Related papers: Finite Element Method (Chapter from "Gratings: The…
We consider in this paper the angular deviation and diffraction efficiency of the reflection gratings in Littrow-configuration for applications of external cavity diode laser using the rigorous coupled-wave analysis method. We consider the…
We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…
This work is devoted to the development of an efficient and robust technique for accurate capturing of the electric field in multi-material problems. The formulation is based on the finite element method enriched by the introduction of…
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,…
This paper studies the theory and applications of the diffraction of electromagnetic waves by space-time periodic (STP) diffraction gratings. We show that, in contrast with conventional spatially periodic grating, a STP diffraction grating…
We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite…
This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…
A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM).…
We present a systematic accuracy assessment of the thin-element approximation (TEA), the beam propagation method (BPM), and the wave propagation method (WPM) for binary diffractive gratings, using the rigorous Fourier modal method (FMM) as…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
The influence of edge roughness in angle resolved scatterometry at periodically structured surfaces is investigated. A good description of the radiation interaction with structured surfaces is crucial for the understanding of optical…
We begin by addressing the time-domain full-waveform inversion using the adjoint method. Next, we derive the scaled boundary semi-weak form of the scalar wave equation in heterogeneous media through the Galerkin method. Unlike conventional…
We report that metamaterial-inspired one-dimensional gratings (or metagratings) can be used to control nonpropagating diffraction orders as well as propagating ones. By accurate engineering of the near field, it becomes possible to satisfy…
We present numerical experiments regarding the diffraction characteristics and their precompensation arising from changing the macroscopic geometry of a flat HOE into a sphere segment. In particular, we discuss a parametric optimization…
A novel general purpose Finite Element framework is presented to study small-scale metal plasticity. A distinct feature of the adopted distortion gradient plasticity formulation, with respect to strain gradient plasticity theories, is the…
We describe a dispersive unit consisting of cascaded volume-phase holographic gratings for spectroscopic applications. Each of the gratings provides high diffractive efficiency in a relatively narrow wavelength range and transmits the rest…
We discuss the applicability of holographically recorded gratings in photopolymers and holographic polymer-dispersed liquid crystals as neutron optical elements. An experimental investigation of their properties for light and neutrons with…
Upper bound limit analysis allows one to evaluate directly the ultimate load of structures without performing a cumbersome incremental analysis. In order to numerically apply this method to thin plates in bending, several authors have…
The aim of this work is to present the details of the finite element approach we developed for solving the Landau-Lifschitz-Gilbert equations in order to be able to treat problems involving complex geometries. There are several…
We develop a stabilized cut finite element method for the stationary convection diffusion problem on a surface embedded in ${\mathbb{R}}^d$. The cut finite element method is based on using an embedding of the surface into a three…