Generalized Alternating-Direction Implicit Finite-Difference Time-Domain Method in Curvilinear Coordinate System

Wei Song,Yang Hao

doi:10.4236/jemaa.2010.25042

Abstract

In this paper, a novel approach is introduced towards an efficient Finite-Difference Time-Domain (FDTD) algorithm by incorporating the Alternating Direction Implicit (ADI) technique to the Nonorthogonal FDTD (NFDTD) method. This scheme can be regarded as an extension of the conventional ADI-FDTD scheme into a generalized curvilinear coordinate system. The improvement on accuracy and the numerical efficiency of the ADI-NFDTD over the conventional nonorthogonal and the ADI-FDTD algorithms is carried out by numerical experiments. The application in the modelling of the Electromagnetic Bandgap (EBG) structure has further demonstrated the advantage of the proposed method.

Highlights

The Finite-Difference Time-Domain (FDTD) Method [1] has been proven to be an effective algorithm in computational electromagnetics
The Alternating Direction Implicit (ADI)-FDTD scheme is extended into the nonorthogonal coordinate system to achieve an ADINFDTD algorithm
It is shown that the CFL condition of Nonorthogonal FDTD (NFDTD) is removed by the use of the ADI scheme

Summary

Introduction

The Finite-Difference Time-Domain (FDTD) Method [1] has been proven to be an effective algorithm in computational electromagnetics. As is the case in the Cartesian FDTD algorithm, the time interval dtmax used in the NFDTD method is constrained by the Courant-Friedrich-Levy (CFL) stability condition [13]. Used in the NFDTD simulation should not exceed the Courant criterion dtmax given by (1), which is the minimum value of dtmaxi,j, in order to guarantee that the CFL condition is satisfied for every cell in the NFDTD meshes. More to the point, when the meshes contain globally large but locally very small or skewed cells, the using of the smallest dtmaxi,j may result in low efficiency in the NFDTD simulations. Various efforts have been made to alleviate this problem [1618]

Formulation

Numerical Results

Application of ADI-NFDTD Algorithm in Bandgap Structure Simulations

Conclusions