Related papers: Generalized Finite Differences Method Applied to F…

Space group theory is pivotal in the design of nanophotonics devices, enabling the characterization of periodic optical structures such as photonic crystals. The aim of this study is to extend the application of nonsymmorphic space groups…

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…

Domain generalization aims to learn a generalizable model from a known source domain for various unknown target domains. It has been studied widely by domain randomization that transfers source images to different styles in spatial space…

We introduce a new approach to analyze the phase diagram of QCD at finite chemical potential and temperature, based on the definition of a generalized QCD action. Several details of the method will be discussed, with particular emphasis on…

A general formula is presented for any order derivative of Chebyshev polynomials instead of the existing recursive relationship. Hence, the Chebyshev finite difference method is made applicable not only to second order problems but also to…

In this paper, we propose an unfitted Nitsche's method to compute the band structures of phononic crystal with impurities of general geometry. The proposed method does not require the background mesh to fit the interfaces of impurities, and…

Here, the frequency degree of freedom is introduced into valley photonic crystals with dual band gaps. Based on the high-order plane wave expansion model, we derive an effective Hamiltonian which characterizes dual band gaps. Metallic…

The iso-frequency contours of a photonic crystal are important for predicting and understanding exotic optical phenomena that are not apparent from high-symmetry band structure visualizations. Here, we demonstrate a method to directly…

We demonstrate that the finite difference grid method (FDM) can be simply modified to satisfy the variational principle and enable calculations of both real and complex poles of the scattering matrix. These complex poles are known as…

In this work, a doubly resonant photonic crystal (PhC) cavity using the merged bound states in the continuum (BICs) is proposed to obtain a higher second harmonic generation (SHG) efficiency. Firstly by scanning geometry parameters the…

Photonic quantum computing is one of the leading approaches to universal quantum computation. However, large-scale implementation of photonic quantum computing has been hindered by its intrinsic difficulties, such as probabilistic…

The finite strain theory is reformulated in the frame of the Tangential Differential Calculus (TDC) resulting in a unification in a threefold sense. Firstly, ropes, membranes and three-dimensional continua are treated with one set of…

Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the…

Here, we report a numerical implementation of the nonlocal homogenization approach recently proposed in [M. Silveirinha, Phys. Rev. B 75, 115104 (2007)], using the finite difference frequency-domain method to discretize the…

In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…

We present a boundary integral method for numerical computation of the capacity of generalized condensers. The presented method applies to a wide variety of generalized condenser geometry including the cases when the plates of the…

Domain generalization is a technique aimed at enabling models to maintain high accuracy when applied to new environments or datasets (unseen domains) that differ from the datasets used in training. Generally, the accuracy of models trained…

We consider bivariate piecewise polynomial finite element spaces for curved domains bounded by piecewise conics satisfying homogeneous boundary conditions, construct stable local bases for them using Bernstein-B\'ezier techniques, prove…

Photonic crystals are characterized by a spatial modulation of the dielectric constant on the length scale of the wavelength of light giving rise to energy ranges where light cannot propagate through the crystal - the photonic band gap.…

Solving partial differential equations (PDEs) on manifolds defined by randomly sampled point clouds is a challenging problem in scientific computing and has broad applications in various fields. In this paper, we develop a two-step…