Related papers: Finite Element Method (Chapter from "Gratings: The…
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…
Numerous vector angular spectrum methods have been presented to model the vectorial nature of diffractive electromagnetic field, facilitating optical field engineering in polarization-related and high numerical aperture systems. However,…
Electron diffraction through a thin patterned silicon membrane can be used to create complex spatial modulations in electron distributions by varying the intensity of different reflections using parameters such as crystallographic…
Discrete ordinate ($S_N$) and filtered spherical harmonics ($FP_N$) based schemes have been proven to be robust and accurate in solving the Boltzmann transport equation but they have their own strengths and weaknesses in different physical…
We use a finite-element method to obtain highly converged results for a nano-optical light scattering setup with a non-periodic geometry.
We demonstrate the interest of combining Finite Element calculations with the Vector Partial Wave formulation (used in T-matrix and Mie theory) in order to characterize the electromagnetic scattering properties of isolated individual…
Photon Green function (GF) is the vital and most decisive factor in the field of quantum light-matter interaction. It is divergent with two equal space arguments in arbitrary-shaped lossy structure and should be regularized. We introduce a…
Methods for solving Maxwell's equations are integral part of optical metrology and computational lithography setups. Applications require accurate geometrical resolution, high numerical accuracy and/or low computation times. We present a…
The problem of diffraction of an electromagnetic plane wave by a perfectly conducting circular disk and its complementary problem, diffraction by a circular hole in an infinite conducting plate, are rigorously solved using the method of the…
Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a…
Future observatories utilizing reflection grating spectrometers for extreme ultraviolet (EUV) and soft X-ray (SXR) spectroscopy require high-fidelity gratings with both blazed groove facets and custom groove layouts that are often fanned or…
The measurement of the spectral diffraction efficiencies of a diffraction grating is essential for improving the manufacturing technique and for assessing the grating's function in practical applications. The drawback of the currently…
A semidiscrete Galerkin finite element method applied to time-fractional diffusion equations with time-space dependent diffusivity on bounded convex spatial domains will be studied. The main focus is on achieving optimal error results with…
We propose a matrix-free finite element (FE) homogenization scheme that is considerably more efficient than generic FE implementations. The efficiency of our scheme follows from a preconditioned well-scaled reformulation allowing for the…
We present a finite element discretization of a non-linear diffusion equation used in the field of critical phenomena and, more recently, in the context of Dynamic Density Functional Theory. The discretized equation preserves the structure…
A novel finite element formulation for gradient-regularized damage models is presented which allows for the robust, efficient, and mesh-independent simulation of damage phenomena in engineering and biological materials. The paper presents a…
The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM…
In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material properties are assumed to be graded…
This dissertation is concerned with understanding and analyzing some of the effects of diffraction in the near field. The contributions of homogeneous and of evanescent waves to two-dimensional near-field diffraction patterns of scalar…
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…