Revisiting the Stability of Crank–Nicolson and ADI-FDTD

Author

Garcia, Salvador G. ; Rubio, R. Godoy ; Bretones, A. Rubio ; López, R. Gómez

Author_Institution

Dept. of Electromagnetismo y F. de la Materia, Granada Univ., Granada

Volume

55

Issue

11

fYear

2007

Firstpage

3199

Lastpage

3203

Abstract

The stability properties of Crank-Nicolson (CN) and alternating direction implicit finite-difference time-domain ADI-FDTD methods to solve Maxwell´s equations are investigated. Since the ADI-FDTD scheme can be formulated in many cases as an approximation to a CN-FDTD scheme, we start by analyzing the stability of CN-FDTD and, from it, we try to derive conditions on ADI-FDTD. We first recall the von Neumann analysis, and then we present a matrix-norm analysis. We show that the matrix-norm stability of CN-FDTD is a necessary condition to find matrix-norm stable conditions for ADI-FDTD.

Keywords

Maxwell equations; finite difference time-domain analysis; matrix algebra; microwaves; numerical stability; ADI-FDTD methods; Maxwell´s equations; alternating direction implicit finite-difference time-domain methods; matrix-norm analysis; stability; von Neumann analysis; Boundary value problems; Conductivity; Differential equations; Eigenvalues and eigenfunctions; Finite difference methods; Functional analysis; Maxwell equations; Stability analysis; Time domain analysis; Alternating direction implicit finite-difference time-domain (ADI-FDTD); FDTD; stability;

fLanguage

English

Journal_Title

Antennas and Propagation, IEEE Transactions on

Publisher

ieee

ISSN

0018-926X

Type

jour

DOI

10.1109/TAP.2007.908794

Filename

4380548