Related papers: Spectral Analysis of Discretized Boundary Integral…
In this contribution we analyze the spectral properties of some commonly used boundary integral operators in computational electromagnetics and of their discrete counterparts, highlighting peculiar features of their spectra. In particular,…
Spectrum of the volume integral operator of the three-dimensional electromagnetic scattering is analyzed. The operator has both continuous essential spectrum, which dominates at lower frequencies, and discrete eigenvalues, which spread out…
The use of boundary integral equations in modeling boundary value problems-such as elastic, acoustic, or electromagnetic ones-is well established in the literature and widespread in practical applications. These equations are typically…
We introduce new numerical integration operators which compose the mass and stiffness matrices of a modified spectral element method for simulation of elastic wave propagation. While these operators use the same quadrature nodes as does the…
The left-right operator splitting method is studied for the efficient calculation of acoustic fields scattered by arbitrary rough surfaces. Here the governing boundary integral is written as a sum of left- and right-going components, and…
We apply the spectral element method to the determination of scattering and bound states of the multichannel Schr\"odinger equation. In our approach the reaction coordinate is discretized on a grid of points whereas the internal coordinates…
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…
In this paper, we consider the problem of mechanical wave scattering from a spatially finite system into an infinite surrounding environment. The goal is to illuminate why the scattering spectrum undergoes peaks and dips (resonances) at…
In this paper we investigate the spectral and scattering theory for operators acting on topological crystals and on their perturbations. A special attention is paid to perturbations obtained by the addition of an infinite number of edges,…
This paper focuses on scattered data fitting problems on spheres. We study the approximation performance of a class of weighted spectral filter algorithms, including Tikhonov regularization, Landaweber iteration, spectral cut-off, and…
We study the propagation, observation and control properties of the 1-d wave equation on a bounded interval discretized in space using the quadratic classical finite element approximation. A careful Fourier analysis of the discrete wave…
Surface integral equations (SIEs)-based boundary element methods are widely used for analyzing electromagnetic scattering scenarii. However, after discretization of SIEs, the spectrum and eigenvectors of the boundary element matrices are…
The explicit connection between the transition matrix and boundary element method integral operators is formulated. This enables the calculation of characteristic modes via eigenvalue problems involving either set of operators, leading to…
We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical…
The behaviour of the spectral edges (embedded eigenvalues and resonances) is discussed at the two ends of the continuous spectrum of non-local discrete Schr\"odinger operators with a $\delta$-potential. These operators arise by replacing…
An ordinary differential operator of the fourth order with coefficients converging at infinity sufficiently rapidly to constant limits is considered. Scattering theory for this operator is developed in terms of special solutions of the…
We are concerned with the acoustic scattering problem, at a frequency $\kappa$, by many small obstacles of arbitrary shapes with impedance boundary condition. These scatterers are assumed to be included in a bounded domain $\Omega$ in…
In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched…
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 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…