Related papers: Rapid computation of far-field statistics for rand…
In this paper, we consider the inverse shape problem of recovering small and extended isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. We will…
We present a method to compute dispersive shock wave solutions of the Korteweg-de Vries equation that emerge from initial data with step-like boundary conditions at infinity. We derive two different Riemann-Hilbert problems associated with…
We propose an inverse scattering scheme of recovering a polyhedral obstacle in $\mathbb{R}^n$, $n=2,3$, by only a few high-frequency acoustic backscattering measurements. The obstacle could be sound-soft or sound-hard. It is shown that the…
Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…
In scattering theory the far field pattern describes the directional dependence of a time-harmonic wave scattered by an obstacle or inhomogeneous medium, when observed sufficiently far away from these objects. Considering plane wave…
We are concerned with the linearized, isotropic and homogeneous elastic scattering problem by (possibly many) small rigid obstacles of arbitrary Lipschitz regular shapes in 3D. Based on the Foldy-Lax approximation, valid under a sufficient…
We consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the scattered field at a collection of receivers outside the…
In this paper, the one-dimensional time-fractional diffusion-wave equation with the fractional derivative of order $1 \le \alpha \le 2$ is revisited. This equation interpolates between the diffusion and the wave equations that behave quite…
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…
The Kirchhoff approximation (K-A) to calculate the acoustic backscattering of a complex structure can be evaluated using a discretized version of its surface (i.e. a $\textit{mesh}$). From the computational viewpoint, the most accesible…
We prove global Strichartz estimates without loss for the wave equation outside two strictly convex obstacles, following the roadmap introduced in [Lafontaine, 2017] for the Schr\"odinger equation. Moreover, we show a first step toward the…
This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…
This paper is concerned with the inverse scattering problem by an unbounded rough surface. A direct imaging method is proposed to reconstruct the rough surface from the scattered near-field Cauchy data generating by point sources and…
This paper aims to show global existence and modified scattering for the solutions of the Cauchy problem to the modified Whitham equations for small, smooth and localized initial data. The main difficulties come from slow decay and…
Scattering of time-harmonic plane wave by two parallel semi-infinite rows, but with staggered edges, is considered on square lattice. The condition imposed on the semi-infinite rows is a discrete analogue of Neumann boundary condition. A…
The scattering of waves by obstacles in a 2D setting is considered, in particular the computation of the scattered field via the collocation or the least-squares methods. In the case of multiple scattering by smooth obstacles, we prove that…
We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain…
This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…
An accurate and efficient numerical simulation approach to electromagnetic wave scattering from two-dimensional, randomly rough, penetrable surfaces is presented. The use of the M\"uller equations and an impedance boundary condition for a…
Consider the scattering of a time-harmonic acoustic plane wave by a bounded elastic obstacle which is immersed in a homogeneous acoustic medium. This paper concerns an inverse acoustic-elastic interaction problem, which is to determine the…