Related papers: In-out decomposition of boundary integral equation…
A novel variational formulation of layer potentials and boundary integral operators generalizes their classical construction by Green's functions, which are not explicitly available for Helmholtz problems with variable coefficients.…
We consider wave propagation problems in which there is a preferred direction of propagation. To account for propagation in preferred directions, the wave equation is decomposed into a set of coupled equations for waves that propagate in…
Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an…
We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission conditions to reduce the…
We present a new integral equation for solving the Maxwell scattering problem against a perfect conductor. The very same algorithm also applies to sound-soft as well as sound-hard Helmholtz scattering, and in fact the latter two can be…
This paper presents smoothed combined field integral equations for the solution of Dirichlet and Neumann exterior Helmholtz problems. The integral equations introduced in this paper are smooth in the sense that they only involve…
Numerical resolution of exterior Helmholtz problems requires some approach to domain truncation. As an alternative to approximate nonreflecting boundary conditions and invocation of the Dirichlet-to-Neumann map, we introduce a new, nonlocal…
Two boundary value problems for the Helmholtz equation in a semi-infinite strip are considered. The main feature of these problems is that, in addition to the function and its normal derivative on the boundary, the functionals of the…
We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
We present non-overlapping Domain Decomposition Methods (DDM) based on quasi-optimal transmission operators for the solution of Helmholtz transmission problems with piece-wise constant material properties. The quasi-optimal transmission…
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 extend the method of layer potentials to manifolds with boundary and cylindrical ends. To obtain this extension along the classical lines, we have to deal with several technical difficulties due to the non-compactness of the boundary,…
This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating half-space in the weak-scattering regime, and the study of boundary effects through an asymptotic analysis of the…
A system of boundary-domain integral equations is derived from the bidimensional Dirichlet problem for the diffusion equation with variable coefficient using the novel parametrix from [22] different from the one in [5,18]. Mapping…
We prove new, sharp, wavenumber-explicit bounds on the norms of the Helmholtz single- and double-layer boundary-integral operators as mappings from $L^2(\partial \Omega)\rightarrow H^1(\partial \Omega)$ (where $\partial\Omega$ is the…
We analyze and develop numerical methods for time-harmonic wave scattering in metallic waveguide structures of infinite extent. We show that radiation boundary conditions formulated via projectors onto outgoing modes determine the…
We study the behaviour of the normal derivative of eigenfunctions of the Helmholtz equation inside billiards with Dirichlet boundary condition. These boundary functions are of particular importance because they uniquely determine the…
The transfer operator due to Bogomolny provides a convenient method for obtaining a semiclassical approximation to the energy eigenvalues of a quantum system, no matter what the nature of the analogous classical system. In this paper, 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…