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...

In this paper we describe a Parallel Performance Estimator suitable for the comparative evaluation of parallel algorithms. The Esti-mator is designed for SPMD programs written in either C or FORTRAN. Simulation is used to produce estimates of execution times for varying numbers of processors and to analyse the communication overheads. Results from the estimator are compared with actual results ...

The computational environment for estimation of unknown regional electrical conductivities of the human head, based on realistic geometry from segmented MRI up to 256 resolution, is described. A finite difference alternating direction implicit (ADI) algorithm, parallelized using OpenMP, is used to solve the forward problem describing the electrical field distribution throughout the head given k...

Large sparse non-symmetric linear systems of equations often occur in many scientific and engineering applications. In this paper, we present a comparative study of some preconditioned Krylov iterative methods, namely CGS, Bi-CGSTAB, TFQMR and GMRES for solving such systems. To demonstrate their efficiency, we test and compare the numerical implementations of these methods on five numerical exa...

Diffusion model is increasingly employed to simulate diffusion of biological compounds including nutrient, oxygen and chemoattractants in the agent-based model (ABM). However, it takes long compute time to employ conventional numerical methods such as alternating direction implicit (ADI) method to approximate the exact solution of the diffusion processed by sequential computing algorithm. To ov...

In the present paper we consider a 2-D shallow-water equations (SWE) model on a βplane solved using an alternating direction fully implicit (ADI) finite-difference scheme (Gustafsson 1971, Fairweather and Navon 1980, Navon and De Villiers 1986, Kreiss and Widlund 1966) on a rectangular domain. The scheme was shown to be unconditionally stable for the linearized equations. The discretization yie...

Alternating Direction Implicit (ADI) methods provide a computationally efficient way to solve for antenna based gains in full polarization. In this paper, we analyze the convergence of such methods in simulations. We show that convergence of a basic implementation can be quite slow and we propose two forms of relaxation to improve convergence behavior. The algorithm can be shown to be statistic...

The Navier-Stokes equations describe a large class of fluid flows but are difficult to solve analytically because of their nonlinearity. We present in this paper a parallel solver for the 3-D Navier-Stokes equations of incompressible unsteady flows with constant coefficients, discretized by the finite difference method. We apply the prediction-projection method which transforms the Navier-Stoke...

This paper deals with an inverse problem of simultaneously determining the dispersion coefficients and the space-dependent source magnitude in 2D advection dispersion equation with finite observations at the final time. The forward problem is solved by using the alternating direction implicit (ADI) finite difference scheme, and then the optimal perturbation algorithm with the regularization par...