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A scheme for rapidly and accurately computing solutions to boundary integral equations (BIEs) on rotationally symmetric surfaces in three dimensions is presented. The scheme uses the Fourier transform to reduce the original BIE defined on a…
We study the elastic time-harmonic wave scattering problems on unbounded domains with boundaries composed of finite collections of disjoints finite open arcs (or cracks) in two dimensions. Specifically, we present a fast spectral Galerkin…
We analyze the well posedness of certain field-only boundary integral equations (BIE) for frequency domain electromagnetic scattering from perfectly conducting spheres. Starting from the observations that (1) the three components of the…
This work presents theoretical and numerical models for the backscattering of two-dimensional Rayleigh waves by an elastic inclusion, with the host material being isotropic and the inclusion having arbitrary shape and crystallographic…
A domain integral method employing a specific Green's function (i.e., incorporating some features of the global problem of wave propagation in an inhomogeneous medium) is developed for solving direct and inverse scattering problems relative…
Surface integral equation (SIE) methods are of great interest for the numerical solution of Maxwell's equations in the presence of homogeneous objects. However, existing SIE algorithms have limitations, either in terms of scalability,…
In this paper, we revisit the classic problem of diffraction of electromagnetic waves by an aperture in a perfectly conducting plane. We formulate the diffraction problem using a boundary integral equation that is defined on the aperture…
This paper presents a novel approach called the boundary integrated neural networks (BINNs) for analyzing acoustic radiation and scattering. The method introduces fundamental solutions of the time-harmonic wave equation to encode the…
In this paper, we develop highly accurate Nystr\"{o}m methods for the volume integral equation (VIE) of the Maxwell equation for 3-D scatters. The method is based on a formulation of the VIE equation where the Cauchy principal value of the…
In this paper, we proposed a single-source surface integral formulation to accurately solve the scattering problems by 2D penetrable objects. In this method, the objects are replaced by their surrounding medium through enforcing a surface…
We utilize the domain integral equation formulation to simulate two-dimensional transverse electric scattering in a homogeneous medium and a summation of modulated Gaussian functions to approximate the dual Gabor window. Then we apply Ewald…
We propose a novel method for the efficient and accurate iterative solution of frequency domain integral equations (IEs) that are used for large/multi-scale electromagnetic scattering problems. The proposed method uses a novel…
In this paper we introduce a method for solving linear and nonlinear scattering problems for wave equations using a new hybrid approach. This new approach consists of a reformulation of the governing equations into a form that can be solved…
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…
We present a new derivation of a boundary integral equation (BIE) for simulating the three-dimensional dynamics of arbitrarily-shaped rigid particles of genus zero immersed in a Stokes fluid, on which are prescribed forces and torques. Our…
Green's function plays a significant role in both theoretical analysis and numerical computing of partial differential equations (PDEs). However, in most cases, Green's function is difficult to compute. The troubles arise in the following…
We consider boundary integral equations (BIEs) met in the scattering by dielectric cylinders and compare numerical algorithms based on elementary and Muller's BIEs near the "numerical resonances". A procedure of partial removal of…
A general approach for the calculation of the incoherent intensity scattered by a random medium with rough boundaries has been developed using a Green function formalism. The random medium consists of spherical particles whose physical…
A scheme for rapidly and accurately computing solutions to boundary integral equations (BIEs) on rotationally symmetric surfaces in R^3 is presented. The scheme uses the Fourier transform to reduce the original BIE defined on a surface to a…
This manuscript presents an efficient boundary integral equation technique for solving two-dimensional Helmholtz problems defined in the half-plane bounded by an infinite, periodic curve with Neumann boundary conditions and an aperiodic…