Related papers: On the determination of the boundary impedance fro…
We derive the semiclassical WKB quantization condition for obtaining the energy band edges of periodic potentials. The derivation is based on an approach which is much simpler than the usual method of interpolating with linear potentials in…
We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a…
We deal with the Cauchy problem for a perturbed wave equation in the half-plane with data given on a part of the space-time boundary. The equation in consideration describes a wave process in a laterally inhomogeneous medium. We propose a…
In [2] we introduced a method combining together an observability inequality and a spectral decomposition to get a logarithmic stability estimate for the inverse problem of determining both the potential and the damping coefficient in a…
A rigorous reduction of the many-body wave scattering problem to solving a linear algebraic system is given bypassing solving the usual system of integral equation. The limiting case of infinitely many small particles embedded into a medium…
We consider the solution of a scalar Helmholtz equation where the potential (or index) takes two positive values, one inside a disk of radius $\epsilon$ and another one outside. We derive sharp estimates of the size of the scattered field…
We analyze and develop numerical methods for time-harmonic wave scattering in metallic waveguide structures of infinite extent. We show that radiation boundary conditions formulated via projectors onto outgoing modes determine the…
We consider the problem of determining the boundary perturbations of an object from far-field electric or acoustic measurements. Assuming that the unknown object boundary is a small perturbation of a circle, we develop a linearized relation…
We deal with the problem of determining the shape of an inclusion embedded in a homogenous background medium. The multifre-quency electrical impedance tomography is used to image the inclusion. For different frequencies, a current is…
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…
The solution of the Helmholtz equation in optical semiclassic approximation is associated with the calculation of ray paths and matrices of variations. The transformation rules for elements of matrices on the boundaries of the waveguide are…
We study 4 problems in the area of scattering of time harmonic acoustic or electromagnetic waves by unbounded rough surfaces/inhomogeneous layers. Specifically we study: i) a boundary value problem (BVP) for the Helmholtz equation, in both…
The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions…
This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is…
In this article, high frequency stability estimates for the determination of the potential in the Schr\"odinger equation are studied when the boundary measurements are made on slightly more than half the boundary. The estimates reflect the…
This paper is devoted to a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we…
This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations…
We discuss a time-harmonic inverse scattering problem for the Helmholtz equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…
This paper is concerned with resolvent estimates on the real axis for the Helmholtz equation posed in the exterior of a bounded obstacle with Dirichlet boundary conditions when the obstacle is trapping. There are two resolvent estimates for…
We consider an inverse problem arising in corrosion detection. We prove a stability result of logarithmic type for the determination of the corroded portion of the boundary and impedance by two measurements on the accessible portion of the…