An updated review of general dispersion relation for conditionally and unconditionally stable FDTD algorithms

Stanislav Ogurtsov, George Pan

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We present a general numerical dispersion equation which is applicable to all known conditionally and unconditionally stable finite-difference time-domain (FDTD) algorithms on staggered rectangular grid, including Yee's FDTD, wavelet-based FDTD, extended curl FDTD, alternating direction implicit (ADI)-FDTD, Crank-Nicolson (CN)-FDTD, Crank-Nicolson split-step (CNSS)-FDTD, and their modifications of higher order spatial stencils. The real part of the complex eigenvalue of the total amplification matrix defines and distinguishes the dispersion relation for each individual scheme. Easy-to-check conditions are provided, under which the numerical dispersion of a particular time-domain scheme is governed by the proposed dispersion equation. These conditions are on the amplification matrix eigenvalues. The proposed dispersion equation includes each considered dispersion relation as a special case, and presents itself a general governing equation to estimate 3-D numerical dispersion of the aforementioned schemes in the frame of plane waves.

Original languageEnglish (US)
Pages (from-to)2572-2583
Number of pages12
JournalIEEE Transactions on Antennas and Propagation
Volume56
Issue number8 II
DOIs
StatePublished - 2008

Fingerprint

Amplification

Keywords

  • Amplification matrix
  • Eigenvalue
  • Finite-difference time-domain (FDTD)
  • Numerical dispersion
  • Numerical phase velocity
  • Skew-Hermitian matrix
  • Stability

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Networks and Communications

Cite this

An updated review of general dispersion relation for conditionally and unconditionally stable FDTD algorithms. / Ogurtsov, Stanislav; Pan, George.

In: IEEE Transactions on Antennas and Propagation, Vol. 56, No. 8 II, 2008, p. 2572-2583.

Research output: Contribution to journalArticle

@article{b03d576d526e4368818d026b3ee0af39,
title = "An updated review of general dispersion relation for conditionally and unconditionally stable FDTD algorithms",
abstract = "We present a general numerical dispersion equation which is applicable to all known conditionally and unconditionally stable finite-difference time-domain (FDTD) algorithms on staggered rectangular grid, including Yee's FDTD, wavelet-based FDTD, extended curl FDTD, alternating direction implicit (ADI)-FDTD, Crank-Nicolson (CN)-FDTD, Crank-Nicolson split-step (CNSS)-FDTD, and their modifications of higher order spatial stencils. The real part of the complex eigenvalue of the total amplification matrix defines and distinguishes the dispersion relation for each individual scheme. Easy-to-check conditions are provided, under which the numerical dispersion of a particular time-domain scheme is governed by the proposed dispersion equation. These conditions are on the amplification matrix eigenvalues. The proposed dispersion equation includes each considered dispersion relation as a special case, and presents itself a general governing equation to estimate 3-D numerical dispersion of the aforementioned schemes in the frame of plane waves.",
keywords = "Amplification matrix, Eigenvalue, Finite-difference time-domain (FDTD), Numerical dispersion, Numerical phase velocity, Skew-Hermitian matrix, Stability",
author = "Stanislav Ogurtsov and George Pan",
year = "2008",
doi = "10.1109/TAP.2008.927569",
language = "English (US)",
volume = "56",
pages = "2572--2583",
journal = "IEEE Transactions on Antennas and Propagation",
issn = "0018-926X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "8 II",

}

TY - JOUR

T1 - An updated review of general dispersion relation for conditionally and unconditionally stable FDTD algorithms

AU - Ogurtsov, Stanislav

AU - Pan, George

PY - 2008

Y1 - 2008

N2 - We present a general numerical dispersion equation which is applicable to all known conditionally and unconditionally stable finite-difference time-domain (FDTD) algorithms on staggered rectangular grid, including Yee's FDTD, wavelet-based FDTD, extended curl FDTD, alternating direction implicit (ADI)-FDTD, Crank-Nicolson (CN)-FDTD, Crank-Nicolson split-step (CNSS)-FDTD, and their modifications of higher order spatial stencils. The real part of the complex eigenvalue of the total amplification matrix defines and distinguishes the dispersion relation for each individual scheme. Easy-to-check conditions are provided, under which the numerical dispersion of a particular time-domain scheme is governed by the proposed dispersion equation. These conditions are on the amplification matrix eigenvalues. The proposed dispersion equation includes each considered dispersion relation as a special case, and presents itself a general governing equation to estimate 3-D numerical dispersion of the aforementioned schemes in the frame of plane waves.

AB - We present a general numerical dispersion equation which is applicable to all known conditionally and unconditionally stable finite-difference time-domain (FDTD) algorithms on staggered rectangular grid, including Yee's FDTD, wavelet-based FDTD, extended curl FDTD, alternating direction implicit (ADI)-FDTD, Crank-Nicolson (CN)-FDTD, Crank-Nicolson split-step (CNSS)-FDTD, and their modifications of higher order spatial stencils. The real part of the complex eigenvalue of the total amplification matrix defines and distinguishes the dispersion relation for each individual scheme. Easy-to-check conditions are provided, under which the numerical dispersion of a particular time-domain scheme is governed by the proposed dispersion equation. These conditions are on the amplification matrix eigenvalues. The proposed dispersion equation includes each considered dispersion relation as a special case, and presents itself a general governing equation to estimate 3-D numerical dispersion of the aforementioned schemes in the frame of plane waves.

KW - Amplification matrix

KW - Eigenvalue

KW - Finite-difference time-domain (FDTD)

KW - Numerical dispersion

KW - Numerical phase velocity

KW - Skew-Hermitian matrix

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=49549103297&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49549103297&partnerID=8YFLogxK

U2 - 10.1109/TAP.2008.927569

DO - 10.1109/TAP.2008.927569

M3 - Article

AN - SCOPUS:49549103297

VL - 56

SP - 2572

EP - 2583

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

SN - 0018-926X

IS - 8 II

ER -