Related papers: Finite Element Calculation of Photonic Band Struct…
We demonstrate that the tuning of the optical properties of a photonic crystal infiltrated with liquid crystal can be calculate using the Von-Laue diffraction condition. We present a simple formula to predict the shift of the stop band for…
We introduce an efficient method for computing the Stekloff eigenvalues associated with the Helmholtz equation. In general, this eigenvalue problem requires solving the Helmholtz equation with Dirichlet and/or Neumann boundary condition…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
Using the Green's function formalism, an ab initio theory for band structures of crystals is derived starting from the Hartree-Fock approximation. It is based on the algebraic diagrammatic construction scheme for the self-energy which is…
The spectrum and eigenstates of any field quadrature operator restricted to a finite number $N$ of photons are studied, in terms of the Hermite polynomials. By (naturally) defining \textit{approximate} eigenstates, which represent highly…
For the eigenvalue problem of the Steklov differential operator, by following Liu's approach, an algorithm utilizing the conforming finite element method (FEM) is proposed to provide guaranteed lower bounds for the eigenvalues. The proposed…
The goal of this paper is to develop numerical methods computing a few smallest elasticity transmission eigenvalues, which are of practical importance in inverse scattering theory. The problem is challenging since it is nonlinear,…
Motivated by Fredholm theory, we develop a framework to establish the convergence of spectral methods for operator equations $\mathcal L u = f$. The framework posits the existence of a left-Fredholm regulator for $\mathcal L$ and the…
We consider PDE eigenvalue problems as they occur in two-dimensional photonic crystal modeling. If the permittivity of the material is frequency-dependent, then the eigenvalue problem becomes nonlinear. In the lossless case, linearization…
In this paper we study the eigenvalues of the angular spheroidal wave equation and its generalization, the Coulomb spheroidal wave equation. An associated differential system and a formula for the connection coefficients between the various…
In this paper, spectral analysis of fractional Sturm Liouville problem defined on (0,1], having the singularity of type at zero and research the fundamental properties of the eigenfunctions and eigenvalues for the operator. We show that the…
We present numerical upscaling techniques for a class of linear second-order self-adjoint elliptic partial differential operators (or their high-resolution finite element discretization). As prototypes for the application of our theory we…
We propose an all-optical method to directly reconstruct the band structure of semiconductors. Our scheme is based on the temporal Young's interferometer realized by high harmonic generation (HHG) with a few-cycle laser pulse. As a…
Key words : The Maxwell equations, band structure calculations, Kohn-Korringa-Rostocker method, and multiple-scattering theory for photons. For those who are interested in how to prepare perfect mirror from a purely transparent material.…
Designing topological materials with specific topological indices is a complex inverse problem, traditionally tackled through manual, intuition-driven methods that are neither scalable nor efficient for exploring the vast space of possible…
The paper presents a finite element scheme for the elastic transmission eigenvalue problem written as a fourth order eigenvalue problem. The scheme uses piecewise cubic polynomials and obtains optimal convergence rate. Compared with other…
Eigenstates of the FQHE hamiltonian problem after to be projected on the LLL are determined for filling factors 1/q, with q an odd number. The solutions are found for an infinite class of finite samples in which the Coulomb potential is…
We estimate the distribution of the eigenvalues of a family of time-frequency localization operators whose eigenfunctions are the well-known Prolate Spheroidal Wave Functions from mathematical physics. These operators are fundamental to the…
We present a framework to solve non-linear eigenvalue problems suitable for a Finite Element discretization. The implementation is based on the open-source finite element software GetDP and the open-source library SLEPc. As template…
Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from measurements of its solution(s). In practical applications, the…