We study, in the context of the full wave equation, an approximate cloaking scheme, that was previously considered for the Helmholtz equation [8], [17]. This cloaking scheme consists in a combination of an absorbing layer with an anisotropic layer, obtained by so-called transformation optics. We give optimal bounds for the visibility that tend to zero as a certain regularization parameter appro...

When a high-frequency acoustic or electromagnetic wave is scattered by a surface with a conical point, the component of the asymptotics of the scattered wave corresponding to diffraction by the conical point can be represented as an asymptotic expansion, valid as the wave number k → ∞. The diffraction coefficient is the coefficient of the principal term in this expansion and is of fundamental i...

We presents a Born; iterative method, for reconstructing optical properties of turbid media by means of frequency-domain data. The approach is based on iterative solution of a linear perturbation equation, which is derived from the integral from of the Helmholtz wave equation for photon-density waves in each iteration the total field and the associated weight matrix are recalculated based on th...

The nonlinear Schrödinger-Helmholtz (SH) equation in N space dimensions with 2σ nonlinear power was proposed as a regularization of the classical nonlinear Schrödinger (NLS) equation. It was shown that the SH equation has a larger regime (1 ≤ σ < 4 N ) of global existence and uniqueness of solutions compared to that of the classical NLS (0 < σ < 2 N ). In the limiting case where the Schrödinger...

The main purpose of this paper is to develop a fast fully discrete Fourier– Galerkin method for solving the boundary integral equations reformulated from the modified Helmholtz equation with boundary conditions. We consider both the nonlinear and the Robin boundary conditions. To tackle the difficulties caused by the two types of boundary conditions, we provide an improved version of the Galerk...

A method for explicitly solving the exterior Dirichlet problem for the threedimensional Helmholtz equation in terms of the Dirichlet Green's function for Laplace's equation has recently been found [6]. The present work shows how a similar technique may be used to solve the exterior Neumann problem in terms of the corresponding Neumann-Green function for Laplace's equation. The existence of the ...

This project’s aim seeks to study the acceleration of numerical algorithms used to solve the Helmholtz equation with Dirichlet boundary conditions. The Helmholtz equation arises naturally in physical problems modeled by partial differential equations in space and time as a time-independent wave equation when applying the technique of separation of variables. Using Dirichlet boundary conditions ...