In this article we develop a finite difference (FDFD) method to compute the band spectra of 2D photonic crystals without impurities. Exploiting periodicity to identify discretization points differing by a period, the computational complexity of the algorithms is reduced significantly. Numerical results on three test problems are presented.

We present a fourth order accurate finite difference method for the elastic wave equation in second order formulation, where the fourth order accuracy holds in both space and time. The key ingredient of the method is a boundary modified fourth order accurate discretization of the second derivative with variable coefficient, (μ(x)ux)x. This discretization satisfies a summation by parts identity ...

We put forward and analyze an explicit finite difference scheme for the Camassa-Holm shallow water equation that can handle general H initial data and thus peakon-antipeakon interactions. Assuming a specified condition restricting the time step in terms of the spatial discretization parameter, we prove that the difference scheme converges strongly in H towards a dissipative weak solution of Cam...

in this paper, a chebyshev finite difference method has been proposed in order to solvenonlinear two-point boundary value problems for second order nonlinear differentialequations. a problem arising from chemical reactor theory is then considered. the approachconsists of reducing the problem to a set of algebraic equations. this method can be regardedas a non-uniform finite difference scheme. t...

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method...

Abstract. Differential algebraic equations have wide applications in the field of engineering and science where the mathematical models form the descriptor systems. Analysis and modeling of the solutions of such systems need to handle with the different equations related to the systems. A time-domain discretization, for example, finite difference, finite volume, etc., may lead to DAEs of descri...

The modeling of physical systems often leads to partial differential equations (PDEs). Usually, the equations or the domain where the equations are posed are so complicated that the analytic solution cannot be found. Thus, the equations must be solved using numerical methods. In order to do this, the PDEs are first discretized using the finite element method (FEM) or the finite difference metho...

analysis of the stresses, displacements, and horizontal strains of the ground subsidence due to underground excavation in rocks can be accomplished by means of a hybridized higher order indirect boundary element/finite difference (be/fd) formulation. a semi-infinite displacement discontinuity field is discretized (numerically) using the cubic displacement discontinuity elements (i.e. each highe...

A continuous space-time Galerkin method is newly proposed for the numerical solution of inverse dynamics problems. The finite element combined with servo-constraints to partially prescribe motion underlying mechanical system. new approach feedforward control infinite-dimensional systems motivated by classical characteristics. In particular, it shown that simultaneous discretization much better ...