An Augmented Regularized Combined Source Integral Equation for Nonconforming Meshes

Felipe Vico, Leslie Greengard, Miguel Ferrando-Bataller, Eva Antonino-Daviu

Research output: Contribution to journalArticle

Abstract

We present a new version of the regularized combined source integral equation (CSIE-AR) for the solution of electromagnetic scattering problems in the presence of perfectly conducting bodies. The integral equation is of the second kind and has no spurious resonances. It is well conditioned at all frequencies for simply connected geometries. Reconstruction of the magnetic field, however, is subject to catastrophic cancelation due to the need for computing a scalar potential from magnetic currents. Here, we show that by solving an auxiliary (scalar) integral equation, we can avoid this form of low-frequency breakdown. The auxiliary scalar equation is used to solve a Neumann-type boundary value problem using data corresponding to the normal component of the magnetic field. This scalar equation is also of the second kind, nonresonant, and well conditioned at all frequencies. A principal advantage of our approach, by contrast with the hypersingular electric field integral equation, the combined field integral equation, or CSIE formulations, is that the standard loop-star and related basis function constructions are not needed, and preconditioners are not required. This permits an easy coupling to fast algorithms such as the fast multipole method. Furthermore, the formalism is compatible with nonconformal mesh discretization and works well with singular (sharp) boundaries.

Original languageEnglish (US)
Article number8605366
Pages (from-to)2513-2521
Number of pages9
JournalIEEE Transactions on Antennas and Propagation
Volume67
Issue number4
DOIs
StatePublished - Apr 2019

Keywords

  • Calderon preconditioning (CP)
  • Maxwell equations
  • charge-current formulations
  • electromagnetic (EM) scattering
  • high-frequency preconditioning

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Fingerprint Dive into the research topics of 'An Augmented Regularized Combined Source Integral Equation for Nonconforming Meshes'. Together they form a unique fingerprint.

  • Cite this