Related papers: Generalized Finite Differences Method Applied to F…
We present a finite-difference method for the topology optimization of permanent magnets that is based on the FFT accelerated computation of the stray-field. The presented method employs the density approach for topology optimization and…
The conditioning of the linear finite volume element discretization for general diffusion equations is studied on arbitrary simplicial meshes. The condition number is defined as the ratio of the maximal singular value of the stiffness…
We propose a method to directly visualize the photonic band-structure of micron size photonic crystals using wide angle spectroscopy. By extending Fourier Imaging Spectroscopy sensitivity into the infrared range we have obtained accurate…
We consider overlap splines that are defined by connecting the patches of piecewise functions via common values at given finite sets of nodes, without using any partitions of the computational domain. It is shown that some classical finite…
Traditional domain generalization methods often rely on domain alignment to reduce inter-domain distribution differences and learn domain-invariant representations. However, domain shifts are inherently difficult to eliminate, which limits…
With the aim of describing bound and continuum states for diatomic molecules, we develop and implement a spectral method that makes use of Generalized Sturmian Functions (GSF) in prolate spheroidal coordinates. In order to master all…
This Comment concerns the effective dielectric constant for 2D photonic crystal. We show that even in the limit of very high dielectric constant of photonic crystal's "atoms", static and quasistatic approaches give the same results, unlike…
We develop a general framework for the electrostatic analysis of point charges in multilayer planar structures with arbitrary layer thicknesses and material parameters. Starting from a Hankel-transform analysis, we derive alternative…
In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, including the first and high order ones, just work on uniform…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
Optical resonances in 1D photonic crystal microcavities are investigated numerically using finite-element light scattering and eigenmode solvers. The results are validated by comparison to experimental and theoretical findings from the…
In data science, individual observations are often assumed to come independently from an underlying probability space. Kernel matrices formed from large sets of such observations arise frequently, for example during classification tasks. It…
Photonic nanostructures simultaneously maximizing spectral and spatial overlap between fundamental and second-harmonic confined modes are highly desirable for enhancing second-order nonlinear effects in nonlinear media. These conditions…
A new criterion on normal bases of finite field extension $\mathbb{F}_{q^n} / \mathbb{F}_{q}$ is presented and explicit criterions for several particular finite field extensions are derived from this new criterion.
This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation.…
Using exhaustion method and finite differences a new method to solve system of partial differential equations and is presented. This method allows design algorithm to solve linear and nonlinear systems in irregular domains. Applying this…
Starting from the total energy expressions within density functional theory, we are able to perform a comparison of several currently used charged-defect finite-size supercell correction schemes in a unified manner. This approach also…
We demonstrate that the resonance frequencies of high-Q microcavities in two-dimensional photonic crystal membranes can be tuned over a wide range by introducing a subwavelength dielectric tip into the cavity mode. Three-dimensional…
In this paper, we consider local multiscale model reduction for problems with multiple scales in space and time. We developed our approaches within the framework of the Generalized Multiscale Finite Element Method (GMsFEM) using space-time…
This study presents a finite-difference-based numerical solver designed for the electric field formulation of vector wave equations in optically linear, non-magnetic, dielectric waveguides. We construct a generalized eigenvalue problem by…