of advanced slot antennas and slotted waveguides. Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)

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15 pages, 2722 KiB

Open AccessArticle

The Statistical Estimation Averaging Method to Express the Effective Electromagnetic Parameters over a Planar Information Meta-Surface

by Ting-Ting Gu and Tie-Jun Cui

Mathematics 2022, 10(15), 2589; https://doi.org/10.3390/math10152589 - 25 Jul 2022

Cited by 1 | Viewed by 1110

Abstract

The electromagnetic scattering of a meta-surface, formed by a honeycomb substrate or periodical arranged meta-materials, has great meanings to communication technologies. In a conventional treatment to investigate the properties of these interfaces, either a variational approach or series expansions had been applied, instead [...] Read more.

The electromagnetic scattering of a meta-surface, formed by a honeycomb substrate or periodical arranged meta-materials, has great meanings to communication technologies. In a conventional treatment to investigate the properties of these interfaces, either a variational approach or series expansions had been applied, instead of estimating the effective permittivity or permeability by the mean value of its spatial discretized statistics due to spatiotemporal fusion. Following this, this study has re-examined the problem by the Statistic Estimation Averaging method (SEAm), through the transferred conditional structural Probability Density Functions (PDFs) to realize the structural determinations by homogenization. The parameters estimated by SEAm, which exploited the concept of a homogenized medium to express properties of a structural complex medium, has been verified of validity and accuracy by comparing with the measured results of a honeycomb structure. The method can be extended to estimate the parameters of an equivalent surface, such as randomly scattering from information metamaterials. As a new wireless communication relay technology, considering that information metamaterials can modulate the electromagnetic characteristics of communication links and wireless channels simultaneously by means of spatiotemporal sequence coding, the study also gives a preliminary proposition on state estimation method of information meta-surface, which would interpret the modulation effect of wireless channels caused by its inhomogeneity of antenna wavefront by statistical estimation average information entropy. Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)

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14 pages, 3760 KiB

Open AccessEditor’s ChoiceArticle

An Efficient Computational Technique for the Electromagnetic Scattering by Prolate Spheroids

by Ludovica Tognolatti, Cristina Ponti, Massimo Santarsiero and Giuseppe Schettini

Mathematics 2022, 10(10), 1761; https://doi.org/10.3390/math10101761 - 21 May 2022

Cited by 2 | Viewed by 1892

Abstract

In this paper we present an efficient Matlab computation of a 3-D electromagnetic scattering problem, in which a plane wave impinges with a generic inclination onto a conducting ellipsoid of revolution. This solid is obtained by the rotation of an ellipse around one [...] Read more.

In this paper we present an efficient Matlab computation of a 3-D electromagnetic scattering problem, in which a plane wave impinges with a generic inclination onto a conducting ellipsoid of revolution. This solid is obtained by the rotation of an ellipse around one of its axes, which is also known as a spheroid. We have developed a fast and ad hoc code to solve the electromagnetic scattering problem, using spheroidal vector wave functions, which are special functions used to describe physical problems in which a prolate or oblate spheroidal reference system is considered. Numerical results are presented, both for TE and TM polarization of the incident wave, and are validated by a comparison with results obtained by a commercial electromagnetic simulator. Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)

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39 pages, 1539 KiB

Open AccessArticle

A Conditioned Probabilistic Method for the Solution of the Inverse Acoustic Scattering Problem

by Antonios Charalambopoulos, Leonidas Gergidis and Eleftheria Vassilopoulou

Mathematics 2022, 10(9), 1383; https://doi.org/10.3390/math10091383 - 20 Apr 2022

Cited by 2 | Viewed by 1509

Abstract

In the present work, a novel stochastic method has been developed and investigated in order to face the time-reduced inverse scattering problem, governed by the Helmholtz equation, outside connected or disconnected obstacles supporting boundary conditions of Dirichlet type. On the basis of the [...] Read more.

In the present work, a novel stochastic method has been developed and investigated in order to face the time-reduced inverse scattering problem, governed by the Helmholtz equation, outside connected or disconnected obstacles supporting boundary conditions of Dirichlet type. On the basis of the stochastic analysis, a series of efficient and alternative stochastic representations of the scattering field have been constructed. These novel representations constitute conceptually the probabilistic analogue of the well known deterministic integral representations involving the famous Green’s functions, and so merit special importance. Their advantage lies in their intrinsic probabilistic nature, allowing to solve the direct and inverse scattering problem in the realm of local methods, which are strongly preferable in comparison with the traditional global ones. The aforementioned locality reflects the ability to handle the scattering field only in small bounded portions of the scattering medium by monitoring suitable stochastic processes, confined in narrow sub-regions where data are available. Especially in the realm of the inverse scattering problem, two different schemes are proposed facing reconstruction from the far field and near field data, respectively. The crucial characteristic of the inversion is that the reconstruction is fulfilled through stochastic experiments, taking place in the interior of conical regions whose base belong to the data region, while their vertices detect appropriately the supporting surfaces of the sought scatterers. Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)

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10 pages, 1159 KiB

Open AccessArticle

Tunable Multi-Band-Stop Filters Using Generalized Fibonacci Photonic Crystals for Optical Communication Applications

by Naim Ben Ali, Serhan Alshammari, Youssef Trabelsi, Haitham Alsaif, Omar Kahouli and Zied Elleuch

Mathematics 2022, 10(8), 1240; https://doi.org/10.3390/math10081240 - 09 Apr 2022

Cited by 4 | Viewed by 1460

Abstract

In this study, a numerical investigation of photonic quasi-periodic Generalized Fibonacci (GF) (m, n) sequences is carried out in the visible spectrum. The transfer matrix method is employed to study the behavior of wave propagation through the photonic structures. Firstly and to highlight [...] Read more.

In this study, a numerical investigation of photonic quasi-periodic Generalized Fibonacci (GF) (m, n) sequences is carried out in the visible spectrum. The transfer matrix method is employed to study the behavior of wave propagation through the photonic structures. Firstly and to highlight the importance of the GF structure, its transmittance spectrum is compared to those of periodic and ordinary Fibonacci structures. It is shown that the GF structure permits one to obtain multi-photonic band gaps (PBGs) separated by several resonance modes. The variation in the parameter m of the GF (m, 1) structure allows for the tuning of the number, the position and the width of these bands. By changing the parameter m, the wavelengths (650, 850, 1300, and 1550 nm) of the plastic and glass optical fibers can be allowed or forbidden to transmit through the structure according to the value of this parameter. In contrast, the variation in the parameter n for GF (1, n) hides all PBGs and only permits the appearance of several Kiessig fringes. The proposed structures can find application as tunable multi-band-stop filters for optical fiber wavelengths. Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)

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11 pages, 335 KiB

Open AccessArticle

Co-Circular Polarization Reflector Revisited: Reflection Properties, Polarization Transformations, and Matched Waves

by Ari Sihvola

Mathematics 2022, 10(4), 641; https://doi.org/10.3390/math10040641 - 18 Feb 2022

Cited by 1 | Viewed by 1614

Abstract

The variety of electromagnetic impedance boundaries is wide since the impedance boundary condition can have a two-dimensional matrix nature. In this article, a particular class of impedance boundary conditions is treated: a boundary condition that produces the so-called co-circular polarization reflector (CCPR). The [...] Read more.

The variety of electromagnetic impedance boundaries is wide since the impedance boundary condition can have a two-dimensional matrix nature. In this article, a particular class of impedance boundary conditions is treated: a boundary condition that produces the so-called co-circular polarization reflector (CCPR). The analysis focuses on the possibilities of manipulating the polarization of the electromagnetic wave reflected from the CCPR surface as well as the so-called matched waves associated with it. The characteristics of CCPR and its special cases (perfectly anisotropic boundary (PAB) and soft-and-hard surface (SHS)) are compared against more classical lossless boundaries: perfect electric, perfect magnetic, and perfect electromagnetic conductors (PEC, PMC, and PEMC). Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)

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17 pages, 1023 KiB

Open AccessArticle

A Direct Method for Solving Singular Integrals in Three-Dimensional Time-Domain Boundary Element Method for Elastodynamics

by Xiaofei Qin, Youhua Fan, Hongjun Li and Weidong Lei

Mathematics 2022, 10(2), 286; https://doi.org/10.3390/math10020286 - 17 Jan 2022

Cited by 4 | Viewed by 1707

Abstract

The analytically time integrable time-space domain (ATI-TSD) is discovered based on which the minimum time-space domain is identified for treatment on singularities in the three-dimensional time-domain boundary element method (3D TD-BEM) formulation. A direct method to solve singular integrals in the 3D TD-BEM [...] Read more.

The analytically time integrable time-space domain (ATI-TSD) is discovered based on which the minimum time-space domain is identified for treatment on singularities in the three-dimensional time-domain boundary element method (3D TD-BEM) formulation. A direct method to solve singular integrals in the 3D TD-BEM formulation for elastodynamic problems is proposed. The wavefront singularity can be analytically eliminated in ATI-TSD, while the dual singularity can be treated by the direct method using Kutt’s quadrature in the identified minimum time-space domain. Three benchmark examples are presented to verify the correctness and the applicability of the direct method for solving the singular integrals in 3D TD-BEM. Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)

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20 pages, 2062 KiB

Open AccessArticle

Analysis of Eigenfrequencies of a Circular Interface Delamination in Elastic Media Based on the Boundary Integral Equation Method

by Mikhail V. Golub and Olga V. Doroshenko

Mathematics 2022, 10(1), 38; https://doi.org/10.3390/math10010038 - 23 Dec 2021

Cited by 4 | Viewed by 2008

Abstract

The widespread of composite structures demands efficient numerical methods for the simulation dynamic behaviour of elastic laminates with interface delaminations with interacting faces. An advanced boundary integral equation method employing the Hankel transform of Green’s matrices is proposed for modelling wave scattering and [...] Read more.

The widespread of composite structures demands efficient numerical methods for the simulation dynamic behaviour of elastic laminates with interface delaminations with interacting faces. An advanced boundary integral equation method employing the Hankel transform of Green’s matrices is proposed for modelling wave scattering and analysis of the eigenfrequencies of interface circular partially closed delaminations between dissimilar media. A more general case of partially closed circular delamination is introduced using the spring boundary conditions with non-uniform spring stiffness distribution. The unknown crack opening displacement is expanded as Fourier series with respect to the angular coordinate and in terms of associated Legendre polynomials of the first kind via the radial coordinate. The problem is decomposed into a system of boundary integral equations and solved using the Bubnov-Galerkin method. The boundary integral equation method is compared with the meshless method and the published works for a homogeneous space with a circular open crack. The results of the numerical analysis showing the efficiency and the convergence of the method are demonstrated. The proposed method might be useful for damage identification employing the information on the eigenfrequencies estimated experimentally. Also, it can be extended for multi-layered composites with imperfect contact between sub-layers and multiple circular delaminations. Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)

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24 pages, 369 KiB

Open AccessArticle

An Analytical Method of Electromagnetic Wave Scattering by a Highly Conductive Sphere in a Lossless Medium with Low-Frequency Dipolar Excitation

by Eleni Stefanidou, Panayiotis Vafeas and Foteini Kariotou

Mathematics 2021, 9(24), 3290; https://doi.org/10.3390/math9243290 - 17 Dec 2021

Cited by 2 | Viewed by 1776

Abstract

The current research involves an analytical method of electromagnetic wave scattering by an impenetrable spherical object, which is immerged in an otherwise lossless environment. The highly conducting body is excited by an arbitrarily orientated time-harmonic magnetic dipole that is located at a reasonable [...] Read more.

The current research involves an analytical method of electromagnetic wave scattering by an impenetrable spherical object, which is immerged in an otherwise lossless environment. The highly conducting body is excited by an arbitrarily orientated time-harmonic magnetic dipole that is located at a reasonable remote distance from the sphere and operates at low frequencies for the physical situation under consideration, wherein the wavelength is much bigger than the size of the object. Upon this assumption, the scattering problem is formulated according to expansions of the implicated magnetic and electric fields in terms of positive integer powers of the wave number of the medium, which is linearly associated to the implied frequency. The static Rayleigh zeroth-order case and the initial three dynamic terms provide an excellent approximation for the obtained solution, while terms of higher orders are of minor significance and are neglected, since we work at the low-frequency regime. To this end, Maxwell’s equations reduce to a finite set of interrelated elliptic partial differential equations, each one accompanied by the perfectly electrically conducting boundary conditions on the metal sphere and the necessary limiting behavior as we move towards theoretical infinity, which is in practice very far from the observation domain. The presented analytical technique is based on the introduction of a suitable spherical coordinated system and yields compact fashioned three-dimensional solutions for the scattered components in view of infinite series expansions of spherical harmonic modes. In order to secure the validity and demonstrate the efficiency of this analytical approach, we invoke an example of reducing already known results from the literature to our complete isotropic case. Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)

12 pages, 426 KiB

Open AccessArticle

Generalization of the Optical Theorem to an Arbitrary Multipole Excitation of a Particle near a Transparent Substrate

by Yuri A. Eremin and Thomas Wriedt

Mathematics 2021, 9(24), 3244; https://doi.org/10.3390/math9243244 - 14 Dec 2021

Cited by 4 | Viewed by 1740

Abstract

In the present paper, the generalization of the optical theorem to the case of a penetrable particle deposited near a transparent substrate that is excited by a multipole of an arbitrary order and polarization has been derived. In the derivation we employ classic [...] Read more.

In the present paper, the generalization of the optical theorem to the case of a penetrable particle deposited near a transparent substrate that is excited by a multipole of an arbitrary order and polarization has been derived. In the derivation we employ classic Maxwell’s theory, Gauss’s theorem, and use a special representation for the multipole excitation. It has been shown that the extinction cross-section can be evaluated by the calculation of some specific derivatives from the scattered field at the position of the multipole location, in addition to some finite integrals which account for the multipole polarization and the presence of the substrate. Finally, the present paper considers some specific examples for the excitation of a particle by an electric quadrupole. Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)

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33 pages, 15821 KiB

Open AccessArticle

Sound Localization through Multi-Scattering and Gradient-Based Optimization

by Feruza Amirkulova, Samer Gerges and Andrew Norris

Mathematics 2021, 9(22), 2862; https://doi.org/10.3390/math9222862 - 11 Nov 2021

Cited by 8 | Viewed by 1882

Abstract

A gradient-based optimization (GBO) method is presented for acoustic lens design and sound localization. GBO uses a semi-analytical optimization combined with the principle of acoustic reciprocity. The idea differs from earlier inverse designs that use topology optimization tools and generic algorithms. We first [...] Read more.

A gradient-based optimization (GBO) method is presented for acoustic lens design and sound localization. GBO uses a semi-analytical optimization combined with the principle of acoustic reciprocity. The idea differs from earlier inverse designs that use topology optimization tools and generic algorithms. We first derive a formula for the gradients of the pressure at the focal point with respect to positions of a set of cylindrical scatterers. The analytic form of the gradients enhances modeling capability when combined with optimization algorithms and parallel computing. The GBO algorithm maximizes the sound amplification at the focal point and enhances the sound localization by evaluating pressure derivatives with respect to the cylinder positions and then perturbatively optimizing the position of each cylinder in the lens while incorporating multiple scattering between the cylindrical scatterers. The results of the GBO of the uni- and multi-directional broadband acoustic lens designs are presented including several performance measures for the frequency dependence and the incidence angle. A multi-directional broadband acoustic lens is designed to localize the sound and to focus acoustic incident waves received from multiple directions onto a predetermined localization region or focal point. The method is illustrated for configurations of sound hard and sound soft cylinders as well as clusters of elastic thin shells in water. Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)

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15 pages, 4507 KiB

Open AccessArticle

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

by Mario Lucido

Mathematics 2021, 9(12), 1429; https://doi.org/10.3390/math9121429 - 19 Jun 2021

Cited by 10 | Viewed by 1812

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)

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