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In this paper, we propose a new nonuniform mesh method to simulate acoustic scattering problems in two dimensional periodic structures with non-periodic incident fields numerically. As existing methods are difficult to extend to higher…
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…
In this paper, an efficient iterative method is proposed for solving multiple scattering problem in locally inhomogeneous media. The key idea is to enclose the inhomogeneity of the media by well separated artificial boundaries and then…
An accurate and fast method is presented for scattering of electromagnetic waves from an array of time-modulated graphene ribbons. We derive a time-domain integral equation for induced surface currents under subwavelength approximation.…
We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach…
Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual…
Many boundary element integral equation kernels are based on the Green's functions of the Laplace and Helmholtz equations in three dimensions. These include, for example, the Laplace, Helmholtz, elasticity, Stokes, and Maxwell's equations.…
The Generalized Method of Moments (GMM) is a partition of unity based technique for solving electromagnetic and acoustic boundary integral equations. Past work on the GMM for electromagnetics was confined to geometries modeled by piecewise…
For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive, since they are formulated on lower-dimension boundaries or interfaces, and can automatically satisfy outgoing radiation…
Using the Green function integral representation the Dyson-Schwinger equations are solved directly in Minkowski space. Essential ideas of the spectral techniques are discussed and applied on two renormalizable models: the Yukawa theory with…
This manuscript presents an efficient boundary integral equation technique for solving two-dimensional Helmholtz problems defined in the half-plane bounded by an infinite, periodic curve with Neumann boundary conditions and an aperiodic…
We provide an analytical formulation to model the propagation of elastic waves in a homogeneous half-space supporting an array of thin plates. The technique provides the displacement field obtained from the interaction between an incident…
This paper proposes an isogeometric boundary element method (IGBEM) to solve the electromagnetic scattering problems for three-dimensional doubly-periodic multi-layered structures. The main concerns are the constructions of (i) an open…
The electromagnetic behavior of plasmonic structures can be predicted after discretizing and solving a linear system of equations, derived from a continuous surface integral equation (SIE) and the appropriate boundary conditions, using a…
We deal with the problem of reconstructing material coefficients from the farfields they generate. By embedding small (single) inclusions to these media, located at points $z$ in the support of these materials, and measuring the farfields…
We propose and analyse a numerical method for time-harmonic acoustic scattering in $\mathbb{R}^n$, $n=2,3$, by a class of inhomogeneities (penetrable scatterers) with fractal boundary. Our method is based on a Galerkin discretisation of the…
The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the…
We consider the numerical solution of the scattering of time-harmonic plane waves from an infinite periodic array of reflection or transmission obstacles in a homogeneous background medium, in two dimensions. Boundary integral formulations…
We consider the scattering problem on locally perturbed periodic penetrable dielectric layers, which is formulated in terms of the full vector-valued time-harmonic Maxwell's equations. The right-hand side is not assumed to be periodic. At…
In this paper, we develop second kind integral formulations for flexural wave scattering problems involving the clamped, supported, and free plate boundary conditions. While the clamped plate problem can be solved with layer potentials…