Examination, clarification, and simplification of stability and dispersion analysis for ADI-FDTD and CNSS-FDTD schemes

S. Ogurtsov, George Pan, Rodolfo Diaz

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


We describe a rigorous analysis of unconditional stability for the alternating-direction-implicit finite-difference time-domain (ADI-FDTD) and Crank-Nicholson split step (CNSS-FDTD) schemes avoiding use of the von Neumann spectral criterion. The proof is performed in the spectral domain, and uses skew-Hermitivity of matrix terms in the ADI and CNSS total amplification matrices. A bound for the total ADI amplification matrix is provided. While the CN and CNSS-FDTD amplification matrices are unitary, the bound on the ADI-FDTD depends on the Courant number. Importantly, we have found that the ADI-FDTD amplification matrix is not normal, i.e., the unit spectral radius alone cannot be used to prove the ADI-FDTD unconditional stability. The paper also shows that the ADI-FDTD and CNSS-FDTD schemes share the same dispersion equation by a similarity of their total amplification matrices, and the two schemes have identical numerical dispersion in the frame of plane waves.

Original languageEnglish (US)
Pages (from-to)3595-3602
Number of pages8
JournalIEEE Transactions on Antennas and Propagation
Issue number12
StatePublished - Dec 2007


  • Amplification
  • Amplification matrix
  • Dispersion equation
  • Finite difference time domain analysis
  • Finite difference time main (FDTD) schemes
  • Hermitian matrices
  • Matrix algebra
  • Normal matrices
  • Skew-Hermitian matrices
  • Stability
  • Time domain analysis
  • Unconditional stability
  • Unitary matrices
  • stability analysis

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this