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We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric, E and…
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…
We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic…
The boundary element method is an efficient algorithm for simulating acoustic propagation through homogeneous objects embedded in free space. The conditioning of the system matrix strongly depends on physical parameters such as density,…
This paper is concerned with a Galerkin boundary element method solving the two dimensional exterior elastic wave scattering problem. The original problem is first reduced to the so-called Burton-Miller (\cite{BM71}) boundary integral…
In this work we consider the method of non-linear boundary integral equation for solving numerically the inverse scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder in three dimensions. We…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
An isogeometric boundary element method (BEM) is presented to solve scattering problems in an isotropic homogeneous medium. We consider wave problems governed by the scalar wave equation as in acoustics and the Lam\'e-Navier equations for…
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…
This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…
This study builds on a recent paper by Lai et al [Appl. Comput. Harmon. Anal., 2018] in which a novel boundary integral formulation is presented for scalar wave scattering analysis in two-dimensional layered and half-spaces. The seminal…
A coupled system of volume integral and hydrodynamic equations is solved to analyze electromagnetic scattering from nanostructures consisting of metallic and dielectric parts. In the metallic part, the hydrodynamic equation relates the free…
Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise in such calculations are the avoidance of spurious…
This paper presents novel methodologies for the numerical simulation of scattering of elastic waves by both closed and open surfaces in three-dimensional space. The proposed approach utilizes new integral formulations as well as an…
This articles first investigates boundary integral operators for the three-dimensional isotropic linear elasticity of a biphasic model with piecewise constant Lam\'e coefficients in the form of a bounded domain of arbitrary shape surrounded…
Consider the scattering of an acoustic plane wave by a bounded elastic obstacle which is immersed in an open space filled with a homogeneous medium. This paper concerns the mathematical analysis of the coupled two- and three-dimensional…
We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…
This work studies time-dependent electromagnetic scattering from obstacles whose interaction with the wave is fully determined by a nonlinear boundary condition. In particular, the boundary condition studied in this work enforces a power…
This paper presents a numerical compression strategy for the boundary integral equation of acoustic scattering in two dimensions. These equations have oscillatory kernels that we represent in a basis of wave atoms, and compress by…
The problem of an electromagnetic wave scattered from a random medium layer with rough boundaries is formulated using integral equations which involve two kinds of Green functions. The first one describes the wave scattered by the random…