A hermitian and well-conditioned EFIE for fast iterative and direct solvers

Simon B. Adrian, Francesco P. Andriulli, Thomas F. Eibert

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

We present a well-conditioned discretization of the electric field integral equation (EFIE) which is Hermitian and positive definite at any frequency. Differently from other preconditioning techniques, like hierarchical methods or Calderón schemes, no refinement of the mesh nor dual basis functions are necessary by the new formulation. This results in substantial computational savings since only the standard system matrix on the regular mesh needs to be stored. Moreover, the coexistence of hermitianity, positive definiteness, and well-conditioning properties allow for a fast direct inversion of the matrix in linear complexity. The new formulation is based on the regularization of the EFIE with a conjugated EFIE. The two matrices are linked with suitably chosen differential operators and Gram matrices that prevent the squaring of the condition number, and instead ensure a uniformly well-conditioned system matrix. Numerical results corroborate the theory and show the practical applicability of the new scheme.

Original languageEnglish
Title of host publication2015 IEEE Antennas and Propagation Society International Symposium, APS 2015 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages742-743
Number of pages2
ISBN (Electronic)9781479978151
DOIs
StatePublished - 22 Oct 2015
EventIEEE Antennas and Propagation Society International Symposium, APS 2015 - Vancouver, Canada
Duration: 19 Jul 201524 Jul 2015

Publication series

NameIEEE Antennas and Propagation Society, AP-S International Symposium (Digest)
Volume2015-October
ISSN (Print)1522-3965

Conference

ConferenceIEEE Antennas and Propagation Society International Symposium, APS 2015
Country/TerritoryCanada
CityVancouver
Period19/07/1524/07/15

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