Analysis and regularization of the TD-EFIE low-frequency breakdown

Francesco P. Andriulli*, Hakan Baǧci, Francesca Vipiana, Giuseppe Vecchi, Eric Michielssen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


Low-frequency breakdown phenomenon plaguing marching-on-in-time solutions of time domain electric field integral equations is analyzed and cured. A theoretical analysis of the breakdown identifies deficiencies in the treatments proposed to date. A scheme for eliminating low frequency breakdown phenomena that leverages hierarchical regularization is presented. It applies to arbitrary meshes and gives rise to linear systems that are better conditioned than those obtained with standard loop-star/tree bases. The scheme's analytical properties and numerical results demonstrate its efficacy in accelerating the iterative solution of the time domain electric field integral equations.

Original languageEnglish (US)
Pages (from-to)2034-2046
Number of pages13
JournalIEEE Transactions on Antennas and Propagation
Issue number7
StatePublished - 2009

Bibliographical note

Funding Information:
Manuscript received December 27, 2007; revised October 13, 2008. Current version published July 09, 2009. This work was supported in part by AFOSR MURI Grant F014432-051936 aimed at modeling installed antennas and their feeds, by NSF Grant DMS 0713771, and in part by DARPA-DSO/AFOSR grant F015123-052587 aimed at constructing compressed scattering matrices and direct solvers.


  • Electric field integral equation (EFIE)
  • Hierarchical methods
  • Integral equations
  • Marching on in time (MOT)
  • Numerical methods
  • Preconditioning
  • Time domain (TD)

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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