Large Time Step and DC Stable TD-EFIE Discretized with Implicit Runge-Kutta Methods

Alexandre Dely, Francesco P. Andriulli*, Kristof Cools

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)
99 Downloads (Pure)


The time domain-electric field integral equation (TD-EFIE) and its differentiated version are widely used to simulate the transient scattering of a time dependent electromagnetic field by a perfect electric conductor (PEC). The time discretization of the TD-EFIE can be achieved by a space-time Galerkin approach or, as it is considered in this contribution, by a convolution quadrature using implicit Runge-Kutta methods. The solution is then computed using the marching-on-in-time (MOT) algorithm. The differentiated TD-EFIE has two problems: 1) the system matrix suffers from ill-conditioning when the time step increases (low frequency breakdown) and 2) it suffers from the DC instability, i.e., the formulation allows for the existence of spurious solenoidal currents that grow slowly in the solution. In this article, we show that 1) and 2) can be alleviated by leveraging quasi-Helmholtz projectors to separate the Helmholtz components of the induced current and rescale them independently. The efficacy of the approach is demonstrated by numerical examples including benchmarks and real-life applications.

Original languageEnglish
Article number8852832
Pages (from-to)976-985
Number of pages10
JournalIEEE Transactions on Antennas and Propagation
Issue number2
Publication statusPublished - 1 Feb 2020


  • DC instability
  • electric field integral equation
  • implicit Runge-Kutta (IRK)
  • low frequency (LF)
  • preconditioning
  • time domain


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