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This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded interval with non-homogeneous Dirichlet boundary data and a…
In this paper, it is shown that three-dimensional stochastic Maxwell equations with multiplicative noise are stochastic Hamiltonian partial differential equations possessing a geometric structure (i.e. stochastic mutli-symplectic…
We present a formalism for light optics starting with the Maxwell equations and casting them into an exact matrix form taking into account the spatial and temporal variations of the permittivity and permeability. This $8 \times 8$ matrix…
This paper is the direct-formulation companion to [Burbano-Gallegos, P\'erez-Arancibia, and Turc, ESAIM: M2AN, 60(1):273--315, 2026], which developed indirect combined-field-only boundary integral equations (BIEs) for time-harmonic…
A novel approach to computing time-harmonic solutions of Maxwell's equations by time-domain simulations is presented. The method, EM-WaveHoltz, results in a positive definite system of equations which makes it amenable to iterative solution…
In this work, we are interested in the analysis of time-harmonic Maxwell's equations in presence of a conical tip of a material with negative dielectric constants. When these constants belong to some critical range, the electromagnetic…
Consider the interaction of biharmonic waves with a periodic array of cavities, characterized by the Kirchhoff--Love model. This paper investigates the perfectly matched layer (PML) formulation and its numerical soution to the governing…
We investigate the representations of the solutions to Maxwell's equations based on the combination of hypercomplex function-theoretical methods with quantum mechanical methods. Our approach provides us with a characterization for the…
The time-dependent Maxwell system describing electromagnetic wave propagation in inhomogeneous isotropic media in the one-dimensional case reduces to a Vekua-type equation for bicomplex-valued functions of a hyperbolic variable (see…
Two recently derived integral equations for the Maxwell transmission problem are compared through numerical tests on simply connected axially symmetric domains for non-magnetic materials. The winning integral equation turns out to be…
This paper presents a class of boundary integral equations for the solution of problems of electromagnetic and acoustic scattering by two dimensional homogeneous penetrable scatterers with smooth boundaries. The new integral equations,…
In this note we discuss the numerical solution of the eddy current approximation of the Maxwell equations using the simple Pragmatic Algebraic Model to include hysteresis effects. In addition to the more standard time-stepping approach we…
In this work, we investigate the propagation of electromagnetic waves in the Cole-Cole dispersive medium by using the discontinuous Galerkin (DG) method to solve the coupled time-domain Maxwell's equations and polarization equation. We…
In this paper, we review the theory of time space-harmonic polynomials developed by using a symbolic device known in the literature as the classical umbral calculus. The advantage of this symbolic tool is twofold. First a moment…
We present a numerical method for solving the free-space Maxwell's equations in three dimensions using compact convolution kernels on a rectangular grid. We first rewrite Maxwell's Equations as a system of wave equations with auxiliary…
A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and…
Whether or not classical solutions of the 2D incompressible MHD equations without full dissipation and magnetic diffusion can develop finite-time singularities is a difficult issue. A major result of this paper establishes the global…
Efficient modeling of dispersive materials via time-domain simulations of the Maxwell equations relies on the technique of auxiliary differential equations. In this approach, a material's frequency-dependent permittivity is represented via…
This paper is devoted to the complete convergence study of the finite-element approximation of Maxwell's equations in the case where the magnetic permeability is constant. Standard linear finite elements for the space discretization are…
The known possibility to consider the (vacuum) Maxwell equations in a curved space-time as Maxwell equations in flat space-time(Mandel'stam L.I., Tamm I.E.) taken in an effective media the properties of which are determined by metrical…