A novel Douglas alternating direction implicit (ADI) method is proposed in this work to solve a two-dimensional (2D) heat equation with interfaces. The ADI scheme is a powerful finite difference method for solving parabolic equations, due to its unconditional stability and high efficiency. However, it suffers from a serious accuracy reduction in space for interface problems with different mater...

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 ...

Alternating Direction Implicit (ADI) schemes are constructed for the solution of two-dimensional higher-order linear and nonlinear diffusion equations, particularly including the fourth-order thin film equation for surface tension driven fluid flows. First and second-order accurate schemes are derived via approximate factorization of the evolution equations. This approach is combined with itera...

We give an algorithmic approach to the approximative solution of operator Lyapunov equations for controllability. Motivated by the successfully applied alternating direction implicit (ADI) iteration for matrix Lyapunov equations, we consider this method for the determination of Gramian operators of infinite-dimensional control systems. In the case where the input space is finitedimensional, thi...

Selective laser melting is developing into a standard manufacturing technology with applications in various sectors. However, the process is still far from being at par with conventional processes such as welding and casting, the primary reason of which is the unreliability of the process. While various numerical modelling and experimental studies are being carried out to better understand and ...

This article is concerned with a level set segmentation algorithm which hybridizes gradient-based methods and the Mumford-Shah (gradient-free) method, for an efficient and reliable segmentation. We introduce a new strategy for the complementary functions u±, which is computed such that the difference between their average and the given image are able to introduce a reliable driving force for th...

In this paper, we extend the Sun and Zhang’s [24] work on high order finite difference method, which is based on the Richardson extrapolation technique and an operator interpolation scheme for the one and two dimensional steady convection diffusion equations to the three dimensional case. Firstly, we employ a fourth order compact difference scheme to get the fourth order accurate solution on th...