The convergence of an alternating direction implicit method for Maxwell’s equations on product domains is investigated. Unlike the classical Yee scheme and most other integrators proposed in the literature, this method is both unconditionally stable and computationally cheap. We prove second-order convergence of the time-discretization in the framework of operator semigroup theory. In contrast ...

Bipolar semiconductor device 2D FDTD modelling suited to parallel computing is investigated in this paper. The performance of a second order explicit approximation, namely the Nessyahu-Tadmor scheme (NT2) associated with the decomposition domain method, are compared to a classical quasi-linear implicit one based on the Alternating Direction Implicit method (ADI). The comparison is performed bot...

tions (PDEs). This class of schemes is based on three principal observations. First, the spatial discretization of parabolic PDEs results in stiff systems of ordinary differential equations (ODEs) in time, and therefore, requires an implicit method for its solution. Spectral Deferred Correction (SDC) methods use repeated iterations of a low-order method (e.g. implicit Euler method) to generate ...

This paper is devoted to the discussion of numerical methods for solving twodimensional time-fractional advection-diffusion equations. Two different three-point combined compact alternating direction implicit (CC-ADI) schemes are proposed and then, the original schemes for solving the two-dimensional problems are divided into two separate one-dimensional cases. Local truncation errors are analy...

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...

Two approaches for approximating the solution of large-scale Lyapunov equations are considered: the alternating direction implicit (ADI) iteration and projective methods by Krylov subspaces. A link between them is presented by showing that the ADI iteration can always be identified by a Petrov-Galerkin projection with rational block Krylov subspaces. Then a unique Krylov-projected dynamical sys...

We present a parallel nite-diierence algorithm for the solution of the 3D cylindrical Poisson equation. The algorithm is based on a data-transpose technique, in which all computations are performed independently on each node, and all communications are restricted to global 3D data-transposition between nodes. The data-transpose technique aids us in implementing two sequential algorithms for the...

Recent study shows that the nonuniform thermal distribution not only has an impact on the substrate but also interconnects. Hence, three–dimensional (3-D) thermal analysis is crucial to analyze these effects. In this paper, the authors present and develop an efficient 3-D transient thermal simulator based on the alternating direction implicit (ADI) method for temperature estimation in a 3-D env...

The fundamental idea behind all multigrid methods is to compute using diierent scales in order to obliterate error components of diierent scales. Error components can be thought of as waves. A long wave, which has low frequency, on one grid is a short wave, or high frequency, on a coarse enough related grid. A number of iterative methods (e.g., relaxation and alternating direction implicit meth...