arXiv subjects

Yehuda Leviatan

Publications and source records attributed to Yehuda Leviatan.

4 recordsLinked to original sources

arXiv2026

Frequency-Domain Analysis of Wave Scattering by Spatially Dispersive Metasurfaces Using the Method of Auxiliary Sources

Spatially dispersive metasurfaces exhibit angle-dependent responses that cannot be accurately modeled using conventional local susceptibilities. Extended Generalized Sheet Transition Conditions (GSTCs) have been introduced to account for spatial dispersion by incorporating spatial derivatives of the electromagnetic fields. In this work, these extended GSTCs are integrated into the Method of Auxiliary Sources (MAS), resulting in a meshless simulation framework for the analysis of spatially dispersive metasurfaces. The proposed formulation is developed for infinite planar, finite planar, polygon shaped, and cylindrical metasurfaces, while it is general and also applicable to bianisotropic spatially dispersive metasurfaces. For validation, the numerical examples consider Lorentz-type spatial resonators, consistent with previously published studies. The extended GSTCs are enforced within the MAS via appropriate placement of auxiliary sources. Numerical results are presented for several geometries, including planar, polygonal, semicircular, and cylindrical metasurfaces. The obtained results show very good agreement with previously published data, demonstrating the accuracy and flexibility of the proposed method.

physics.optics↗

arXiv2026

A Time-Domain Method of Auxiliary Sources for Analyzing Transient Electromagnetic Interactions with GSTC-Modeled Metasurfacess

This paper presents a time domain (TD) formulation for modeling the transient electromagnetic response of two-dimensional (2D) metasurfaces using the Method of Auxiliary Sources (MAS) combined with the Generalized Sheet Transition Condition (GSTC). In the proposed approach, the frequency-domain impedance type GSTC is transformed into a causal, convolution-based TD representation and integrated within the MAS formulation. rfaces.

physics.comp-ph↗

arXiv2025

A Time-Domain Method of Auxiliary Sources for Efficient Analysis of Transient Electromagnetic Scattering by Moderately Conductive Cylinders

This paper presents a time-domain implementation of the Method of Auxiliary Sources (MAS) combined with the Standard Impedance Boundary Condition (SIBC) for electromagnetic scattering problems involving cylindrical scatterers with finite but moderate conductivity. The proposed approach focuses on solving the two-dimensional problem using a first-order SIBC, which is valid when the conductivity is sufficiently higher than the maximum spectral frequency times the dielectric permittivity of the scatterer. This regime includes moderately conductive materials--such as carbon-based composites, conductive polymers, and doped dielectrics--that are increasingly used in real-world radio-frequency applications, including wearable electronics, electromagnetic interference shielding, and biomedical sensors. Under the above validity conditions, the interaction between the incident wave and the scatterer is dominated by surface effects, allowing for an efficient and accurate modeling strategy without the need to compute internal fields. The theoretical formulation of the time-domain MAS-SIBC method is developed, followed by extensive numerical testing on various geometries whose cross section is a closed curve. Such geometries include circular, elliptical, super-circular, rounded-triangular, and inverted-elliptical scatterers. A planar geometry is also tested. All results are validated against analytical solutions and commercial frequency-domain solvers, demonstrating the accuracy and practical potential of the proposed method. The findings suggest that time-domain MAS-SIBC offers a promising and computationally efficient approach for modeling scattering from materials even with moderate conductivity.

physics.class-ph↗

arXiv2012

On the use of rational-function fitting methods for the solution of 2D Laplace boundary-value problems

A computational scheme for solving 2D Laplace boundary-value problems using rational functions as the basis functions is described. The scheme belongs to the class of desingularized methods, for which the location of singularities and testing points is a major issue that is addressed by the proposed scheme, in the context of the 2D Laplace equation. Well-established rational-function fitting techniques are used to set the poles, while residues are determined by enforcing the boundary conditions in the least-squares sense at the nodes of rational Gauss-Chebyshev quadrature rules. Numerical results show that errors approaching the machine epsilon can be obtained for sharp and almost sharp corners, nearly-touching boundaries, and almost-singular boundary data. We show various examples of these cases in which the method yields compact solutions, requiring fewer basis functions than the Nyström method, for the same accuracy. A scheme for solving fairly large-scale problems is also presented.

math-ph↗