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...

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...

Balanced truncation (BT), as applied to date in model order reduction (MOR), is known for its superior accuracy and computable error bounds. Positive-real balanced truncation (PRBT) is a particular BT procedure that preserves passivity and stability, and imposes no structural constraints on the original state space. However, PRBT requires solving two algebraic Riccati equations (AREs), whose co...

A new method is formulated and analyzed for the approximate solution of a twodimensional time-fractional diffusion-wave equation. In this method, orthogonal spline collocation is used for the spatial discretization and, for the time-stepping, a novel alternating direction implicit (ADI) method based on the Crank-Nicolson method combined with the L1-approximation of the time Caputo derivative of...

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...

In this article we discuss a combination between fourth-order finite difference methods and fourth-order splitting methods for 2D parabolic problems with mixed derivatives. The finite difference methods are based on higher-order spatial discretization methods, whereas the timediscretization methods are higher-order discretizations using CrankNicolson or BDF methods. The splitting methods are hi...

With a combined compact difference scheme for the spatial discretization and the CrankNicolson scheme for the temporal discretization, respectively, a high-order alternating direction implicit method (ADI) is proposed for solving unsteady two dimensional convectiondiffusion equations. The method is sixth-order accurate in space and second-order accurate in time. The resulting matrix at each ADI...

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...

In this paper, two different finite differences schemes are presented for numerical solution of two-dimensional moving boundary problem. The methods are illustrated by solving sample problem in two-dimensional solidification of the square prism. The finite difference schemes developed for this purpose are based on the method of lines using interpolation polynomials. The fully explicit method de...

Wide-angle full-vector Beam Propagation Methods (BPMs) for three dimensional wave-guiding structures can be derived based on rational approximants of a square root operator or its exponential (i.e. the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the Alternating Direction Implicit (ADI) method, the wide-angle va...