Modulation of the refractive index of glass using ion exchange is a common fabrication method for various micro-optics components, such as waveguide devices, microlenses, and diiractive elements. The design of elements with complicated optical functions has increased the demand for fast numerical simulation of the nonlinear ion-exchange process of two monovalent ions. In this paper, a linear im...

This paper describes the implementation of a solver for systems of semi-linear parabolic partial di erential equations in two and three space dimensions. The solver is based on a parallel implementation of a non-linear Alternating Direction Implicit (ADI) scheme which uses a Cartesian grid in space and an implicit time-stepping algorithm. Various reordering strategies for the linearized equatio...

A new numerical method for the full-wave physical modelling of semiconductor devices using a combination of the meshless and finite-difference time-domain (FDTD) approaches is described. The model consists of the electron equations for the active part and Maxwell’s equations for the electromagnetic effects, which describe the complete behaviour of a high-frequency active device. The uncondition...

A computationally efficient numerical method is developed for solving sea ice momentum equations that employ a nonlinear viscous-plastic rheology. The method is based on an alternating direction implicit (ADI) technique that involves a direct solution of the momentum equations. This method is therefore more computationally efficient than those employing an iterative procedure in solving the equ...

Ground Penetrating Radar (GPR) is a shallow geophysical method for detecting and locating subsurface targets. The GPR image echo characteristics of complex underground structures can be obtained by carrying out forward modeling research. traditional finite-difference time-domain (FDTD) has low efficiency accuracy. alternating direction implicit FDTD (ADI-FDTD) algorithm surmounts the stability ...

This paper introduces alternating-direction implicit (ADI) solvers of higher order of timeaccuracy (orders two to six) for the compressible Navier-Stokes equations in twoand threedimensional curvilinear domains. The higher-order accuracy in time results from 1) An application of the backward differentiation formulae time-stepping algorithm (BDF) in conjunction with 2) A BDF-like extrapolation t...

A two-dimensional two-phase numerical model is developed to predict transport and fate of oil slicks which resulted the concentration distribution of oil on the water surface. Two dimensional governing equation of fluid flow which consists mass and momentum conservation was solved using the finite difference method on the structured staggered grid system. The resulted algebric equations were so...

The simulation of core collapse supernovæ calls for the time accurate solution of the (Euler) equations for inviscid hydrodynamics coupled with the equations for neutrino transport. The time evolution is carried out by evolving the Euler equations explicitly and the neutrino transport equations implicitly. Neutrino transport is modeled by the multi-group Boltzmann transport (MGBT) and the multi...