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...

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 ...

We study domain decomposition counterparts of the classical alternating direction implicit (ADI) and fractional step (FS) methods for solving the large linear systems arising from the implicit time stepping of parabolic equations. In the classical ADI and FS methods for parabolic equations, the elliptic operator is split along coordinate axes; they yield tridiagonal linear systems whenever a un...

In this paper, some new approaches are proposed for moving boundary/interface problems, particularly for the Stefan problems and the problem of unstable crystal growth. We will focus on the issues of accuracy and speed-up. A modiied Crank-Nicolson method which is second order accurate and stable is developed. The ADI (alternating implicit directional method) is also developed to speed up the si...

in general plane regions and with respect to linear boundary conditions, is a classical problem of numerical analysis. Many such boundary value problems have been solved successfully on high-speed computing machines, using the (iterative) Young-Frankel "successive overrelaxation" (SOR) method as defined in [l] and [2], and variants thereof ("line" and "block" overrelaxation). For this method, e...

For the approximate representation of large data sets over a parameter domain in IR2, many geological and other applications require the construction of surfaces which have minimal energy, i.e., minimal curvature. One way to achieve this is by solving a fourth order elliptic partial di erential equation. Its discretization by a di erence scheme makes it particularly easy to incorporate (appropr...

The numerical solution of the time-dependent neutron transport problem in 2-D Cartesian geometry is considered. The problem is described by a coupled system of hyperbolic partial differential equations with the parameters of multiple groups. The system, for given group parameter, is discretized by a discrete ordinate method (SN) in angular direction and adaptive spline wavelet method with alter...

This article describes the derivation and implementation of a numerical method to solve constant-coefficient, parabolic partial differential equations in two space dimensions on rectangular domains. The method is based on a formula for the Green’s function for the problem obtained via reflections at the boundary of the domain from the corresponding formula for the fundamental solution in the wh...

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...