Related papers: Non-singular field-only surface integral equations…
In this paper we introduce a method for solving linear and nonlinear scattering problems for wave equations using a new hybrid approach. This new approach consists of a reformulation of the governing equations into a form that can be solved…
In this contribution we analyze the spectral properties of some commonly used boundary integral operators in computational electromagnetics and of their discrete counterparts, highlighting peculiar features of their spectra. In particular,…
Considering two-body integral equations we show how they can be dimensionally reduced by integrating exactly over the azimuthal angle of the intermediate momentum. Numerical solution of the resulting equation is feasible without employing a…
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…
This paper introduces a novel class of indirect boundary integral equation (BIE) formulations for the solution of electromagnetic scattering problems involving smooth perfectly electric conductors (PECs) in three-dimensions. These…
Boundary integral equation methods for analyzing electromagnetic scattering phenomena typically suffer from several of the following problems: (i) ill-conditioning when the frequency is low; (ii) ill-conditioning when the discretization…
We introduce a boundary integral method for two-dimensional quantum billiards subjected to a constant magnetic field. It allows to calculate spectra and wave functions, in particular at strong fields and semiclassical values of the magnetic…
The scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this…
We present a new approach to three-dimensional electromagnetic scattering problems via fast isogeometric boundary element methods. Starting with an investigation of the theoretical setting around the electric field integral equation within…
We study differential equations, describing interaction of electromagnetic field with moving sidebars and surfaces, coming from integral electrodynamics laws. It is shown that differential equations contain but the such features of…
In the frame of volume integral equation methods, we introduce an alternative representation of the electromagnetic field scattered by a homogeneous object of arbitrary shape at a given frequency, in terms of a set of modes independent of…
The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series…
An explicit formula is derived for the electromagnetic (EM) field scattered by one small impedance particle $D$ of an arbitrary shape. If $a$ is the characteristic size of the particle, $\lambda$ is the wavelength, $a<<\lambda$ and $\zeta$…
This article is concerned with the time-harmonic electromagnetic (EM) scattering from a generic inhomogeneous medium. It is shown that if there is a right corner on the support of the medium, then it scatters every pair of incident EM…
Metasurfaces, consisting of large arrays of interacting subwavelength scatterers, pose significant challenges for general-purpose computational methods due to their large electric dimensions and multiscale nature. This paper introduces an…
This paper presents a robust numerical solution to the electromagnetic scattering problem involving multiple multi-layered cavities in both transverse magnetic and electric polarizations. A transparent boundary condition is introduced at…
Conventional surface integral equation (SIE)-based characteristic mode formulation for the patch antenna structure with a finite substrate is susceptible to the spurious (nonphysical) modes due to the dielectric part. To avoid the…
This paper presents a re-formulation of the boundary integral method (BIM) for the Debye-Huckel model of molecular and colloidal electrostatics that removes the mathematical singularities that have been accepted as an intrinsic part of the…
Scattering of electromagnetic waves by many small particles of arbitrary shapes is reduced rigorously to solving linear algebraic system of equations bypassing the usual usage of integral equations. The matrix elements of this linear…
In this paper, we consider the scattering of a plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in three dimensions. Based on the Helmholtz decomposition, the elastic scattering problem is reduced to a…