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Scattering resonances have important applications in many areas of science and engineering. They are the replacement of discrete spectral data for problems on non-compact domains. In this paper, we consider the computation of scattering…
In this work we developed a new problem solution methodology of contact interaction of acoustic medium with resilient finite bodies of cylindrical form, based on application of boundary integral equations method in conjunction with series…
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…
The boundary element method is an efficient algorithm for simulating acoustic propagation through homogeneous objects embedded in free space. The conditioning of the system matrix strongly depends on physical parameters such as density,…
Two-dimensional Stokes flow through a periodic channel is considered. The channel walls need only be Lipschitz continuous, in other words they are allowed to have corners. Boundary integral methods are an attractive tool for numerically…
Sound-soft fractal screens can scatter acoustic waves even when they have zero surface measure. To solve such scattering problems we make what appears to be the first application of the boundary element method (BEM) where each BEM basis…
Scattering from large, open cavity structures is of importance in a variety of electromagnetic applications. In this paper, we propose a new well conditioned integral equation for scattering from general open cavities embedded in an…
This paper investigates the problem of time-harmonic acoustic scattering in an inhomogeneous medium with a complex topological structure. Specifically, the medium is anisotropic and contains several disjoint sound-soft obstacles. This model…
We investigate integral formulations and fast algorithms for the steady-state radiative transfer equation with isotropic and anisotropic scattering. When the scattering term is a smooth convolution on the unit sphere, a model reduction step…
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 article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…
We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain…
This paper is devoted to a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we…
The paper presents a globally convergent algorithm for solving coefficient inverse problems. Being rooted in the globally convergent numerical method (SIAM J. Sci. Comput., 31, No.1 (2008), pp. 478-509) for solving multidimensional…
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…
In this paper, we will introduce a high order numerical method to solve the scattering problems with non-periodic incident fields and (locally perturbed) periodic surfaces. For the problems we are considering, the classical methods to treat…
In this paper, we develop a high order numerical method for the numerical solutions of scattering problems with slightly perturbed periodic surfaces in two dimensional spaces. Based on the regularity property introduced in Part I, the…
Consider the problem of inverse scattering of time-harmonic point sources from an infinite, penetrable rough interface with bounded obstacles buried in the lower half-space, where the interface is assumed to be a local perturbation of a…
In this paper, we present a fast boundary integral method accelerated by the fast multipole method (FMM) for acoustic wave scattering governed by the scalar Helmholtz equation in multi-layered two-dimensional media. Multiple scatterers are…
This paper presents novel methodologies for the numerical simulation of scattering of elastic waves by both closed and open surfaces in three-dimensional space. The proposed approach utilizes new integral formulations as well as an…