Related papers: A High Order Numerical Method for Scattering from …
We develop a method for computing the scattering of flexural waves off of a periodic wall or a periodic line of scatterers. These waves model the fluctuations of thin plates with periodic clamped, supported, or free edges. We use the…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
This paper introduces a fast algorithm, applicable throughout the electromagnetic spectrum, for the numerical solution of problems of scattering by periodic surfaces in two-dimensional space. The proposed algorithm remains highly accurate…
This manuscript presents a fast direct solution technique for solving two dimensional wave scattering problems from quasi-periodic multilayered structures. When the interface geometries are complex, the dominant term in the computational…
A numerical algorithm is presented for solving the direct scattering problems by the Modified Rayleigh Conjecture Method (MRC) introduced by A.G.Ramm. Some numerical examples are given. They show that the method is numerically efficient.
We consider a general family of nonlocal in space and time diffusion equations with space-time dependent diffusivity and prove convergence of finite difference schemes in the context of viscosity solutions under very mild conditions. The…
The three-body scattering problem in Coulombic systems is widespread, however yet unresolved problem by the mathematically rigorous methods. In this work this long term challenge has been undertaken by combining distorted waves and…
We consider the problem of numerically solving the Schr\"odinger equation with a potential that is quasi periodic in space and time. We introduce a numerical scheme based on a newly developed multi-time scale and averaging technique. We…
For problems of time-harmonic scattering by polygonal obstacles, embedding formulae provide a useful means of computing the far-field coefficient induced by any incident plane wave, given the far-field coefficient of a relatively small set…
A numerical method of solving the problem of acoustic wave radiation in the presence of a rigid scatterer is described. It combines the finite element method and the boundary algebraic equations. In the proposed method, the exterior domain…
We present a perturbative technique for modeling the scattering of light by a nonlinear material. This approach eliminates the need for an iterative algorithm to solve the fully coupled nonlinear problem. We demonstrate its effectiveness in…
We introduce a new class of computationally tractable scattering problems in unbounded domains, which we call decomposable problems. In these decomposable problems, the computational domain can be split into a finite collection of…
A numerical method for solving the equations modeling acoustic scattering is presented. The method is capable of handling several dozen scatterers, each of which is several wave-lengths long, on a personal work station. Even for geometries…
This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…
We study the non-equilibrium dynamics obtained by an abrupt change (a {\em quench}) in the parameters of an integrable classical field theory, the nonlinear Schr\"odinger equation. We first consider explicit one-soliton examples, which we…
Although high-order Maxwell integral equation solvers provide significant advantages in terms of speed and accuracy over corresponding low-order integral methods, their performance significantly degrades in presence of non-smooth…
This study investigates numerical methods to solve nonlinear transport problems characterized by various sorption isotherms with a focus on the Freundlich type of isotherms. We describe and compare second order accurate numerical schemes,…
We present a novel hybrid numerical-asymptotic boundary element method for high frequency acoustic and electromagnetic scattering by penetrable (dielectric) convex polygons. Our method is based on a standard reformulation of the associated…
In this paper, a novel QR decomposition-based compression scheme is combined with a volume integral equations method for the fast and efficient numerical computation of the scattering of electromagnetic fields from large scale metasurfaces,…