Related papers: Finite Element Calculation of Photonic Band Struct…
We propose a new method to compute band structures of dispersive photonic crystals. It can treat arbitrarily frequency-dependent, lossy or lossless materials. The band structure problem is first formulated as the eigenvalue problem of an…
Calculations of the photonic band structure, transmission coefficients, and quality factors of various two-dimensional, periodic and aperiodic, dielectric photonic crystals by using the finite element method (FEM) are reported. The…
A spectrally formulated finite element analysis based methodology has been proposed to calculate phononic band structure of reticulated honeycomb lattices having translationally invariant repetitive elements called unit cells. Bloch…
Vibrations of structures subjected to concentrated point loads have many applications in mechanical engineering. Experiments are expensive and numerical methods are often used for simulations. In this paper, we consider the plate vibration…
Regular convergence, together with various other types of convergence, has been studied since the 1970s for the discrete approximations of linear operators. In this paper, we consider the eigenvalue approximation of compact operators whose…
The transmission eigenvalue problem arises from the inverse scattering theory for inhomogeneous media and has important applications in many qualitative methods. The problem is posted as a system of two second order partial differential…
Investigating the stability of nonlinear waves often leads to linear or nonlinear eigenvalue problems for differential operators on unbounded domains. In this paper we propose to detect and approximate the point spectra of such operators…
We give a general method to calculate photonic band structure in the form of wave number $k$ as a function of frequency $\omega$, which is required whenever we want to calculate signal intensity related with photonic band structure. This…
In this paper we describe an application of the finite difference method to obtain the transverse magnetic photonic band gap diagram of a photonic crystal. The strategy of this method is to formulate the Maxwell equations in finite…
We present here a Finite Element Method devoted to the simulation of 3D periodic structures of arbitrary geometry. The numerical method based on ARPACK and PARDISO libraries, is discussed with the aim of extracting the eigenmodes of…
In this paper, we consider the optimal design of photonic crystal band structures for two-dimensional square lattices. The mathematical formulation of the band gap optimization problem leads to an infinite-dimensional Hermitian eigenvalue…
In this paper, we compute the band structure of one- and two-dimensional phononic composites using the extended finite element method (X-FEM) on structured higher-order (spectral) finite element meshes. On using partition-of-unity…
We propose a Generalized Finite-Differences in the Frequency Domain method for the computation of photonic band structures of finite photonic crystals. Our approach is to discretize some fundamental domain instead of a single unit cell,…
The present paper introduces the analysis of the eigenvalue problem for the elasticity equations when the so called Navier-Lam\'e system is considered. Such a system introduces the displacement, rotation and pressure of some linear and…
We consider the numerical computation of resonances for metallic grating structures with dispersive media and small slit holes. The underlying eigenvalue problem is nonlinear and the mathematical model is multiscale due to the existence of…
Scattering resonances arise in wave phenomena and play an important role in many applications. While extensive theoretical studies have been conducted, effective numerical computation remains limited, and most existing methods suffer from…
Scattering resonances have important applications in many areas of science and engineering. They are the replacement of discrete spectral data for problems on non-compact domains. In this paper, we consider the computation of scattering…
In this paper we present a mathematical and numerical analysis of an eigenvalue problem associated to the elasticity-Stokes equations stated in two and three dimensions. Both problems are related through the Herrmann pressure. Employing the…
Calculation of band structure of three dimensional photonic crystals amounts to solving large-scale Maxwell eigenvalue problems, which are notoriously challenging due to high multiplicity of zero eigenvalue. In this paper, we try to address…
We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres, characterized by Lam\'e coefficients which may be complex and frequency dependent, arranged…