Related papers: A Singularity-free Boundary Equation Method for Wa…
We analyze electromagnetic scattering of TM polarized waves from a diffraction grating consisting of a periodic, anisotropic, and possibly negative-index dielectric material. Such scattering problems are important for the modelization of,…
Invariant discretization schemes are derived for the one- and two-dimensional shallow-water equations with periodic boundary conditions. While originally designed for constructing invariant finite difference schemes, we extend the usage of…
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
We apply the spectral element method to the determination of scattering and bound states of the multichannel Schr\"odinger equation. In our approach the reaction coordinate is discretized on a grid of points whereas the internal coordinates…
This paper describes a trapezoidal quadrature method for the discretization of singular and hypersingular boundary integral operators (BIOs) that arise in solving boundary value problems for elliptic partial differential equations. The…
Based on the perfectly matched layer (PML) technique, this paper develops a high-accuracy boundary integral equation (BIE) solver for acoustic scattering problems in locally defected layered media in both two and three dimensions. The…
We develop a non-overlapping domain decomposition method (DDM) for scalar wave scattering by periodic layered media. Our approach relies on robust boundary-integral equation formulations of Robin-to-Robin (RtR) maps throughout the frequency…
Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
We study the one-point and two-point Green's functions in a complex random matrix model to sub-leading orders in the large N limit. We take this complex matrix models as a model for the two-state scattering problem, as applied to spin…
The 2D space-fractional Schrodinger equation in the time-independent and time-dependent cases for the scattering problem in the fractional quantum mechanics is studied. We define and give the mathematical expression of the Green's functions…
Boundary integral equation is derived for the problem of scattering of electromagnetic waves by 3D homogeneous body of arbitrary shape.
This paper is concerned with a numerical solution to the scattering of a time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in three dimensions. The electromagnetic wave propagation is modeled by a boundary value…
A multi-channel scattering problem is studied from a point of view of integral equations system. The system appears while natural one-particle wave function equation of the electron under action of a potential with non-intersecting ranges…
In this paper, we study the propagation of singularities (in the sense of $\mathcal{C}^{\infty}$ wave front set) of the solution of a model case initial-boundary value problem with glancing rays for a concave domain on an asymptotically…
A novel method of solving scattering problems for bound pairs on a lattice is developed. Two different break ups of the hamiltonian are employed to calculate the full Green operator and the wave function of the scattered pair. The…
Maxwell's equations are considered with transparent boundary conditions, for initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The numerical…
Problems with topological uncertainties appear in many fields ranging from nano-device engineering to the design of bridges. In many of such problems, a part of the domains boundaries is subjected to random perturbations making inefficient…
To solve boundary integral equations for potential problems using collocation Boundary Element Method (BEM) on smooth curved 3D geometries, an analytical singularity extraction technique is employed. By adopting the isoparametric approach,…
The Calder\'on formulas (i.e., the combination of single-layer and hyper-singular boundary integral operators) have been widely utilized in the process of constructing valid boundary integral equation systems which could possess highly…