Related papers: An integral equation technique for scattering prob…
In this paper we explore the possibility for solving the 3D Maxwell's equations in the presence of nonlinear and/or inhomogeneous material response. We propose using a hybrid approach which combines a bound- ary integral representation with…
Recently, reduced order modeling methods have been applied to solving inverse boundary value problems arising in frequency domain scattering theory. A key step in projection-based reduced order model methods is the use of a sesquilinear…
We present and analyze fully discrete Nystr\"om methods for the solution of three classes of well conditioned boundary integral equations for the solution of two dimensional scattering problems by homogeneous dielectric scatterers.…
An original boundary integral formulation is proposed for the problem of a semi-infinite crack at the interface between two dissimilar elastic materials in the presence of heat flows and mass diffusion. Symmetric and skew-symmetric weight…
We propose a time-domain boundary integral method to model linear wave propagation with refractive, focusing, and Doppler effects arising from medium heterogeneities and moving obstacles. In contrast to existing techniques, our method…
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 propose some variational formulations with the use of high order impedance boundary condition (HOIBC) to solve the scattering problem. We study the existence and uniqueness of the solution. Then, a discretization of these…
Boundary integral equation methods for analyzing electromagnetic scattering phenomena typically suffer from several of the following problems: (i) ill-conditioning when the frequency is low; (ii) ill-conditioning when the discretization…
We develop a novel method of virtual sources to formulate boundary integral equations for exterior wave propagation problems. However, by contrast to classical boundary integral formulations, we displace the singularity of the Green's…
In this paper we consider the electromagnetic scattering problem by an obstacle characterised by a Generalized Impedance Boundary Condition in the harmonic regime. These boundary conditions are well known to provide accurate models for thin…
We consider the time-harmonic acoustic wave scattering by a bounded {\it anisotropic inhomogeneity} embedded in an unbounded {\it anisotropic} homogeneous medium. The material parameters may have discontinuities across the interface between…
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 introduce a boundary integral method for two-dimensional quantum billiards subjected to a constant magnetic field. It allows to calculate spectra and wave functions, in particular at strong fields and semiclassical values of the magnetic…
An integrable Kondo problem in the one-dimensional supersymmetric extended Hubbard model is studied by means of the boundary graded quantum inverse scattering method. The boundary $K$ matrices depending on the local moments of the…
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…
In this paper we suggest a new approach for the multichannel Coulomb scattering problem. The Schr\"{o}dinger equation for the problem is reformulated in the form of a set of inhomogeneous equations with a finite-range driving term. The…
We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic…
The Poisson-Boltzmann equation offers an efficient way to study electrostatics in molecular settings. Its numerical solution with the boundary element method is widely used, as the complicated molecular surface is accurately represented by…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
The acoustic scattering problem is modeled by the exterior Helmholtz equation, which is challenging to solve due to both the unboundedness of the domain and the high dispersion error, known as the pollution effect. We develop high-order…