Related papers: A fast solver for multi-particle scattering in a l…
This paper presents a robust numerical solution to the electromagnetic scattering problem involving multiple multi-layered cavities in both transverse magnetic and electric polarizations. A transparent boundary condition is introduced at…
This paper is concerned with efficient representations and approximations of the solution to the scattering problem by a system of strongly coupled plasmonic particles. Three schemes are developed: the first is the resonant expansion which…
This paper introduces a boundary integral equation for time-harmonic electromagnetic scattering by composite dielectric objects. The formulation extends the classical M\"uller equation to composite structures through the global multi-trace…
A symmetric boundary integral formulation for the transient scattering of acoustic waves off homogeneous and isotropic elastic obstacles is analyzed. Both the acoustic scattered field and the elastodynamic excited field are represented…
The atmospheres of planets (including Earth) and the outer layers of stars have often been treated in radiative transfer as plane-parallel media, instead of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give an…
We obtain a nonperturbative, analytical solution to integral equation of scattering theory by assuming the field within the scattering object is a spherical wave with a scattering amplitude equal to that of the far field. This approximation…
Reflection of particles from a disordered or chaotic medium is characterized by a scattering matrix that can be represented as a superposition of resonances. Each resonance corresponds to an eigenstate inside the medium and has a width…
An efficient hybrid numerical method for multiple scattering calculations is proposed. We use the well established doubling--adding method to find the reflection function of the lowermost homogeneous slab comprising the atmosphere of our…
We consider the global existence and scattering for solutions of magnetic Zakharov system in three-dimensional space. When the initial data is small, we prove the existence of smooth global solutions and scattering results, by combining the…
This article is the first part of a two-fold study, the objective of which is the theoretical analysis and numerical investigation of new approximate corrector problems in the context of stochastic homogenization. We present here three new…
In this paper we review the results of the author on the theory of scalar and vector wave scattering by small bodies of an arbitrary shape with the emphasis on practical applicability of the formulas obtained and on the mathematical rigor…
We consider a formulation of initial problem for Kolmogorov equation that corresponds a localized source of particles to be scattered by medium with given scattering amplitude density (scattering indicatrix). The multiple scattering…
We introduce an arbitrary order, computationally efficient method to smooth corners on curves in the plane, as well as edges and vertices on surfaces in $\mathbb R^3$. The method is local, only modifying the original surface in a…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
The Helmholtz equation arises in the study of electromagnetic radiation, optics, acoustics, etc. In spherical coordinates, its general solution can be written as a spherical harmonic series which satisfies the radiation condition at…
This paper employs layer potential techniques to investigate wave scattering in two-dimensional elastic media exhibiting high contrasts in both Lam\'{e} parameters and density. Our contributions are fourfold. First, we construct an…
In this paper, we consider a numerical method to solve scattering problems with multi-periodic layers with different periodicities. The main tool applied in this paper is the Bloch transform. With this method, the problem is written into an…
In this work the numerical solution of acoustic tomography problem based on the iterative and functional-analytical algorithms is considered. The mathematical properties of these algorithms were previously described in works of R.G.Novikov…
We present a numerical approach to the solution of elastic phonon scattering problems based on a frequency domain decomposition of the atomistic equations of motion and the use of perfectly matched layer or PML boundaries. Unlike MD…
The left-right operator splitting method is studied for the efficient calculation of acoustic fields scattered by arbitrary rough surfaces. Here the governing boundary integral is written as a sum of left- and right-going components, and…