Special Issue "Numerical and Analytical Methods in Electromagnetics"

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Applied Physics".

Deadline for manuscript submissions: closed (31 May 2020).

Special Issue Editor

Prof. Dr. Hristos Anastassiu
Website
Guest Editor
Department of Informatics Engineering, Technological and Educational Institute of Central Macedonia at Serres, End of Magnisias Str., GR-62124 Serres, Greece

Special Issue Information

Dear Colleagues,

Like all branches of physics and engineering, electromagnetics relies on mathematical methods for modelling, simulation, and design procedures in all of its aspects (radiation, propagation, scattering, imaging, etc.). Originally, rigorous, analytical techniques were the only machinery available to produce any useful results. Basically, the aim was the solution of partial differential equations (such as the Laplace, Poisson, Helmholtz, and wave equations) since the electric and magnetic fields are the unkown quantities in such expressions, although exact, analytical methods (e.g., the Wiener–Hopf technique) were limited to canonical geometries, which are unfortunetely rare in nature. Hence, in the 60s and 70s, emphasis was placed on asympotic techniques, which produced approximations of the fields for very high frequencies when closed form solutions were not feasible. Typical examples of such techniques were the Geometrical and Physical Optics (GO and PO, respectively), improved by the Geometrical, Physical, and Uniform Theories of Diffraction (GTD, PTD and UTD respectively). Later, when computers demonstrated explosive progress, numerical techniques were utilized to develop approximate results of controllable accuracy for arbitrary geometries. Either differential or integral equations were discretized, leading to standard techniques, such as the Method of Moments (MoM), finite element method (FEM), finite difference time domain method (FDTD), finite integration technique (FIT), and Method of Auxiliary Sources (MAS). Researchers soon realized that several practical problems required extremely high computational resources, in terms of memory and CPU time, to handle, typically, millions of unknowns. Therefore, “fast” variants of the latter techniques were developed to suppress the computational cost, such as the adaptive integral method (AIM); the fast multipole method (FMM); its parallel version, called the multi-level fast multipole algorithm (MLFMA); and its time domain counterpart, i.e., the plane wave time domain (PWTD) method. The lists above are by no means exhaustive; there is a plethora of additional algorithms, having evolved particularly over the last few years, designed to reduce the complexity and simultaneously improve the accuracy of calculations. In this Special Issue, the most recent advances thereof will be presented, to  illustrate the state of the art in mathematical techniques in electromagnetics. 

Prof. Dr. Hristos Anastassiu
Guest Editor

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Keywords

  • GTD
  • UTD
  • PTD
  • MoM
  • FEM
  • FDTD
  • MAS
  • AIM
  • FMM
  • MLFMA

Published Papers (12 papers)

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Editorial

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Open AccessEditorial
Special Issue “Numerical and Analytical Methods in Electromagnetics”
Appl. Sci. 2020, 10(20), 7242; https://doi.org/10.3390/app10207242 - 16 Oct 2020
Abstract
Like all branches of physics and engineering, electromagnetics relies on mathematical methods for modeling, simulation, and design procedures in all of its aspects (radiation, propagation, scattering, imaging, etc [...] Full article
(This article belongs to the Special Issue Numerical and Analytical Methods in Electromagnetics)

Research

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Open AccessArticle
Numerical 3D Simulation of a Full System Air Core Compulsator-Electromagnetic Rail Launcher
Appl. Sci. 2020, 10(17), 5903; https://doi.org/10.3390/app10175903 - 26 Aug 2020
Cited by 2
Abstract
Multiphysics problems represent an open issue in numerical modeling. Electromagnetic launchers represent typical examples that require a strongly coupled magnetoquasistatic and mechanical approach. This is mainly due to the high velocities which make comparable the electrical and the mechanical response times. The analysis [...] Read more.
Multiphysics problems represent an open issue in numerical modeling. Electromagnetic launchers represent typical examples that require a strongly coupled magnetoquasistatic and mechanical approach. This is mainly due to the high velocities which make comparable the electrical and the mechanical response times. The analysis of interacting devices (e.g., a rail launcher and its feeding generator) adds further complexity, since in this context the substitution of one device with an electric circuit does not guarantee the accuracy of the analysis. A simultaneous full 3D electromechanical analysis of the interacting devices is often required. In this paper a numerical 3D analysis of a full launch system, composed by an air-core compulsator which feeds an electromagnetic rail launcher, is presented. The analysis has been performed by using a dedicated, in-house developed research code, named “EN4EM” (Equivalent Network for Electromagnetic Modeling). This code is able to take into account all the relevant electromechanical quantities and phenomena (i.e., eddy currents, velocity skin effect, sliding contacts) in both the devices. A weakly coupled analysis, based on the use of a zero-dimensional model of the launcher (i.e., a single loop electrical equivalent circuit), has been also performed. Its results, compared with those by the simultaneous 3D analysis of interacting devices, show an over-estimate of about 10–15% of the muzzle speed of the armature. Full article
(This article belongs to the Special Issue Numerical and Analytical Methods in Electromagnetics)
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Open AccessArticle
Destruction of Fibroadenomas Using Photothermal Heating of Fe3O4 Nanoparticles: Experiments and Models
Appl. Sci. 2020, 10(17), 5844; https://doi.org/10.3390/app10175844 - 24 Aug 2020
Cited by 1
Abstract
Conventionally, observation (yearly breast imaging) is preferred to therapy to manage small-sized fibroadenomas because they are normally benign tumors. However, recent reports of increased cancer risk coupled with patient anxiety due to fear of malignancy motivate the need for non-aggressive interventions with minimal [...] Read more.
Conventionally, observation (yearly breast imaging) is preferred to therapy to manage small-sized fibroadenomas because they are normally benign tumors. However, recent reports of increased cancer risk coupled with patient anxiety due to fear of malignancy motivate the need for non-aggressive interventions with minimal side-effects to destroy such tumors. Here, we describe an integrated approach composed of experiments and models for photothermal therapy for fibroadenomas destruction. We characterized the optical and structural properties and quantified the heat generation performance of Fe3O4 nanoparticles (NPs) by experiments. On the basis of the optical and structural results, we obtained the optical absorption coefficient of the Fe3O4 NPs via predictions based on the Mie scattering theory and integrated it into a computational model to predict in-vivo thermal damage profiles of NP-embedded fibroadenomas located within a multi-tissue breast model and irradiated with near-infrared 810 nm laser. In a series of temperature-controlled parametric studies, we demonstrate the feasibility of NP-mediated photothermal therapy for the destruction of small fibroadenomas and the influence of tumor size on the selection of parameters such as NP concentration, treatment duration and irradiation protocols (treatment durations and laser power). The implications of the results are then discussed for the development of an integrated strategy for a noninvasive photothermal therapy for fibroadenomas. Full article
(This article belongs to the Special Issue Numerical and Analytical Methods in Electromagnetics)
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Open AccessArticle
3-D Integral Formulation for Thin Electromagnetic Shells Coupled with an External Circuit
Appl. Sci. 2020, 10(12), 4284; https://doi.org/10.3390/app10124284 - 22 Jun 2020
Cited by 2
Abstract
The aim of this article is to present a hybrid integral formulation for modelling structures made by conductors and thin electromagnetic shell models. Based on the principle of shell elements, the proposed method provides a solution to various problems without meshing the air [...] Read more.
The aim of this article is to present a hybrid integral formulation for modelling structures made by conductors and thin electromagnetic shell models. Based on the principle of shell elements, the proposed method provides a solution to various problems without meshing the air regions, and at the same time helps to take care of the skin effect. By integrating the system of circuit equations, the method presented in this paper can also model the conductor structures. In addition, the equations describing the interaction between the conductors and the thin shell are also developed. Finally, the formulation is validated via an axisymmetric finite element method and the obtained results are compared with those implemented from another shell formulation. Full article
(This article belongs to the Special Issue Numerical and Analytical Methods in Electromagnetics)
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Open AccessArticle
Distribution of Magnetic Field in 400 kV Double-Circuit Transmission Lines
Appl. Sci. 2020, 10(9), 3266; https://doi.org/10.3390/app10093266 - 08 May 2020
Cited by 3
Abstract
A high-voltage AC double-circuit 400 kV overhead power transmission line runs from the city of Elk (Poland) to the city of Alytus (Lithuania). This international 400 kV power transmission line is potentially one of the strongest magnetic field-generating sources in the area. This [...] Read more.
A high-voltage AC double-circuit 400 kV overhead power transmission line runs from the city of Elk (Poland) to the city of Alytus (Lithuania). This international 400 kV power transmission line is potentially one of the strongest magnetic field-generating sources in the area. This 400 kV voltage double-circuit overhead transmission line and its surroundings were analyzed using the mathematical analytical methods of superposition and reflections. This research paper includes the calculation of the numerical values of the magnetic field and its distribution. The research showed that the values of the magnetic field strength near the international 400 kV power transmission line exceed the threshold values permitted by relevant standards. This overhead power line is connected to the general (50 Hz) power system and generates a highly intense magnetic field. It is suggested that experimental trials should be undertaken in order to determine the maximum values of the magnetic field strength. For the purpose of mitigating these values, it is suggested that the height of the support bars should be increased or that any individual and commercial activities near the object under investigation should be restricted. Full article
(This article belongs to the Special Issue Numerical and Analytical Methods in Electromagnetics)
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Open AccessArticle
Optimisation of Energy Transfer in Reluctance Coil Guns: Application to Soccer Ball Launchers
Appl. Sci. 2020, 10(9), 3137; https://doi.org/10.3390/app10093137 - 30 Apr 2020
Cited by 2
Abstract
Reluctance coil guns are electromagnetic launchers having a good ratio of energy transmitted to actuator volume, making them a good choice for propelling objects with a limited actuator space. In this paper, we focus on an application, which is launching real size soccer [...] Read more.
Reluctance coil guns are electromagnetic launchers having a good ratio of energy transmitted to actuator volume, making them a good choice for propelling objects with a limited actuator space. In this paper, we focus on an application, which is launching real size soccer balls with a size constrained robot. As the size of the actuator cannot be increased, kicking strength can only be improved by enhancing electrical to mechanical energy conversion, compared to existing systems. For this, we propose to modify its inner structure, splitting the coil and the energy storage capacitor into several ones, and triggering the coils successively for propagating the magnetic force in order to improve efficiency. This article first presents a model of reluctance electromagnetic coil guns using a coupled electromagnetic, electrical and mechanical models. Four different coil gun structures are then simulated, concluding that splitting the kicking coil into two half size ones is the best trade-off for optimizing energy transfer, while maintaining an acceptable system complexity and controllability. This optimization results in robust enhancement and leads to an increase by 104 % of the energy conversion compared to a reference launcher used. This result has been validated experimentally on our RoboCup robots. This paper also proves that splitting the coil into a higher number of coils is not an interesting trade-off. Beyond results on the chosen case study, this paper presents an optimization technique based on mixed mechanic, electric and electromagnetic modelling that can be applied to any reluctance coil gun. Full article
(This article belongs to the Special Issue Numerical and Analytical Methods in Electromagnetics)
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Open AccessArticle
Electromagnetic Scattering from Surfaces with Curved Wedges Using the Method of Auxiliary Sources (MAS)
Appl. Sci. 2020, 10(7), 2309; https://doi.org/10.3390/app10072309 - 27 Mar 2020
Cited by 1
Abstract
The method of auxiliary sources (MAS) is utilized in the analysis of Transverse Magnetic (TM) plane wave scattering from infinite, conducting, or dielectric cylinders, including curved wedges. The latter are defined as intersections of circular arcs. The artificial surface, including the auxiliary sources, [...] Read more.
The method of auxiliary sources (MAS) is utilized in the analysis of Transverse Magnetic (TM) plane wave scattering from infinite, conducting, or dielectric cylinders, including curved wedges. The latter are defined as intersections of circular arcs. The artificial surface, including the auxiliary sources, is shaped in various patterns to study the effect of its form on the MAS accuracy. In juxtaposition with the standard, conformal shape, several deformations are tested, where the auxiliary sources are forced to approach the tip of the wedge. It is shown that such a procedure significantly improves the accuracy of the numerical results. Comparisons of schemes are presented, and the optimal auxiliary source location is proposed. Full article
(This article belongs to the Special Issue Numerical and Analytical Methods in Electromagnetics)
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Open AccessArticle
A Simple Analytical Solution for the Designing of the Birdcage RF Coil Used in NMR Imaging Applications
Appl. Sci. 2020, 10(7), 2242; https://doi.org/10.3390/app10072242 - 26 Mar 2020
Cited by 2
Abstract
A novel analytical solution for the designing of the birdcage RF coil has been demonstrated in this paper. A new concept of dominant resonance path has been introduced in this paper which is used to identify the specific closed current loop in the [...] Read more.
A novel analytical solution for the designing of the birdcage RF coil has been demonstrated in this paper. A new concept of dominant resonance path has been introduced in this paper which is used to identify the specific closed current loop in the birdcage RF coil which is responsible for the dominant resonance frequency mode. This concept is used to determine the precise numerical values of the lumped capacitance deployed in the legs and/or end-rings of the birdcage RF coil for its proper operation at the desired resonance frequency. The analytical solution presented in this paper has been established by performing the two-port network based equivalent circuit modeling of the birdcage RF coil. The proposed analytical solution uses T-matrix theory and develops a relationship between the input impedance of the birdcage coil and the impedances of its leg and end-ring segments. The proposed analytical solution provides the information about the resonance frequency spectrum of the birdcage RF coil and solves the issue of its interfacing with external circuits without affecting its resonance characteristics. Based upon the proposed analysis and designing strategy presented in this paper, the low pass, high pass and band pass configurations of the birdcage RF coil were successfully implemented with FPCB (Flexible Printed Circuit board) technique for small volume NMR imaging applications at 1.5 T and 3.0 T MRI system. The results obtained for the implemented birdcage coils using the proposed analysis and designing technique are in closed agreement with already established methods. Full article
(This article belongs to the Special Issue Numerical and Analytical Methods in Electromagnetics)
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Open AccessArticle
Super-Gain Optical Parametric Amplification in Dielectric Micro-Resonators via BFGS Algorithm-Based Non-Linear Programming
Appl. Sci. 2020, 10(5), 1770; https://doi.org/10.3390/app10051770 - 04 Mar 2020
Cited by 3
Abstract
The goal of this paper is to show that super-gain optical parametric amplification can be achieved even in a small micro-resonator using high-intensity ultrashort pump waves, provided that the frequencies of the ultrashort pulses are tuned to maximize the intracavity magnitude of the [...] Read more.
The goal of this paper is to show that super-gain optical parametric amplification can be achieved even in a small micro-resonator using high-intensity ultrashort pump waves, provided that the frequencies of the ultrashort pulses are tuned to maximize the intracavity magnitude of the wave to be amplified, which we call the stimulus wave. In order to accomplish this, we have performed a dispersion analysis via computational modeling of the electric polarization density in terms of the non-linear electron cloud motion and we have concurrently solved the electric polarization density and the wave equation for the electric field. Based on a series of non-linear programming-integrated finite difference time-domain simulations, we have identified the optimal pump wave frequencies that simultaneously maximize the stored electric energy density and the polarization density inside a micro-resonator by using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimization algorithm. When the intracavity energy and the polarization density (which acts as an energy coupling coefficient) are simultaneously high, an input wave can be strongly amplified by efficiently drawing energy from a highly energized cavity. Therefore, we propose that micrometer-scale achievement of super-gain optical parametric amplification is possible in a micro-resonator via high-intensity ultrashort “pump wave” pulses, by determining the optimal frequencies that concurrently maximize the stored electric energy density and the polarization density in a dielectric interaction medium. Full article
(This article belongs to the Special Issue Numerical and Analytical Methods in Electromagnetics)
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Open AccessArticle
Percolation and Transport Properties in The Mechanically Deformed Composites Filled with Carbon Nanotubes
Appl. Sci. 2020, 10(4), 1315; https://doi.org/10.3390/app10041315 - 15 Feb 2020
Cited by 2
Abstract
The conductivity and percolation concentration of the composite material filled with randomly distributed carbon nanotubes were simulated as a function of the mechanical deformation. Nanotubes were modelled as the hard-core ellipsoids of revolution with high aspect ratio. The evident anisotropy was observed in [...] Read more.
The conductivity and percolation concentration of the composite material filled with randomly distributed carbon nanotubes were simulated as a function of the mechanical deformation. Nanotubes were modelled as the hard-core ellipsoids of revolution with high aspect ratio. The evident anisotropy was observed in the percolation threshold and conductivity. The minimal mean values of the percolation of 4.6 vol. % and maximal conductivity of 0.74 S/m were found for the isotropic composite. Being slightly aligned, the composite demonstrates lower percolation concentration and conductivity along the orientation of the nanotubes compared to the perpendicular arrangement. Full article
(This article belongs to the Special Issue Numerical and Analytical Methods in Electromagnetics)
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Open AccessArticle
3D Numerical Modeling of Induced-Polarization Grounded Electrical-Source Airborne Transient Electromagnetic Response Based on the Fictitious Wave Field Methods
Appl. Sci. 2020, 10(3), 1027; https://doi.org/10.3390/app10031027 - 04 Feb 2020
Cited by 1
Abstract
The grounded electrical-source airborne transient electromagnetic (GREATEM) system is widely used in mineral exploration. Meanwhile, the induced polarization (IP) effect, which indicates the polarizability of the earth, is often found. In this paper, the Maxwell equations in the frequency domain are transformed into [...] Read more.
The grounded electrical-source airborne transient electromagnetic (GREATEM) system is widely used in mineral exploration. Meanwhile, the induced polarization (IP) effect, which indicates the polarizability of the earth, is often found. In this paper, the Maxwell equations in the frequency domain are transformed into fictitious wave domain, where Maxwell equations are solved by the time domain finite difference method. Then, an integral transformation method is used to convert the calculation results back to the time domain. A three-dimensional (3D) numerical simulation in a polarizable medium is presented. The accuracy of this method is proven by comparing it with the analytical solution and the existing method, and the calculation efficiency is increased five-fold. The simulation results show that the GREATEM system has a higher response amplitude in the conductive region, while IP effects cannot be identified in the conductive area. The GREATEM system has a higher response amplitude in the low-resistance region, but IP effects cannot be identified in the low-resistance area, and the detection of IP effects is more suitable for the high-resistance area. Therefore, it is necessary to improve the detection ability of the GREATEM system in the low-resistance area. Full article
(This article belongs to the Special Issue Numerical and Analytical Methods in Electromagnetics)
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Open AccessArticle
Optical Soliton Solutions of the Cubic-Quartic Nonlinear Schrödinger and Resonant Nonlinear Schrödinger Equation with the Parabolic Law
Appl. Sci. 2020, 10(1), 219; https://doi.org/10.3390/app10010219 - 27 Dec 2019
Cited by 26
Abstract
In this paper, the cubic-quartic nonlinear Schrödinger and resonant nonlinear Schrödinger equation in parabolic law media are investigated to obtain the dark, singular, bright-singular combo and periodic soliton solutions. Two powerful methods, the m + G G improved expansion method and the [...] Read more.
In this paper, the cubic-quartic nonlinear Schrödinger and resonant nonlinear Schrödinger equation in parabolic law media are investigated to obtain the dark, singular, bright-singular combo and periodic soliton solutions. Two powerful methods, the m + G G improved expansion method and the exp φ ξ expansion method are utilized to construct some novel solutions of the governing equations. The obtained optical soliton solutions are presented graphically to clarify their physical parameters. Moreover, to verify the existence solutions, the constraint conditions are utilized. Full article
(This article belongs to the Special Issue Numerical and Analytical Methods in Electromagnetics)
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