Related papers: A Fast Algorithm for Solving Scalar Wave Scatterin…

Scattering of electromagnetic (EM) waves by many small particles (bodies), embedded in a thin layer, is studied. Physical properties of the particles are described by their boundary impedances. The thin layer of depth of the order $O(a)$…

The model problem of scattering of a sound wave by an infinite plane structure formed by a semi-infinite acoustically hard screen and a semi-infinite sandwich panel perforated from one side and covered by a membrane from the other is…

Energy transmission over long distances by waves is a key mechanism for many natural processes. This possibility arises when an inhomogeneous medium is arranged in such a manner that it enables a certain type of wave to propagate with…

Traditionally resonant interactions among short waves, with large real wave-numbers, were described statistically and only a small domain in spectral space with integer wave-numbers, discrete resonances, had to be studied separately in…

The paper concerns scattering of plane waves by a bounded obstacle with complex valued impedance boundary conditions. We study the spectrum of the Neumann-to-Dirichlet operator for small wave numbers and long wave asymptotic behavior of the…

Scattering of a time harmonic anti-plane shear wave due to either a pair of crack tips or a pair of rigid constraint tips on square lattice is considered. The two problems correspond to the so called zero-offset case of scattering due to a…

The Helmholtz equation with variable wavenumbers is challenging to solve numerically due to the pollution effect, which often results in a huge ill-conditioned linear system. In this paper, we present a high-order wavelet Galerkin method to…

Electromagnetic scattering on a sphere is one of the most fundamental problems, which has a closed form analytical solution in the form of Mie series. Being initially formulated for a plane incident wave, the formalism can be extended to…

This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly incompressible materials. The…

The wave scattering by moving particles (dynamic scattering) is a well known physical problem routinely occurring in practice. For the particles which are much smaller than the incident wavelength, the static scattering problem can be…

The paper continues the analysis, started in [1] (Part I,arXiv:2302.04353), of the model open wave-guide problem defined by 2 semi-infinite, rectangular wave-guides meeting along a common perpendicular line. In Part I we reduce the solution…

The scalar wave equation is solved using higher order immersed finite elements. We demonstrate that higher order convergence can be obtained. Small cuts with the background mesh are stabilized by adding penalty terms to the weak…

In the study of time-dependent waves, it is computationally expensive to solve a problem in which high frequencies (shortwaves, with wavenumber k = kmax) and low frequencies (longwaves, near k=kmin) mix. Consider a problem in which low…

We analyze the scattering of linear internal waves in a two dimensional channel with subcritical bottom topography. We construct the scattering matrix for the internal wave problem in a channel with straight ends, mapping incoming data to…

This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…

Wave scattering is considered in a medium in which many small particles are embedded. Equations for the effective field in the medium are derived when the number of particles tends to infinity.

The theory of acoustic wave scattering by many small bodies is developed for bodies with impedance boundary condition. It is shown that if one embeds many small particles in a bounded domain, filled with a known material, then one can…

Scattering properties of a material are changed when the material is injected with small acoustically soft particles. It is shown that its new scattering behavior can be understood as a solution of a potential scattering problem with the…

The scattering of wave packets from a single slit and a double slit with the Schr\"odinger equation, is studied numerically and theoretically. The phenomenon of diffraction of wave packets in space and time in the backward region,…

The topographical scattering of gravity waves is investigated using a spectral energy balance equation that accounts for first order wave-bottom Bragg scattering. This model represents the bottom topography and surface waves with spectra,…