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
Interests: analytical–numerical methods for electromagnetics; electromagnetic diffraction and scattering; waveguide and optical waveguide; microwave circuits and antennas
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Interests: rigorous mathematical techniques for electromagnetic wave problems; radar cross-section; scattering and diffraction
Interests: modelling of planar transmission lines, antennas and circuits using optimized integral equation methods; (bi)anisotropic structures; metamaterials and periodic electromagnetic structures
Interests: methods of analytical regularization; propagation and scattering of waves; open waveguides; antennas and lasers; history of microwaves
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
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;
- 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
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- convergence and accuracy
- regularizing Galerkin methods
- Abel integral equation techniques
- Muller boundary integral equations
- Wiener–Hopf-based techniques
- eigenvalue problems
- regularizing asymptotic techniques