Non-conformal domain decomposition method with second-order transmission conditions for time-harmonic electromagnetics

Zhen Peng, Jin Fa Lee

Research output: Contribution to journalArticlepeer-review

Abstract

Non-overlapping domain decomposition (DD) methods provide efficient algorithms for solving time-harmonic Maxwell equations. It has been shown that the convergence of DD algorithms can be improved significantly by using high order transmission conditions. In this paper, we extend a newly developed second-order transmission condition (SOTC), which involves two second-order transverse derivatives, to facilitate fast convergence in the non-conformal DD algorithms. However, the non-conformal nature of the DD methods introduces an additional technical difficulty, which results in poor convergence in many real-life applications. To mitigate the difficulty, a corner-edge penalty method is proposed and implemented in conjunction with the SOTC to obtain truly robust solver performance. Numerical results verify the analysis and demonstrate the effectiveness of the proposed methods on a few model problems. Finally, drastically improved convergence, compared to the conventional Robin transmission condition, was observed for an electrically large problem of practical interest.

Original languageEnglish (US)
Pages (from-to)5615-5629
Number of pages15
JournalJournal of Computational Physics
Volume229
Issue number16
DOIs
StatePublished - Aug 2010
Externally publishedYes

Keywords

  • Domain decomposition methods
  • Maxwell's equations
  • Second-order transmission conditions

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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