Related papers: A Windowed Green Function method for elastic scatt…
Conventional surface-relief gratings are inefficient at deflecting normally-incident light by large angles. This constrains their use in many applications and limits the overall efficiency of any optical instrument integrating gratings.…
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…
Recently there has been a growing interest in computational methods for quantum scattering equations that avoid the traditional decomposition of wave functions and scattering amplitudes into partial waves.The aim of the present work is to…
We propose a novel framework, called moving window method, for solving the linear Schr\"odinger equation with an external potential in $\mathbb{R}^d$. This method employs a smooth cut-off function to truncate the equation from Cauchy…
This paper is concerned with the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know that the whole line Green's function is given by a Gaussian.…
In this work, we develop a fast and accurate method for the scattering of flexural-gravity waves by a thin plate of varying thickness overlying a fluid of infinite depth. This problem commonly arises in the study of sea ice and ice shelves,…
In the paper we revisit the basic problem of tunneling near a nondegenerate global maximum of a potential on the line. We reduce the semiclassical Schr\"odinger equation to a Weber normal form by means of the Liouville-Green transform. We…
This paper introduces a novel matrix-free approach for full waveform inversion in anisotropic elastic media, incorporating density variation through the utilization of the distorted Born iterative method. This study aims to overcome the…
Flexible boundary condition methods couple an isolated defect to bulk through the bulk lattice Green's function. The inversion of the force-constant matrix for the lattice Green's function requires Fourier techniques to project out the…
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…
Strings propagating along surfaces with Dirichlet boundaries are studied in this paper. Such strings were originally proposed as a possible candidate for the QCD string. Our approach is different from previous ones and is simple and general…
Acoustic room modes and the Green's function mode expansion are well-known for rectangular rooms with perfectly reflecting walls. First-order approximations also exist for nearly rigid boundaries; however, current analytical methods fail to…
A new weak Galerkin (WG) finite element method for solving the second-order elliptic problems on polygonal meshes by using polynomials of boundary continuity is introduced and analyzed. The WG method is utilizing weak functions and their…
A new numerical method is proposed for a 1-D inverse medium scattering problem with multi-frequency data. This method is based on the construction of a weighted cost functional. The weight is a Carleman Weight Function (CWF). In other…
Several classic problems for particles diffusing outside an arbitrary configuration of non-overlapping partially reactive spherical traps in three dimensions are revisited. For this purpose, we describe the generalized method of separation…
Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…
Standard fractional models on manifolds often conflate geometric anisotropy with medium heterogeneity. In this Letter, we overcome this rigidity by deriving the fundamental solution for a weighted space-time fractional ultrahyperbolic…
We investigate the influence of a time dependent, homogeneous electric field on scattering properties of non-interacting electrons in an arbitrary static potential. We develop a method to calculate the (Keldysh) Green's function in two…
Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-form expression necessitates surrogate modeling to guide the…
Sub-wavelength arrays of quantum emitters offer an efficient free-space approach to coherent light-matter interfacing, using ultracold atoms or two-dimensional solid-state quantum materials. The combination of collectively suppressed…