Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrödinger equation

• Main Authors: Tay, Wei Choon, Tan, Eng Leong
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2014
• Subjects: DRNTU::Engineering::Electrical and electronic engineering
• Online Access: https://hdl.handle.net/10356/79681; http://hdl.handle.net/10220/20345
• Institution: Nanyang Technological University

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.