In this paper the numerical solution of the two-dimensional sine-Gordon equation is studied. Split local artificial boundary conditions are obtained by the operator splitting method. Then the original problem is reduced to an initial boundary value problem on a bounded computational domain, which can be solved by the finite differencemethod. Several numerical examples are provided to demonstrat...

Abstract. Here we investigate the kinematic transports of the defects in the nematic liquid crystal system by numerical experiments. The model is a shear flow case of the viscoelastic continuummodel simplified from the Ericksen-Leslie system. The numerical experiments are carried out by using a differencemethod. Based on these numerical experiments we find some interesting and important relatio...

A stable and explicit second order accurate finite difference method for the elastic wave equation in curvilinear coordinates is presented. The discretization of the spatial operators in the method is shown to be self-adjoint for free-surface, Dirichlet and periodic boundary conditions. The fully discrete version of the method conserves a discrete energy to machine precision. AMS subject classi...

In this paper, using annular resonator we have designed an adding and dropping filter light based ontwo-dimensional photonic crystals. The shape of ring resonator filter adding and dropping that wehave proposed is Race Track. This filter has a hexagonal lattice structure of silicon bars withrefractive index 3/46 that is located in the context of air with refractive index 1. Transmissionefficien...

in this paper, using annular resonator we have designed an adding and dropping filter light based ontwo-dimensional photonic crystals. the shape of ring resonator filter adding and dropping that wehave proposed is race track. this filter has a hexagonal lattice structure of silicon bars withrefractive index 3/46 that is located in the context of air with refractive index 1. transmissionefficien...

In this chapter, the strong and weak forms for several one-dimensional physical problems are developed. Thestrong formconsists of thegoverningequationsand theboundaryconditions for aphysical system.The governingequations areusuallypartial differential equations, but in theone-dimensional case theybecome ordinary differential equations. The weak form is an integral form of these equations, which...

An approach to detect and image multiple damages in a platelike structure is presented. A structural health monitoring system (SHMS) with a linear array of actuators/sensors is proposed. The integrated actuators/sensors are used to activate/receive lowest-order antisymmetric A0 mode Lamb waves. A migration technique used in geophysical exploration and seismic prospecting is adopted to interpret...

A fast adaptive diffusion wavelet method is developed for solving the Burger’s equation. The diffusion wavelet is developed in 2006 (Coifman and Maggioni, 2006) and its most important feature is that it can be constructed on any kind ofmanifold. Classes of operators which can be used for construction of the diffusion wavelet include second order finite difference differentiation matrices. The e...

We propose a variational-difference method for designing the optical free form surface of progressiveaddition lenses (PALs). The PAL, which has a front surface with three important zones including the far-view, near-view and intermediate zones, is often used to remedy presbyopia by distributing optical powers of the three zones progressively and smoothly. The problem for designing PALs could be...