Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrödinger equation
Tay, Wei Choon
Tan, Eng Leong
Date of Issue2014
School of Electrical and Electronic Engineering
In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schr¨odinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is further simplified into pentadiagonal fundamental ADI (Penta-FADI) method, which has matrix-operator-free right-hand-sides (RHS), leading to the simplest and most concise update equations. As the Penta-FADI method involves five stencils in the left-hand-sides (LHS) of the pentadiagonal update equations, special treatments that are required for the implementation of the Dirichlet’s boundary conditions will be discussed. Using the Penta-FADI method, a significantly higher efficiency gain can be achieved over the conventional Tri-ADI method, which involves a tridiagonal system of equations.
DRNTU::Engineering::Electrical and electronic engineering
Computer physics communications
© 2014 Elsevier. This is the author created version of a work that has been peer reviewed and accepted for publication by Computer Physics Communications, Elsevier. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1016/j.cpc.2014.03.014].