Conference Agenda

This study introduces a method for modeling large-scale electromagnetic wave propagation by combining the finite element method with a domain decomposition strategy. The Finite Element Tearing and Interconnecting (FETI) technique is used to create consistent system matrices across subdomains with conforming interfaces. This consistency makes it possible to develop surrogate models using regression analysis, allowing for faster computations in complex vegetation scenarios such as forest modeling. The work explores the challenges of building statistical finite element models and validate the idea by solving a synthetic example.

In this work the precise integration time domain (PITD) method is coupled with Monte Carlo (MC) and multilevel Monte Carlo (MLMC) methods to release the constraint of the Courant–Friedrichs–Lewy (CFL) condition in the finite difference time domain (FDTD) method for electromagnetic problems with random materials. Compared to the MC-FDTD method, the MC-PITD method can provide accurate estimations of mean and variance of electromagnetic field quantities using a large time step size. In contrast to the MLMC-FDTD method, where the allowable time step size decreases with increasing levels (i.e., finer grids) due to the stricter CFL condition, the MLMC-PITD method enables all model levels to use the maximum time step size determined by the coarsest grid, allowing the MLMC method to fully leverage its advantages.

Dielectric rings are crucial components in integrated photonics, enabling applications such as optical filters and sensors. Accurate determination of their effective refractive indices and resonant mode profiles is vital for performance optimization. While methods such as finite element and finite-difference time-domain provide accurate results, they may not fully exploit the unique resonant condition of dielectric rings: phase continuity. This work provides the coupled wave equations in cylindrical coordinates for electromagnetic waves in dielectric rings. A two-step algorithm, inspired by the shooting method, is proposed to solve these coupled nonlinear equations. The accuracy of the formulation is validated through comparisons with numerical results obtained from commercial full-wave solvers for various geometries.

We introduce a method of lines (MoL) formulation for analyzing and designing periodic multi-element millimeter-wave (mmWave) metasurfaces (MS) in a computationally tractable manner. As the complexity of MSs increases, analysis by full-wave methods becomes challenging. The MoL offers a considerably faster alternative, as it is a semi-analytical method where the electromagnetic equations are solved analytically along the direction perpendicular to the MS layers and numerically on the MS plane, hence decreasing the required degrees of freedom. We employ an extended MoL formulation, where a first-order differential equation involving both the total tangential electric and magnetic field components is solved and the transfer matrix of each layer is obtained. As a proof of concept, we analyze various MS filter supercells; a very good agreement with finite element method (FEM) simulations is observed in all cases. The presented analysis paves the way for the fast synthesis of optimized MSs by changing only the boundary conditions applied to the layer interfaces. The advantages of our method will be even more pronounced when designing more complex devices.

Partial discharge (PD) localization is important for monitoring and maintaining power transformers. In this digest, the electromagnetic time reversal (EMTR) technique is applied to locate PD sources. To minimize focusing time and position errors, the maximum electric field intensity criterion and the combination of multiple sensors are used for positioning. In addition, a stable discontinuous Galerkin time-domain (DGTD) method with a new efficient implicit-explicit scheme is proposed for modeling PD in transformers. The lossy terms are discretized using the implicit Crank-Nicolson (CN) scheme while the remaining terms are discretized using the explicit Runge-Kutta (RK) scheme, i.e. the CN-RK scheme, which can avoid the influence of the lossy media in transformers on the time-step size and improve computational efficiency. Numerical results demonstrate that the proposed method can effectively locate PD sources in transformers.

Abruptly time-varying materials have garnered significant attention in fields such as optics and wave dynamics. This paper presents a full-wave finite- difference time-domain (FDTD) scheme to investigate the interaction of electromagnetic (EM) waves with these dynamic materials. Specifically, the study focuses on the polarization conversion of EM waves propagating in an anisotropic and dispersive medium, such as magnetized plasma, that experiences abrupt temporal variations. When the propagation of the incident EM waves is aligned with the ambient magnetic field, the linearly polarized light is split into left-handed and right-handed circularly

polarized waves with different angular frequencies. The results demonstrate that the polarization of the EM waves can be effectively controlled by modulating the external magnetic field and the plasma frequency.

When free electrons travel photonic crystals (PCs), multiple transition radiations are generated, yielding highly directional resonance radiation if the emitted electromagnetic (EM) waves are coherent. In this work, we have investigated the resonance transition radiation regulated by Moire lattices, which can offer greater flexibility in manipulating EM waves compared to conventional PCs, facilitating more intricate free-electron radiation phenomena. In particular, an exponential scattering matrix cascading approach is proposed, which can significantly decreases the necessary cascading steps, signifying a substantial reduction in computational resources. The angular energy density distribution is obtained and the velocity forbidden zone is observed. Our work will provide a foundation for exploring the promising wave behaviors within Moire lattices.

The electromagnetic response of devices as dielectric resonator is determined by resonant modes. It turns out that methods capable of properly designing scatterers to achieve prescribed resonance modes at prescribed frequencies are of great interest, enabling precise control of the electromagnetic field by taking advantage of improvements in the fabrication of meta-materials.

In this contribution, a new design method is proposed to compute the dielectric permittivity tensor of a scatterer exhibiting prescribed resonance modes, at prescribed frequencies. The dielectric permittivity is computed via an explicit and analytical formula that, moreover, highlights two relevant results: (i) only two distinct modes can be prescribed at the same resonance frequency, and (ii) the electromagnetic response can be changed at will (tunability) by scaling the dielectric susceptivity by a proper multiplicative constant.

In this paper a new electromagnetic solver, specifically tailored for scattering by meta-surfaces, is presented. The solver is based on a source integral volume formulation and implements a novel QR-compression approach that exploits the specific geometric structure of the meta-surface. Together with a specifically designed pre-conditioner, the proposed solver shows the capability to handle a large number of variables.

A summation-by-part precise-integration time-domain (SBP-PITD) method with provable energy stability is proposed based on modified Yee's cells, where the discrete energy depends entirely on boundary fields. On this foundation, a novel memory-efficient domain decomposition SBP-PITD (DD-SBP-PITD) method is proposed to guarantee the energy stability for coupling different subdomains. Numerical results confirm the effectiveness and advantage of SBP-PITD and DD-SBP-PITD.

In these notes, we examine a family of dissipative Schr\"{o}dinger equations with cubic nonlinearity. Equations of this type are used to describe the propagation of waves in weakly nonlinear, dispersive and dissipative media. The study focuses on determining exact solutions to equations of the considered class. The general solution to this problem is given through Weierstrass elliptic functions when the parameter that characterizes the dissipation is real. Another class of exact solutions is specified within the framework of the so-called small-phase approximation.

This work presents a finite-difference time-domain (FDTD) scheme that mitigates numerical errors in two-dimensional electromagnetic-wave propagation within Lorentz media. Rather than relying on traditional fourth-order spatial approximations, a new design approach is introduced for the spatial operators that minimizes dispersion flaws along the two principal axes at a specified frequency, affecting simultaneously all possible propagation angles. Performance enhancement over extended frequency bands is also possible in a controllable fashion that involves the least-squares solution of an overdetermined system, derived from single-frequency equations. The results verify that the proposed algorithm outperforms the conventional method without incurring additional computational costs, offering efficient computations for FDTD simulations in dispersive media.

The high-frequency electromagnetic field analysis code being developed by the authors is a finite element analysis software that can be run on parallel computer systems. Although this code is capable of detailed, fast, and efficient finite element analysis of large-scale electromagnetic problems using the Iterative Domain Decomposition Method (IDDM) and the corresponding parallel distributed processing environment, it still requires a large number of iterative computation trials and computation time. In this study, a sparse direct solver, which can be set and solved with larger subdomain sizes, is applied to the subdomain problem to reduce the load on the iterative solver and improve convergence. In addition, this improvement also significantly reduced memory consumption.