Related papers: Finite Element Method (Chapter from "Gratings: The…
In this work, we develop a fast and accurate method for the scattering of flexural-gravity waves by a thin plate of varying thickness overlying a fluid of infinite depth. This problem commonly arises in the study of sea ice and ice shelves,…
We discuss realization, properties and performance of the adaptive finite element approach to the design of nano-photonic components. Central issues are the construction of vectorial finite elements and the embedding of bounded components…
A computational algorithm for the exact equations representing the scattering coefficients of an infinite grating of insulating dielectric circular cylinders associated with obliquely incident vertically polarized plane electromagnetic…
One of the reasons for the success of the finite element method is its versatility to deal with different types of geometries. This is particularly true of problems posed in curved domains of arbitrary shape. In the case of second order…
Partial differential equations posed on surfaces arise in a number of applications. In this survey we describe three popular finite element methods for approximating solutions to the Laplace-Beltrami problem posed on an $n$-dimensional…
The modeling and simulation of electromagnetic wave propagation is often accompanied by a restriction to bounded domains which requires the introduction of artificial boundaries. The corresponding boundary conditions should be chosen in…
In this article a simplified weak Galerkin finite element method is developed for the Dirichlet boundary value problem of convection-diffusion-reaction equations. The simplified weak Galerkin method utilizes only the degrees of freedom on…
A theoretical approach for uniformly extracting light propagating through a light guide plate is developed here. Typically, liquid crystal display modalities utilize a backlit lighting system illuminated from the edge with light emitting…
A two-step preconditioned iterative method based on the Hermitian/Skew-Hermitian splitting is applied to the solution of nonsymmetric linear systems arising from the Finite Element approximation of convection-diffusion equations. The…
We have studied atomic diffraction at normal incidence from an evanescent standing wave with a high resolution using velocity selective Raman transitions. We have observed up to 3 resolved orders of diffraction, which are well accounted for…
We theoretically formulate and experimentally demonstrate an analytical formalism for the design of printed circuit board (PCB) metagratings (MGs) exercising individual control over the amplitude and phase of numerous diffracted modes, in…
This paper proposes an efficient FDTD technique for determining electromagnetic fields interacting with a finite-sized 2D and 3D periodic structures. The technique combines periodic boundary conditions---modelling fields away from the edges…
It has recently been shown that optical reflection gratings fabricated directly into an atom chip provide a simple and effective way to trap and cool substantial clouds of atoms [1,2]. In this article we describe how the gratings are…
We propose a method to integrate dissipative PDEs rigorously forward in time with the use of Finite Element Method (FEM). The technique is based on the Galerkin projection on the FEM space and estimates on the residual terms. The proposed…
We develop a versatile theoretical approach to the study of cold-atom diffractive scattering from light-field gratings by combining calculations of the optical near-field, generated by evanescent waves close to the surface of periodic…
In this article we present a theoretical study for Fraunhofer diffraction of a Laguerre-Gaussian laser beam with zeroth radial mode number and azimuthal mode number l by diffractive grating with embedded fork-shaped dislocations of integer…
We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…
Efficient imaging of biomolecules, 2D materials and electromagnetic fields depends on retrieval of the phase of transmitted electrons. We demonstrate a method to measure phase in a scanning transmission electron microscope using a…
We present a technique capable of producing subwavelength focal spots in the far-field of the source in planar non-resonant structures. The approach combines the diffraction gratings that generate the high-wavevector-number modes and planar…
In this paper, we construct a class of Mixed Generalized Multiscale Finite Element Methods for the approximation on a coarse grid for an elliptic problem in thin two-dimensional domains. We consider the elliptic equation with homogeneous…