This research includes of the numerical modeling of fluids in two-dimensional cavity. The cavity flow is an important theoretical problem. In this research, modeling was carried out based on an alternating direction implicit via Vorticity-Stream function formulation. It evaluates different Reynolds numbers and grid sizes. Therefore, for the flow field analysis and prove of the ability of the sc...

A new Peaceman–Rachford alternating direction implicit (PR-ADI) method is proposed in this work for solving two-dimensional (2D) parabolic interface problems with discontinuous solutions. The classical ADI schemes are known to be inaccurate for handling interfaces. This motivates the development of a matched Douglas ADI (D-ADI) method in the literature, in which the finite difference is locally...

This paper describes the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method for physical modeling of high-frequency semiconductor devices. The model contains the semiconductor equations in conjunction with the Maxwell’s equations which describe the complete behavior of highfrequency active devices. Using ADI approach leads to a significant reduction of the full-wave ...

We study accuracy of alternating direction implicit (ADI) methods for parabolic equations. The original ADI method applied to parabolic equations is a perturbation of the Crank-Nicolson di erence equation and has second-order accuracy both in space and time. The perturbation error is on the same order as the discretization error, in terms of mathematical description. However, we often observe i...

The alternating direction implicit (ADI) method is an attractive option to use in avoiding the CourantFriedrichs-Lewy (CFL) condition that limits the size of the time step required by explicit finite-difference time-domain (FDTD) methods for stability. Implicit methods like Crank-Nicholson offer the same advantages as ADI methods but they do not rely on simple, one-dimensional, tridiagonal syst...

An algorithm is presented for constructing an approximate numerical solution to a large scale Lyapunov equation in low rank factored form. The algorithm is based upon a synthesis of an approximate power method and an alternating direction implicit (ADI) method. The former is parameter free and tends to be efficient in practice, but there is little theoretical understanding of its convergence pr...

In this paper, a new algorithm for twodimensional (2-D) finite-difference time-domain (FDTD) method is presented. By this new method, the maximum time step size can be increased over the Courant-FriedrichLevy (CFL) condition restraint. This new algorithm is adapted from an Alternating-Direction Implicit FDTD (ADI-FDTD) method. However, unlike the ADI-FDTD algorithm, the alternation is performed...

A Poisson-type equation arising in a commonly used numerical weather forecasting model is solved using an alternating direction implicit (ADI) method with Wachpress optimum parameters on a trapezoidal domain which coincides with the operational forecast domain. Various optimum parameter sequences were obtained for the corresponding squares which enclose the region under consideration, computati...

The Fokker-Planck (FP) model is one of the commonly used methods for studies of the dynamical evolution of dense spherical stellar systems such as globular clusters and galactic nuclei. The FP model is numerically stable in most cases, but we find that it encounters numerical difficulties rather often when the effects of tidal shocks are included in two-dimensional (energy and angular momentum ...

In this paper, a new alternating direction implicit (ADI) method is introduced to solve potential driven geometric flow PDEs for biomolecular surface generation. For such PDEs, an extra factor is usually added to stabilize the explicit time integration. However, two existing implicit ADI schemes are also based on the scaled form, which involves nonlinear cross derivative terms that have to be e...