Related papers: Shape Taylor expansion for wave scattering problem…
High frequency estimates for the Dirichlet-to-Neumann and Neumann-to-Dirichlet operators are obtained for the Helmholtz equation in the exterior of bounded obstacles. These a priori estimates are used to study the scattering of plane waves…
In this paper, we describe the structure of shape derivatives around sets which are only assumed to be of finite perimeter in $\R^N$. This structure allows us to define a useful notion of positivity of the shape derivative and we show it…
We derive new, explicit representations for the solution to the scalar wave equation in the exterior of a sphere, subject to either Dirichlet or Robin boundary conditions. Our formula leads to a stable and high-order numerical scheme that…
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…
In this paper we present a theory of vessels and its application to the classical inverse scattering of the Sturm-Liouville differential equation. The classical inverse scattering theory, including all its ingredients: Jost solutions, the…
Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods…
We derive analytical shape derivative formulas of the system matrix representing electric field integral equation discretized with Raviart-Thomas basis functions. The arising integrals are easy to compute with similar methods as the entries…
We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…
A lesser-known but powerful application of parabolic equation methods is to the target scattering problem. In this paper, we use noncanonically shaped objects to establish the limits of applicability of the traditional approach, and…
The derivative expansion of the effective action is considered in the model with two interacting real scalar fields in curved spacetime. Using the functional approach and local momentum representation, the coefficient of the derivative term…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
We formulate a new family of high order on-surface radiation conditions to approximate the outgoing solution to the Helmholtz equation in exterior domains. Motivated by the pseudo-differential expansion of the Dirichlet-to-Neumann operator…
Conventional X-ray methods use incoming plane waves and result in discrete diffraction patterns when scattered at crystals. Here we find, by a systematic method, incoming waveforms which exhibit discrete diffraction patterns when scattered…
We establish and develop a novel methodology to treat higher-order non-linear effects of gravitational radiation that is scattered from binary inspirals, which employs modern scattering-amplitudes methods on the effective picture of the…
Mie theory is a powerful method to model electromagnetic scattering from a multilayered sphere. Usually, the incident beam is expanded to its vector spherical harmonic representation defined by beam shape coefficients, and the multilayer…
When a plane electromagnetic wave impinges upon a diffraction grating or other periodic structures, reflected and transmitted waves propagate away from the structure in different radiation channels. A diffraction anomaly occurs when the…
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…
Multiple scattering of polarised electromagnetic waves in diffusive media is investigated by means of radiative transfer theory. The method becomes exact in several situations of interest, such as a thick-slab experiment (slab thickness L…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
We propose a novel finite-difference time-domain (FDTD) scheme for the solution of the Maxwell's equations in which linear dispersive effects are present. The method uses high-order accurate approximations in space and time for the…