Related papers: Shape Taylor expansion for wave scattering problem…
Study of scattering process in the nonlocal interaction framework leads to an integro-differential equation. The purpose of the present work is to develop an efficient approach to solve this integro-differential equation with high degree of…
To avoid instabilities in the continuum semi-classical limit of loop quantum cosmology models, refinement of the underlying lattice is necessary. The lattice refinement leads to new dynamical difference equations which, in general, do not…
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…
Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different…
We numerically investigate the sensitivity of the scattered wave field to perturbations in the shape of a scattering body illuminated by an incident plane wave. This study is motivated by recent work on the inverse problem of reconstructing…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
We are concerned with the reconstruction of a sound-soft obstacle using far field measurements of the scattered waves associated with incident plane waves sent from one direction but at multiple frequencies. We define, for each frequency,…
Taylor's formula holds significant importance in function representation, such as solving differential difference equations, ordinary differential equations, partial differential equations, and further promotes applications in visual…
In this paper, we introduce a novel category of central compact schemes inspired by existing cell-node and cell-centered compact finite difference schemes, that offer a superior spectral resolution for solving the dispersive wave equation.…
This paper presents high-order integral equation methods for evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced…
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical…
In this paper, we consider the direct and inverse problem for isotropic scatterers with two conductive boundary conditions. First, we show the uniqueness for recovering the coefficients from the known far-field data at a fixed incident…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
We discuss here the direct and inverse problems for wave propagation in a waveguide with rough internal surface and arbitrary mean shape. The high degree of multiple scattering inside the waveguide poses significant challenges both for the…
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 wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and that the initial conditions and forcing terms are radially…
In this paper, we consider a sorting scheme for potentially spurious scattering resonant pairs in one- and two-dimensional electromagnetic problems and in three-dimensional acoustic problems. The novel sorting scheme is based on a…
The inverse scattering problem is of critical importance in a number of fields, including medical imaging, sonar, sensing, non-destructive evaluation, and several others. The problem of interest can vary from detecting the shape to the…
We consider the reconstruction of the shape and the impedance function of an obstacle from measurements of the scattered field at receivers outside the object. The data is assumed to be generated by plane waves impinging on the obstacle…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…