Cylindrical FDTD formulation for low frequency applications

Abdullah Algarni*, Atef Z. Elsherbeni, Mohammed Hadi

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


This chapter presents two important concepts related to proper implementation of convolutional perfectly matched-layer absorbing boundary conditions (CPML) and lumped circuit modeling within the finite-difference time-domain (FDTD) method when implemented in cylindrical coordinates (CFDTD). The first concept is a critical treatment to ensure consistent cylindrical waves absorption at the truncated numerical boundaries, regardless of wave-mode order or propagation projection off the z-axis. Previous CPML implementations within CFDTD simulations applied the requisite CPML radial variable stretching in all occurrences of this variable within CFDTD's update equations. This was an over-simplification which only works for rotationally invariable cylindrical waves that are strictly propagating in the radial direction. Under such restrictions, the troublesome side-effects of this over-simplification do not present themselves as the adversely affected field components vanish in the first place. In this chapter we demonstrate that coordinate stretching should be implemented on only a specific subset of CFDTD's update equations to ensure appropriate CPML absorption for other cylindrical wave modes and oblique wave propagations. This treatment concludes with presenting sensitivity analysis of CPML's performance at higher wave modes. The second presented concept in this chapter relates to updating previously developed lumped circuit element models for Cartesian coordinates FDTD to work seamlessly within the cylindrical coordinates CFDTD method, complete with derivations and simulation examples.

Original languageEnglish
Title of host publicationAdvances in Time-Domain Computational Electromagnetic Methods
Number of pages47
ISBN (Electronic)9781119808404
ISBN (Print)9781119808374
StatePublished - 18 Nov 2022

Bibliographical note

Publisher Copyright:
© 2023 The Institute of Electrical and Electronics Engineers, Inc. All rights reserved.


  • Absorbing boundary conditions
  • Convolutional perfectly matched-layer
  • Cylindrical coordinates
  • Finite-difference time-domain method
  • Lumped-element-circuit modeling

ASJC Scopus subject areas

  • General Physics and Astronomy


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