Challenge of Guaranteed Convergence in Applied Electromagnetics: Recent Progress in the Methods of Analytical Regularization

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Electrical, Electronics and Communications Engineering".

Deadline for manuscript submissions: closed (30 December 2023) | Viewed by 5150

Special Issue Editors

Department of Electrical and Information Engineering “Maurizio Scarano”, University of Cassino and Southern Lazio, Via G. Di Biasio 43, 03043 Cassino, FR, Italy
Interests: analytical–numerical methods for electromagnetics; electromagnetic diffraction and scattering; waveguide and optical waveguide; microwave circuits and antennas
* Leading GE
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Kazuya Kobayashi
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Guest Editor
Department of Electrical, Electronic, and Communication Engineering, Chuo University, Tokyo 112-8551, Japan
Interests: rigorous mathematical techniques for electromagnetic wave problems; radar cross-section; scattering and diffraction
Department of Electronics and Electromagnetism, Universidad de Sevilla, 41012 Seville, Spain
Interests: modelling of planar transmission lines, antennas and circuits using optimized integral equation methods; (bi)anisotropic structures; metamaterials and periodic electromagnetic structures
Laboratory of Micro and Nano Optics, Institute of Radio-Physics and Electronics of the National Academy of Sciences of Ukraine (IRE-NASU), 61085 Kharkiv, Ukraine
Interests: methods of analytical regularization; propagation and scattering of waves; open waveguides; antennas and lasers; history of microwaves
Prof. Dr. Elena D. Vinogradova
E-Mail Website1 Website2 Website3 Website4 Website5
Guest Editor
School of Mathematical and Physical Sciences, Macquarie University, Sydney 2109, Australia
Interests: rigorous methods for solving the dual and triple integral and series equations arising from the potential theory of the acoustic and electromagnetic wave diffraction

Special Issue Information

Dear Colleagues,

The development of new, powerful electromagnetic solvers in the last few years has been strictly related to the recent advances in telecommunications due to the introduction of amazing new materials and meta-materials, the new interest in wireless communications at higher frequencies than usual (millimetre and THz frequencies), and the increasing number of applications in photonics and nano-optics. Among the various techniques developed, those based on integral equation formulations are widely preferred because the unknowns are defined on finite supports and the radiation condition is automatically satisfied. Since a closed-form solution is not available for a general integral equation, suitable analytical/numerical techniques have to be adopted to achieve an approximate solution of the problem. Unfortunately, the existence of a solution of an integral equation cannot be generally stated and, even if such a solution exists, the convergence of a discretization scheme cannot always be established. For these reasons, the results provided by commercial software need to be validated ex post. On the other hand, the family of methods collectively called methods of analytical regularization (MAR) completely overcome these problems, allowing the conversion of first-kind weakly singular and various kinds of strongly singular integral equations to Fredholm second-kind integral or matrix equations. As a result, MAR has been attracting growing interest from the electromagnetic community in recent years.

This Special Issue is aimed at showing the recent developments of MAR theory and its latest applications. 

The topics of interest include, but are not limited to:

  • Optical and microwave antennas;
  • Plasmonic scatterers;
  • Patterned graphene;
  • Metasurfaces;
  • Dielectric resonators and lenses;
  • Waveguide circuits;
  • Laser modes on threshold.

Prof. Dr. Mario Lucido
Prof. Dr. Kazuya Kobayashi
Prof. Dr. Francisco Medina
Prof. Dr. Alexander I. Nosich
Prof. Dr. Elena D. Vinogradova
Guest Editors

Manuscript Submission Information

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Keywords

  • convergence and accuracy
  • regularizing Galerkin methods
  • Abel integral equation techniques
  • Muller boundary integral equations
  • Wiener–Hopf-based techniques
  • eigenvalue problems
  • regularizing asymptotic techniques

Published Papers (7 papers)

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Research

12 pages, 3655 KiB  
Article
Controlling the Focusing Ability of the Parabolic Graphene Reflector in Free Space at Microwave Frequencies
Appl. Sci. 2024, 14(4), 1520; https://doi.org/10.3390/app14041520 - 14 Feb 2024
Viewed by 299
Abstract
The studied configuration is a two-dimensional, very thin parabolic reflector made of graphene and illuminated by an H-polarized electromagnetic plane wave. We present basic scattering and focusing properties of such a graphene reflector depending on the graphene parameters at microwave frequencies, using the [...] Read more.
The studied configuration is a two-dimensional, very thin parabolic reflector made of graphene and illuminated by an H-polarized electromagnetic plane wave. We present basic scattering and focusing properties of such a graphene reflector depending on the graphene parameters at microwave frequencies, using the resistive boundary condition for very thin sheets. The scattering is formulated as an electromagnetic boundary-value problem; it is transformed to a singular integral equation that is further treated with the method of analytical regularization (MAR) based on the known solution of the Riemann–Hilbert Problem (RHP). The numerical results are computed by using a Fredholm second-kind matrix equation that guarantees convergence and provides easily controlled accuracy. Compared to THz range, in microwaves, the scattering pattern of reflector and the field level at geometrical focus can be controlled in a wide range by adjusting the chemical potential of graphene. Even though here no dielectric substrate supporting the graphene is considered, the practical realization can also be possible as a thin layer graphene material in GHz range. As we demonstrate, the variation of the chemical potential from 0 to 1 eV can improve the focusing ability within the factor of three. The high accuracy of the used method and the full wave formulation of the problem support our findings. Full article
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13 pages, 12744 KiB  
Article
Tunability of Radiation Pattern of the H-Polarized Natural Waves of Dielectric Waveguide with Infinite Graphene Plane and Finite Number of Graphene Strips at THz
Appl. Sci. 2023, 13(19), 10563; https://doi.org/10.3390/app131910563 - 22 Sep 2023
Viewed by 421
Abstract
We investigate the radiation of the THz natural waves of the dielectric waveguide with graphene plane scattered by finite number of graphene strips. Our mathematically accurate analysis uses the singular integral equations method. The discretization scheme employs the Nystrom-type algorithm. The complex-valued propagation [...] Read more.
We investigate the radiation of the THz natural waves of the dielectric waveguide with graphene plane scattered by finite number of graphene strips. Our mathematically accurate analysis uses the singular integral equations method. The discretization scheme employs the Nystrom-type algorithm. The complex-valued propagation constants of the natural waves and corresponding fields are determined numerically from the equation, which also involves the kernel-function of the singular integral equation. The method we use is meshless and full-wave. The convergence is provided by the mathematical theorems. By varying the chemical potential of graphene and structural geometrical parameters, we examine the elevation angle of the main lobe of the radiation pattern and the radiated power. Full article
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23 pages, 878 KiB  
Article
Wave Diffraction from a Bicone Conjoined with an Open-Ended Conical Cavity
Appl. Sci. 2023, 13(14), 8517; https://doi.org/10.3390/app13148517 - 23 Jul 2023
Cited by 1 | Viewed by 601
Abstract
The problem of axially symmetric TM-wave diffraction from a bicone conjoined with an open-ended conical cavity is analysed rigorously. The scatterer is formed by the perfectly conducting semi-infinite and truncated semi-infinite conical surfaces; the spherical termination of an internal area of the truncated [...] Read more.
The problem of axially symmetric TM-wave diffraction from a bicone conjoined with an open-ended conical cavity is analysed rigorously. The scatterer is formed by the perfectly conducting semi-infinite and truncated semi-infinite conical surfaces; the spherical termination of an internal area of the truncated cone creates the open-ended cavity. In this paper the certain physical aspects of diffraction which are known to cause mathematical difficulties are considered. It includes an accurate analysis of the wave-mode transformation phenomena at the open end of the cavity, as well as a study of wave radiation from the cavity into the biconical waveguide. The primary outcome of this paper is a precise treatment of the wave diffraction problem mentioned above using new techniques and establishing new properties of resonance modes’ penetration into the biconical waveguide region. Full article
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14 pages, 5841 KiB  
Article
Plane-Wave Diffraction from Resistive-Filled Circular Hole in Infinite Resistive Plane: An Analytically Regularizing Approach
Appl. Sci. 2023, 13(13), 7465; https://doi.org/10.3390/app13137465 - 24 Jun 2023
Viewed by 575
Abstract
The study of the electromagnetic diffraction from penetrable screens with apertures and/or inhomogeneities is of great relevance today due to the huge number of modern applications in which they are involved. In this paper, the analysis of the plane wave scattering from a [...] Read more.
The study of the electromagnetic diffraction from penetrable screens with apertures and/or inhomogeneities is of great relevance today due to the huge number of modern applications in which they are involved. In this paper, the analysis of the plane wave scattering from a resistive-filled circular hole in a resistive plane is addressed. The uniquely solvable boundary value problem for the Maxwell equations, obtained via imposing generalized boundary conditions, power boundedness condition, and Silver–Muller radiation condition, is equivalently formulated in terms of an infinite set of singular dual integral equations in the vector Hankel transform domain. The Helmholtz–Galerkin technique allows for the discretization and, simultaneously, analytical regularization of the obtained integral equations. Fast convergence is guaranteed by a suitable choice of the basis functions reconstructing the physical behavior of the fields at the discontinuity between the two involved media. Moreover, the full-wave nature of the proposed approach allows the direct assessment of near-field and far-field parameters. Full article
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13 pages, 446 KiB  
Article
A Dual Integral Equation Approach for Evaluating the Shielding of Thick Circular Disks against a Coaxial Loop
Appl. Sci. 2023, 13(9), 5819; https://doi.org/10.3390/app13095819 - 08 May 2023
Cited by 1 | Viewed by 921
Abstract
The electromagnetic interaction between a circular disk with finite conductivity and finite thickness and a coaxial circular loop of constant current is addressed here. The finite conductivity and thickness of the material disk lead to the adoption of suitable generalized boundary conditions, and [...] Read more.
The electromagnetic interaction between a circular disk with finite conductivity and finite thickness and a coaxial circular loop of constant current is addressed here. The finite conductivity and thickness of the material disk lead to the adoption of suitable generalized boundary conditions, and the problem is thereby reduced to the solution of two sets of dual integral equations in the Hankel transform domain. Such equations are then solved by expanding the spectral unknowns in Neumann series of Bessel functions. An alternative formulation that is valid for purely conductive screens with no magnetic properties, which is computationally much faster, is proposed as well. The magnetic shielding effectiveness of the structure is studied in detail, pointing out its dependencies and possible critical situations. Full article
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11 pages, 880 KiB  
Article
The Regularization Technique in Modeling of the Plane E-Polarized EM Wave Scattering by Coplanar System of Electrically Conducting Flat Strips
Appl. Sci. 2023, 13(9), 5488; https://doi.org/10.3390/app13095488 - 28 Apr 2023
Viewed by 649
Abstract
The integral equations technique has been successfully modified for studying the plane E-polarized electromagnetic wave scattering by multilevel coplanar systems of zero-thickness impedance strips. Reformulation of the scattering problem in the form of the second-kind regular integral equations has been realized on [...] Read more.
The integral equations technique has been successfully modified for studying the plane E-polarized electromagnetic wave scattering by multilevel coplanar systems of zero-thickness impedance strips. Reformulation of the scattering problem in the form of the second-kind regular integral equations has been realized on the base of the Carleman regularization technique. Two novel and original classes of specific Cantor functions have been presented and analyzed. Using new Cantor functions, it is easy to create a lot of non-classical orderings for specific multilevel coplanar strips systems. That sort of system can be useful for modeling irregular natural processes and zones in the future. Considerable attention was focused on the plane E-polarized electromagnetic wave scattering by sparsely filled coplanar systems of electrically narrow impedance strips. An explicit solution of the scattering problem has been obtained for such case of strips system. Full article
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22 pages, 9578 KiB  
Article
Diffraction by a Semi-Infinite Parallel-Plate Waveguide with Five-Layer Material Loading: The Case of H-Polarization
Appl. Sci. 2023, 13(6), 3715; https://doi.org/10.3390/app13063715 - 14 Mar 2023
Cited by 1 | Viewed by 855
Abstract
In this paper, the plane wave diffraction from a semi-infinite parallel-plate waveguide with five-layer material loading is rigorously analyzed for H-polarization using the Wiener–Hopf technique. The Fourier transform of the scattered field is introduced and boundary conditions are applied in the transform domain [...] Read more.
In this paper, the plane wave diffraction from a semi-infinite parallel-plate waveguide with five-layer material loading is rigorously analyzed for H-polarization using the Wiener–Hopf technique. The Fourier transform of the scattered field is introduced and boundary conditions are applied in the transform domain to formulate the problem as simultaneous Wiener–Hopf equations, which are solved by the factorization and decomposition procedure leading to exact and approximate solutions. The scattered field in real space is explicitly derived by taking the Fourier inverse of the solution in the transform domain. For the region inside the waveguide, the scattered field is represented by the waveguide TM modes, and the field outside the waveguide is evaluated asymptotically by applying the saddle-point method to obtain a far-field expression. Numerical examples of the radar cross section (RCS) for various physical parameters are presented, and far-field scattering characteristics of the waveguide are discussed in detail. Full article
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