Related papers: Numerical solution of many-body wave scattering pr…
Scattering of electromagnetic (EM) waves by many small particles (bodies) embedded in a homogeneous medium is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for…
In this paper a mathematical model is given for the scattering of an incident wave from a surface covered with microscopic small Helmholtz resonators, which are cavities with small openings. More precisely, the surface is built upon a…
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…
In this paper we review the results of the author on the theory of scalar and vector wave scattering by small bodies of an arbitrary shape with the emphasis on practical applicability of the formulas obtained and on the mathematical rigor…
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…
Let $M$ be the number of bounded and Lipschitz regular obstacles $D_j, j:=1, ..., M$ having a maximum radius $a$, $a<<1$, located in a bounded domain $\Omega$ of $\mathbb{R}^3$. We are concerned with the acoustic scattering problem with a…
Scattering problem by several bodies, small in comparison with the wavelength, is reduced to linear algebraic systems of equations, in contrast to the usual reduction to some integral equations.
A new proof is given of the existence of the solution to electromagnetic (EM) wave scattering problem for an impedance body of an arbitrary shape. The proof is based on the elliptic systems theory and elliptic estimates for the solutions of…
Electromagnetic (EM) wave scattering by many parallel infinite cylinders is studied asymptotically as a tends to 0, where a is the radius of the cylinders. It is assumed that the centres of the cylinders are distributed so that their…
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 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 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 interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the…
We study 4 problems in the area of scattering of time harmonic acoustic or electromagnetic waves by unbounded rough surfaces/inhomogeneous layers. Specifically we study: i) a boundary value problem (BVP) for the Helmholtz equation, in both…
In this paper, we consider acoustic or electromagnetic scattering in two dimensions from an infinite three-layer medium with thousands of wavelength-size dielectric particles embedded in the middle layer. Such geometries are typical of…
This paper presents a numerical compression strategy for the boundary integral equation of acoustic scattering in two dimensions. These equations have oscillatory kernels that we represent in a basis of wave atoms, and compress by…
The study of capillary wave scattering by a circular region with different interfacial properties from the rest of an otherwise homogeneous interface is motivated by experiments on wave attenuation at a monolayer covered air-water interface…
A fast method for the computation of layer potentials that arise in acoustic scattering is introduced. The principal idea is to split the singular kernel into a smooth and a local part. The potential due to the smooth part is computed…
We are concerned with the acoustic scattering problem by many small rigid obstacles of arbitrary shapes. We give a sufficient condition on the number $M$ and the diameter $a$ of the obstacles as well as the minimum distance $d$ between them…
Rapid advancements in the micro and nano-technology create unlimited opportunities for design of novel optical materials and their applications. Recently, the possibility of the fast refractive index modulation was demonstrated in…