Overcoming low-frequency breakdown of the magnetic field integral equation

Felipe Vico, Zydrunas Gimbutas, Leslie Greengard, Miguel Ferrando-Bataller

Research output: Contribution to journalArticlepeer-review


In the electromagnetics literature, significant attention has been paid to the problem of low-frequency breakdown in the electric field integral equation. By contrast, the magnetic field integral equation is well-conditioned (in simply connected domains) and can be used in the low frequency limit without modification or preconditioning. Reconstruction of the electric field, however, is subject to catastrophic cancellation unless appropriate measure are taken. In this paper, we show that solving an auxiliary (scalar) integral equation for the charge overcomes this form of low frequency breakdown, both in the near and far fields. Moreover, both the current and charge can be discretized using simple piecewise polynomial basis functions on triangulated surfaces. We also analyze an alternative formulation involving magnetic current and charge and illustrate the performance of the methods with several numerical examples.

Original languageEnglish (US)
Article number6373698
Pages (from-to)1285-1290
Number of pages6
JournalIEEE Transactions on Antennas and Propagation
Issue number3
StatePublished - 2013


  • Charge-current formulations
  • Maxwell equations
  • electromagnetic (EM) scattering
  • electromagnetic theory
  • low-frequency breakdown
  • magnetic field integral equation (MFIE)

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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