Magnetic and Combined Field Integral Equations Based on the Quasi-Helmholtz Projectors

Adrien Merlini, Yves Beghein, Kristof Cools, Eric Michielssen, Francesco P. Andriulli

Research output: Contribution to journalArticleScientificpeer-review


Boundary integral equation methods for analyzing electromagnetic scattering phenomena typically suffer from several of the following shortcomings: 1) ill-conditioning when the frequency is low; 2) ill-conditioning when the discretization density is high; 3) ill-conditioning when the structure contains global loops (which are computationally expensive to detect); 4) incorrect solution at low frequencies due to a loss of significant digits; and 5) the presence of spurious resonances. In this article, quasi-Helmholtz projectors are leveraged to obtain magnetic field integral equation (MFIE) that is immune to drawbacks 1)-4). Moreover, when this new MFIE is combined with a regularized electric field integral equation (EFIE), a new quasi-Helmholtz projector-combined field integral equation (CFIE) is obtained that also is immune to 5). The numerical results corroborate the theory and show the practical impact of the newly proposed formulations.

Original languageEnglish
Article number8963862
Pages (from-to)3834-3846
Number of pages13
JournalIEEE Transactions on Antennas and Propagation
Issue number5
Publication statusPublished - 1 May 2020


  • Calderon strategies
  • combined field integral equations
  • electric
  • magnetic
  • preconditioning


Dive into the research topics of 'Magnetic and Combined Field Integral Equations Based on the Quasi-Helmholtz Projectors'. Together they form a unique fingerprint.

Cite this