Domain decomposition preconditioning for surface integral equations in solving challenging electromagnetic scattering problems

Zhen Peng, Ralf Hiptmair, Yang Shao, Brian MacKie-Mason

Research output: Contribution to journalArticle

Abstract

We propose and study a nonoverlapping and nonconforming domain decomposition method for the integral-equationbased solution of large, complex electromagnetic (EM) scattering problems. The continuity of the electric surface current across the boundary between adjacent subdomains is enforced by a skew-symmetric interior penalty formulation. A nonoverlapping additive Schwarz preconditioner is designed and analyzed for the solution of the linear system of equations resulting from Galerkin boundary-element discretization. We show that the preconditioned system exhibits a uniformly confined eigenspectrum with respect to changing problem and discretization parameters. Numerical examples are presented to demonstrate the fast convergence of iterative solvers and the superior accuracy of the solutions obtained by our method. The proposed work can be viewed as an effective preconditioning scheme that reduces the condition number of very large systems of equations in challenging EMscattering problems. The strength and capability of the proposed method will be illustrated by means of several examples of practical interest.

Original languageEnglish (US)
Article number7329961
Pages (from-to)210-223
Number of pages14
JournalIEEE Transactions on Antennas and Propagation
Volume64
Issue number1
DOIs
StatePublished - Jan 2016
Externally publishedYes

Keywords

  • Black interior penalty discontinuous Galerkin method
  • Domain decomposition (DD) method
  • Electromagnetic (EM) scattering
  • Integral equation method
  • Maxwell's equations

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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